content large_string | quality_label int64 | extract large_string |
|---|---|---|
0.999.../Proof by multiplication by 10 - Wikibooks, open books for an open world
0.999.../Proof by multiplication by 10
x = 0.999 β¦ 10 x = 9.999 β¦ 10 x β x = 9.999 β¦ β 0.999 β¦ 9 x = 9 x = 1.000 β¦ {\displaystyle {\begin{aligned}x&=0.999\ldots \\10x&=9.999\ldots \\10x-x&=9.999\ldots -0.999\ldots \\9x&=9\\x&=1.000... | 4 | x = 0.999 β¦
10 x = 9.999 β¦
10 x β x = 9.999 β¦ β 0.999 β¦
9 x = 9
x = 1.000 β¦
{\displaystyle {\begin{aligned}x&=0.999\ldots \\10x&=9.999\ldots \\10x-x&=9.999\ldots -0.999\ldots \\9x&=9\\x&=1.000\ldots \\\end{aligned}}} |
If z = x β i y and z^1/3 = p+ iq , thenΒ
Solution
B.
-2
D.
-1
(x - iy) = (p + iq)
^3
β (x - iy) = p
^3
+(iq)
^3
+ 3p
^2
qi + 3pq
^2
i
^2
β (x - iy) = p
^3
- iq
^3
+ 3p
^2
qi - 3pq
^2
β (x - iy) = (p
^3
- 3pq
^2
) + i (3p
^2
q - q
^3
) On comparing both sides, we get
β x = (p
^3
- 3... | 5 | If z = x β i y and z^1/3 = p+ iq , then
Solution
B.
-2
D.
-1
(x - iy) = (p + iq)
^3
β (x - iy) = p
^3
+(iq)
^3
+ 3p
^2
qi + 3pq
^2
i
^2
β (x - iy) = p
^3
- iq
^3
+ 3p
^2
qi - 3pq
^2
β (x - iy) = (p
^3
- 3pq
^2
) + i (3p
^2
q - q
^3
) On comparing both sides, we get
β x = (p
^3
- 3p... |
ocumentation
# compute 4 estimates of the K function
X <- runifrect(42)
K <- Kest(X)
plot(K)
# derive 4 estimates of the L function L(r) = sqrt(K(r)/pi)
L <- with(K, sqrt(./pi))
plot(L)
# compute 4 estimates of V(r) = L(r)/r
V <- with(L, ./.x)
plot(V)
# compute the maximum absolute difference b... | 4 | # compute 4 estimates of the K function
X <- runifrect(42)
K <- Kest(X)
plot(K)
# derive 4 estimates of the L function L(r) = sqrt(K(r)/pi)
L <- with(K, sqrt(./pi))
plot(L)
# compute 4 estimates of V(r) = L(r)/r
V <- with(L, ./.x)
plot(V)
# compute the maximum absolute difference between
# the isotropic and translat... |
If m, n\in Z^+ such that m+n+mn=34, find the value of m+n
Question
If m, n\in Z^+ such that m+n+mn=34, find the value of m+n
Answer
Express m in terms of n from the given condition
\because m +n+mn=34
m(1+n)=34-n
m=\dfrac{34-n}{1+n}
=\dfrac{35-n-1}{1+n}
=\dfrac{35}{1+n}-1
In order for m+n to be integers, 35 m... | 4 | If m, n\in Z^+ such that m+n+mn=34, find the value of m+n
Answer
Express m in terms of n from the given condition
\because m +n+mn=34
m(1+n)=34-n
m=\dfrac{34-n}{1+n}
=\dfrac{35-n-1}{1+n}
=\dfrac{35}{1+n}-1
In order for m+n to be integers, 35 must be divisible by n+1 . In other words n+1 is equal to one of facto... |
None
<p>So, to get the <strong><span style="color:#27ae60;">Total Number of Factors</span></strong> using Prime Factorization, simply do the "trick" we discussed in the Positive Factors with PF
entry in the Quant Mountain, and multiply the result by $2$.</p> <p>Example</p> <p>How many TOTAL (positive and nega... | 4 | So, to get the **Total Number of Factors** using Prime Factorization, simply do the "trick" we discussed in the Positive Factors with PF
entry in the Quant Mountain, and multiply the result by $2$.
Example
How many TOTAL (positive and negative) factors does $400$ have?
- $400 = 2^45^2$
- # of
positive factors $=(4+1... |
How do you write y = 4(x - 2)^2 - 1 in standard form? | Socratic
How do you write #y = 4(x - 2)^2 - 1# in standard form?
1 Answer
$y = 4 {x}^{2} - 16 x + 15$
Explanation:
Standard form is as follows:
$y = a {x}^{2} + b x + c$
1. $y = 4 {\left(x - 2\right)}^{2} - 1$
2. $y = 4 \left(x - 2\right) \left(x - 2\right)... | 4 | How do you write #y = 4(x - 2)^2 - 1# in standard form?
$y = 4 {x}^{2} - 16 x + 15$
Explanation:
Standard form is as follows:
$y = a {x}^{2} + b x + c$
1. $y = 4 {\left(x - 2\right)}^{2} - 1$
2. $y = 4 \left(x - 2\right) \left(x - 2\right) - 1$
3. $y = 4 \left({x}^{2} - 4 x + 4\right) - 1$
4. $y = 4 {x}^{2} - 1... |
None
Since AB and CD are parallel, we can see AD as the hypotenuse of a right triangle with sides 4 and 8. Hence AD=sqrt(80)=4sqrt(5).
Triangle AED has right angle given, from which ED=8.
From here there are several ways to prove AC parallel to DE. One way is to use the law of cosines to show the alternate interior... | 4 | Since AB and CD are parallel, we can see AD as the hypotenuse of a right triangle with sides 4 and 8. Hence AD=sqrt(80)=4sqrt(5).
Triangle AED has right angle given, from which ED=8.
From here there are several ways to prove AC parallel to DE. One way is to use the law of cosines to show the alternate interior angles... |
Algebra
#1
-1
The solutions are 5 and 6.
learnmgcat Jun 16, 2024
#2
+1
0
9
2
Find all values of $x$ such that $x^2 - 5x + 4 = -x^2 - 25x - 14$. If you find more than one value, then list your solutions, separated by commas.
Hi6942O Jun 16, 2024
First, let's move all terms to one side and combine all like term... | 4 | Find all values of $x$ such that $x^2 - 5x + 4 = -x^2 - 25x - 14$. If you find more than one value, then list your solutions, separated by commas.
First, let's move all terms to one side and combine all like terms.
We get
\(x^{2}+10x+9=0\)
We can put this into factored form to find x. We get
\((x+9)(x+1)=0\)
From... |
A125821 - OEIS
COMMENTS
Proof that all numbers in this sequence are divisible by 3:
if n=(3k+1), then 8n+7=8(3k+1)+7=3(5+8 k) (composite)
if n=(3k+2), then 8n+5=8(3k+2)+5=3(7+8 k) (composite),
so if we require that both 8n+5 and 8n+7 are primes, then n=3k, hence all terms in this sequence are multiples of 3. QED. (... | 4 | Proof that all numbers in this sequence are divisible by 3:
if n=(3k+1), then 8n+7=8(3k+1)+7=3(5+8 k) (composite)
if n=(3k+2), then 8n+5=8(3k+2)+5=3(7+8 k) (composite),
so if we require that both 8n+5 and 8n+7 are primes, then n=3k, hence all terms in this sequence are multiples of 3. QED.
Do[If[PrimeQ[8n + 5] && P... |
solutions
Prove that every convex function \(f\) defined on an open interval \(I \subset \mathbf{R}\) is differentiable at all but (at most) countably many points of \(I\). Hint: Observe that \(d^{+} f(x)(1)=\
lim _{t \rightarrow 0+} \frac{f(x+t)-f(x)}{t}\), the derivative of \(f\) at \(x\) from the right, is a nonde... | 4 | Prove that every convex function \(f\) defined on an open interval \(I \subset \mathbf{R}\) is differentiable at all but (at most) countably many points of \(I\). Hint: Observe that \(d^{+} f(x)(1)=\lim _{t \rightarrow 0+} \frac{f(x+t)-f(x)}{t}\), the derivative of \(f\) at \(x\) from the right, is a nondecreasing func... |
Theorem 6.2 - Class 9 - Alternate interior angles are equal
Theorem 6.2 - Chapter 6 Class 9 Lines and Angles
Last updated at April 16, 2024 by Teachoo
Transcript
Theorem 6.2 :- If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal. Given :- Two parallel lines AB and CD... | 4 | Theorem 6.2 :- If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal.
Given :- Two parallel lines AB and CD. Let PS be the transversal intersecting AB at Q and CD at R.
To Prove :- Each pair of alternate interior angles are equal. i.e, BQR = CRQ and AQR = QRD
Proof :- Fir... |
A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives
Administrator
Staff member
A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives the value of the house, v, as a function of y, the number of years after 1989.
Let's deter... | 4 | A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives the value of the house, v, as a function of y, the number of years after 1989.
Let's determine the years:
2000 - 1989 = 11
Let's determine the change in value:
125,000 - 70,000 = 55,000
Assuming a linear progression, ... |
The plans for a shed call for a rectangular floor with a perimeter of 344 ft. The length is three times the width. What is the length and width? | Socratic
The plans for a shed call for a rectangular floor with a perimeter of 344 ft. The length is three times the width. What is the length and width?
1 Answer
$\text{W... | 4 | The plans for a shed call for a rectangular floor with a perimeter of 344 ft. The length is three times the width. What is the length and width?
$\text{Width"=43" feet}$
$\text{Length"=129" feet}$
Explanation:
$\text{Let "l="length and let "w="width}$
$\text{Perimeter} = 2 l + 2 w$
$344 = 2 l + 2 w$
$l = 3 w$
$34... |
None
1) gcd(m^3,n^2)=2^2*3^2
2) lcm(m^2,n^3)=2^4*3^4*5^6
from 1 we can deduce that both m,n are divisible by 2 and 3.
from 2 we know that one of them is divisible by 5, however it can't
be both because otherwise 1 would have a factor of 5.
let
m=2^a*3^b*5^i
n=2^c*3^d*5^j
where either i=3,j=0 or i=0,j=2 to... | 4 | 1) gcd(m^3,n^2)=2^2*3^2
2) lcm(m^2,n^3)=2^4*3^4*5^6
from 1 we can deduce that both m,n are divisible by 2 and 3.
from 2 we know that one of them is divisible by 5, however it can't
be both because otherwise 1 would have a factor of 5.
let
m=2^a*3^b*5^i
n=2^c*3^d*5^j
where either i=3,j=0 or i=0,j=2 to refl... |
How do you find f'(x) using the definition
Jasiah Vincent
Answered question
2022-04-17
How do you find f'(x) using the definition of a derivative for f(x)=10?
Answer & Explanation
Explanation:
${f}^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{f\left(x+h\right)-f\left(x\right)}{h}$
${f}^{\prime }\left(x\ri... | 4 | How do you find f'(x) using the definition of a derivative for f(x)=10?
Explanation:
${f}^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{f\left(x+h\right)-f\left(x\right)}{h}$
${f}^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{10-10}{h}=\underset{h\to 0}{lim}\frac{0}{h}=\underset{h\to 0}{lim}0=0$
The defin... |
What is the trigonometric form of (2-i)*(3+i) ? | Socratic
What is the trigonometric form of # (2-i)*(3+i) #?
1 Answer
Explanation:
Let $z = \left(2 - i\right) \cdot \left(3 + i\right) = 6 + 2 i - 3 i - {i}^{2} = 7 + \left(- 1\right) i$
Modulus:
$| z | = \sqrt{{7}^{2} + {\left(- 1\right)}^{2}} = \sqrt{50} = 5 \sqr... | 4 | What is the trigonometric form of # (2-i)*(3+i) #?
Explanation:
Let $z = \left(2 - i\right) \cdot \left(3 + i\right) = 6 + 2 i - 3 i - {i}^{2} = 7 + \left(- 1\right) i$
Modulus:
$| z | = \sqrt{{7}^{2} + {\left(- 1\right)}^{2}} = \sqrt{50} = 5 \sqrt{2}$
Argument:
Let $a r g \left(z\right) = \Theta$
$\tan \Theta = - ... |
Newton's law as a function of linear momentum
We are going to express Newton's Law as a function of linear momentum. We write Newton's Second Law,
$$F_x=ma_x=m\frac{dv_x}{dt}=\frac{d(mv_x)}{dt}=\frac{dp_x}{dt}$$
Substituting into Newton's Law of viscosity:
$$\frac{dp_x}{dt}=-\eta A\frac{dv_x}{dz}$$
$dp_x/dt$ (flow ... | 4 | We are going to express Newton's Law as a function of linear momentum. We write Newton's Second Law,
$$F_x=ma_x=m\frac{dv_x}{dt}=\frac{d(mv_x)}{dt}=\frac{dp_x}{dt}$$
Substituting into Newton's Law of viscosity:
$$\frac{dp_x}{dt}=-\eta A\frac{dv_x}{dz}$$
$dp_x/dt$ (flow quantity of movement), represents the variatio... |
Algebrarules.com
Algebra Rule 15
A fraction raised to a negative exponent equals the inverse of the fraction raised to a positive exponent
```\left({a \over b}\right)^{-n} = \left({b\over a}\right)^n```
Description:
The reciprocal of a fraction is the fraction turned on its head: the reciprocal of ``{2 \over 3}``... | 4 | Algebra Rule 15
A fraction raised to a negative exponent equals the inverse of the fraction raised to a positive exponent
$$\left({a \over b}\right)^{-n} = \left({b\over a}\right)^n$$
Description:
The reciprocal of a fraction is the fraction turned on its head: the reciprocal of ${2 \over 3}$ is ${3 \over 2}$. We k... |
None
Let Numerator be x and Denominator be y So, Fraction is π/π Given that, If 1 is added to numerator and 1 is subtracted from the denominator, fraction becomes 1. (ππ’πππππ‘ππ + 1)/(π·ππππππππ‘ππ β1)= 1 (π₯
+ 1)/(π¦ β 1)= 1 (x + 1) = (y β 1) x β y = β1 β 1 x β y = β2 Also, If we add 1 to the denomi... | 4 | Let Numerator be x and Denominator be y So, Fraction is π/π
Given that, If 1 is added to numerator and 1 is subtracted from the denominator, fraction becomes 1.
(ππ’πππππ‘ππ + 1)/(π·ππππππππ‘ππ β1)= 1
(π₯ + 1)/(π¦ β 1)= 1
(x + 1) = (y β 1)
x β y = β1 β 1
x β y = β2
Also, If we add 1 to the denominator... |
A coil of inductance 300mh and resistance 2Omega is connected to a sou
A coil of inductance 300mh and resistance 2Ξ© is connected to a source of voltage 2V. The current reaches half of its steady state value is
The correct Answer is:D
i=i0(1βeβt/Ο)
Ο=LR=300Γ10β32=0.15
βi02=i0(1βeβt/0.15)
βeβt0.15=12ββt0.15ln (e) =ln(1... | 5 | A coil of inductance 300mh and resistance 2Ξ© is connected to a source of voltage 2V. The current reaches half of its steady state value is
i=i0(1βeβt/Ο)
Ο=LR=300Γ10β32=0.15
βi02=i0(1βeβt/0.15)
βeβt0.15=12ββt0.15ln (e) =ln(12)
βt=0.69Γ0.15βt=0.1sec |
How do you use the quadratic formula to solve x^2+6x+10=0? | Socratic
How do you use the quadratic formula to solve #x^2+6x+10=0#?
1 Answer
Solution: $x = - 3 + 1 i \mathmr{and} x = - 3 - 1 i$
Explanation:
${x}^{2} + 6 x + 10 = 0$
Comparing with standard quadratic equation $a {x}^{2} + b x + c = 0$
$a = 1 , b = 6... | 4 | How do you use the quadratic formula to solve #x^2+6x+10=0#?
Solution: $x = - 3 + 1 i \mathmr{and} x = - 3 - 1 i$
Explanation:
${x}^{2} + 6 x + 10 = 0$
Comparing with standard quadratic equation $a {x}^{2} + b x + c = 0$
$a = 1 , b = 6 , c = 10$ Discriminant $D = {b}^{2} - 4 a c$ or
$D = 36 - 40 = - 4$ If discrim... |
more geometric series and sequences
#1
0
0
107
1
Fill in the blanks to make a true equation:
(the question marks are the blanks, and the two question marks don't have to be the same number)
\(\frac{1}{n(n + 3)} = \frac{?}{n} - \frac{?}{n + 3}.\)
youngwolf May 5, 2023
Let the constants be A and B, so 1/(n(n + 3... | 4 | Fill in the blanks to make a true equation:
(the question marks are the blanks, and the two question marks don't have to be the same number)
\(\frac{1}{n(n + 3)} = \frac{?}{n} - \frac{?}{n + 3}.\)
Let the constants be A and B, so 1/(n(n + 3)) = A/n + B/(n + 3).
We can solve for A and B by multiplying both sides of ... |
A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of 9 , 8 , and 22 , respectively. What is the rectangle's area? | Socratic
A right triangle has sides A, B, and C. Side A is the hypotenuse... | 4 | A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of 9 , 8 , and 22 , respectively. What is the rectangle's area?
$\approx 90.71 \text{ square units to 2 dec. places}$
Explanation:
$... |
omputation
Anatomy of the Human Visual system
Primary visual cortex
[Hubel & Wiesel, 1962]
Primary visual cortex
[Hubel & Wiesel, 1962]
CNN: Mathematics
β’ One-dimensional discrete convolution (eg in time) with a kernel $g$ of radius $K$: $$ (f \ast g)[n]=\sum_{m=-K}^{K} f[n-m] \cdot g[m] $$
CNN: Mathematics
... | 4 | CNN: Mathematics
β’ One-dimensional discrete convolution (eg in time) with a kernel $g$ of radius $K$: $$ (f \ast g)[n]=\sum_{m=-K}^{K} f[n-m] \cdot g[m] $$
CNN: Mathematics
β’ Convolution of an image (two-dimensional) with a kernel $g$ of radius $K\times K$:
$$ (f \ast g)[x, y] = \sum_{i=-K}^{K} \sum_{j=-K}^{K} ... |
diff
Returns a vector or matrix of differences.
Syntax
R = diff(x)
R = diff(x, k)
R = diff(x, k, dim)
Inputs
x
The matrix from which to compute differences.
Type: double | integer | logical | struct | cell
Dimension: scalar | vector | matrix
k
The number of differences to compute.
Type: integ... | 4 | Returns a vector or matrix of differences.
Syntax
R = diff(x)
R = diff(x, k)
R = diff(x, k, dim)
Inputs
x
The matrix from which to compute differences.
Type: double | integer | logical | struct | cell
Dimension: scalar | vector | matrix
k
The number of differences to compute.
Type: integer
... |
Skolits Corp. issued 15-year bonds 2 years ago at a coupon rate
of 8.8 percent. The...
Skolits Corp. issued 15-year bonds 2 years ago at a coupon rate of 8.8 percent. The...
Skolits Corp. issued 15-year bonds 2 years ago at a coupon rate of 8.8 percent. The bonds make semiannual payments. If these bonds currently sell... | 5 | Skolits Corp. issued 15-year bonds 2 years ago at a coupon rate of 8.8 percent. The bonds make semiannual payments. If these bonds currently sell for 109 percent of par value, what is the YTM? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
YTM %
ANSW... |
How to Find dy/dx, Implicit differentiation? 2xy^3 + y = 2x | Socratic
How to Find dy/dx, Implicit differentiation? 2xy^3 + y = 2x
1 Answer
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 - 2 {y}^{3}}{6 x {y}^{2} + 1}$
Explanation:
1. $\frac{d}{\mathrm{dx}} \left(2 x {y}^{3} + y\right) = \frac{d}{\mathrm{dx}} \cdot 2 x... | 5 | How to Find dy/dx, Implicit differentiation? 2xy^3 + y = 2x
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 - 2 {y}^{3}}{6 x {y}^{2} + 1}$
Explanation:
1. $\frac{d}{\mathrm{dx}} \left(2 x {y}^{3} + y\right) = \frac{d}{\mathrm{dx}} \cdot 2 x$
2. $2 \cdot \frac{d}{\mathrm{dx}} \left(x {y}^{3}\right) + \frac{d}{\mathrm{d... |
A block slides down an inclined plane, starting from rest and
being pushed with a constant...
A block slides down an inclined plane, starting from rest and being pushed with a constant...
A block slides down an inclined plane, starting from rest and being pushed with a constant acceleration of 5.25 m/s2 over a distanc... | 4 | A block slides down an inclined plane, starting from rest and being pushed with a constant acceleration of 5.25 m/s2 over a distance of 18.0 cm. It then decelerates at a constant rate of 1.10 m/s2
(because of friction), until it again comes to rest. Find the total time the block is in motion.
1st Part
givens:
vo = 0 m... |
Collection of Maths Problems
Matrix equation
Task number: 2485
Find a matrix \(\mathbf A\), that over \(\mathbb Z_5\) satisfies
\(\mathbf A \begin{pmatrix} 4 & 4 & 0 & 1 \\ 3 & 1 & 2 & 2 \\ 2 & 3 & 1 & 3 \\ 3 & 2 & 3 & 4 \\ \end{pmatrix} = \begin{pmatrix} 1 & 0 & 2 & 3 \\ 3 & 1 & 2 & 2 \\ 2 & 3 & 1 & 3 \\ 1 & 2 & 3 ... | 5 | Find a matrix \(\mathbf A\), that over \(\mathbb Z_5\) satisfies
\(\mathbf A \begin{pmatrix} 4 & 4 & 0 & 1 \\ 3 & 1 & 2 & 2 \\ 2 & 3 & 1 & 3 \\ 3 & 2 & 3 & 4 \\ \end{pmatrix} = \begin{pmatrix} 1 & 0 & 2 & 3 \\ 3 & 1 & 2 & 2 \\ 2 & 3 & 1 & 3 \\ 1 & 2 & 3 & 4 \\ \end{pmatrix} \)
Hint
From \(\mathbf A \mathbf B = \math... |
Inverse Completion Theorem
Theorem
Every commutative semigroup containing cancellable elements admits an inverse completion.
Proof
Let $\struct {S, \circ}$ be a commutative semigroup which has cancellable elements.
From Construction of Inverse Completion, we can construct an inverse completion $\struct {T', \oplu... | 4 | Inverse Completion Theorem
Theorem
Every commutative semigroup containing cancellable elements admits an inverse completion.
Proof
Let $\struct {S, \circ}$ be a commutative semigroup which has cancellable elements.
From Construction of Inverse Completion, we can construct an inverse completion $\struct {T', \oplu... |
What is the derivative of f(x)=5^lnx?
poetinjam4gj4
Answered question
2023-03-26
What is the derivative of $f\left(x\right)={5}^{\mathrm{ln}x}$?
Answer & Explanation
Take both sides' natural logarithms.
$\mathrm{ln}\left(f\left(x\right)\right)=\mathrm{ln}\left({5}^{\mathrm{ln}x}\right)$
Using the following rule,... | 5 | What is the derivative of $f\left(x\right)={5}^{\mathrm{ln}x}$?
Take both sides' natural logarithms.
$\mathrm{ln}\left(f\left(x\right)\right)=\mathrm{ln}\left({5}^{\mathrm{ln}x}\right)$
Using the following rule, the right side can be made simpler: $\mathrm{log}\left({a}^{b}\right)=b\mathrm{log}\left(a\right)$
$\mathrm... |
What is the probability of drawing an ace from a deck of 52 cards?
What is the probability of drawing an ace from a deck of 52 cards?
The probability of picking up an ace in a 52 deck of cards is 4/52 since there are 4 aces in the deck.
What is the probability of getting either a spade or a jack when drawing a singl... | 4 | What is the probability of drawing an ace from a deck of 52 cards?
The probability of picking up an ace in a 52 deck of cards is 4/52 since there are 4 aces in the deck.
What is the probability of getting either a spade or a jack when drawing a single card from a deck of 52 cards?
There are 4 jacks in the deck and 1... |
Consider a 2-year bond with a principal of $100 that provides
coupons at the rate of...
Consider a 2-year bond with a principal of $100 that provides coupons at the rate of...
1. Consider a 2-year bond with a principal of $100 that provides coupons at the rate of 3.6% per annum semiannually. Suppose the yield on this... | 5 | Consider a 2-year bond with a principal of $100 that provides coupons at the rate of 3.6% per annum semiannually. Suppose the yield on this bond is 5.8% per annum with continuous compounding.
(a) What is the duration of this bond?
(b) Suppose the yield on this bond decreases by 0.1%.
1. Calculate the new bond price ex... |
What is the slope of any line perpendicular to the line passing through (-2,5) and (-8,1)? | Socratic
What is the slope of any line perpendicular to the line passing through #(-2,5)# and #(-8,1)#?
1 Answer
Explanation:
The formula for slope m = $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
m = $\frac{{y}_{2} - {y}_... | 4 | What is the slope of any line perpendicular to the line passing through #(-2,5)# and #(-8,1)#?
Explanation:
The formula for slope m = $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
m = $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
m = $\frac{1 - 5}{- 8 - \left(- 2\right)}$
m = $- \frac{4}{6}$
m = $- \frac{2}{3}$
... |
The area of a rectangle is defined as the total space occupied by it and perimeter is defined as the total length of the boundary of the rectangle.
Answer: The dimensions of the rectangle with a perimeter of 100m, and as large an area as possible, are 25 m and 25 m.
Area of rectangle = length Γ breadth
Perimeter of... | 4 | The area of a rectangle is defined as the total space occupied by it and perimeter is defined as the total length of the boundary of the rectangle.
Answer: The dimensions of the rectangle with a perimeter of 100m, and as large an area as possible, are 25 m and 25 m.
Area of rectangle = length Γ breadth
Perimeter of ... |
A219540 - OEIS
COMMENTS
R. Mestrovic conjectures that, for n >= 3, 2*sum(j = 1, n) j^n == -n^2 (mod n^3) implies that n is prime. See proposition 2.2(ii) - the conjecture is proved to be equivalent to Giuga's conjecture.
This proves the first half of Mestrovic's conjecture and hence the first half of Giuga's conjectu... | 5 | R. Mestrovic conjectures that, for n >= 3, 2*sum(j = 1, n) j^n == -n^2 (mod n^3) implies that n is prime. See proposition 2.2(ii) - the conjecture is proved to be equivalent to Giuga's conjecture.
This proves the first half of Mestrovic's conjecture and hence the first half of Giuga's conjecture : If n>2 is prime, a(n... |
Find the area bounded by the ellipse and the ordinates x = ae and x = 0, where b 2 = a 2 (1 - e 2 ) and e<1.
Given equations are:
...... (1)
And x = ae, x = 0 ...... (2)
equation (1) represents an eclipse that is symmetrical about the x - axis and also about the y - axis, with center at origin and passes through (Β±a... | 5 | Find the area bounded by the ellipse and the ordinates x = ae and x = 0, where b^2 = a^2 (1 - e^2) and e<1.
Given equations are:
...... (1)
And x = ae, x = 0 ...... (2)
equation (1) represents an eclipse that is symmetrical about the x - axis and also about the y - axis, with center at origin and passes through (Β±a... |
A 20 mW 360 nm laser is incident on a metal anode. The metal in
the...
For the external photoelectric effect we have
Photon energy = Work function + Electron kinetic energy
h*F = W + Ek
h*F = W +eU
where U is the stopping potential that need to be applied to completely stop all electrons
U =[(h*c/lambda)-W)/ e = 6... | 5 | For the external photoelectric effect we have
Photon energy = Work function + Electron kinetic energy
h*F = W + Ek
h*F = W +eU
where U is the stopping potential that need to be applied to completely stop all electrons
U =[(h*c/lambda)-W)/ e = 6.62*10^-34*3*10^8/360*10^-9/1.6*10^-19 - 1.8 =1.648 V
If N/t is number... |
Lecture Notes :-
Let us solve Numericals Explaining the range of the readings.
Q.1. Resistances R[1] and R[2] have respectively nominal values of 10Ξ© and 5 Ξ© and tolerances of Β±5% and Β±10%. The range of values for the parallel combination of R[1 ]and R[2] is [ Gate 2001]
a) 3.077 Ξ© to 3.636 Ξ©
b) 2.805 Ξ© to 3.371 Ξ©... | 4 | Q.1. Resistances R[1] and R[2] have respectively nominal values of 10Ξ© and 5 Ξ© and tolerances of Β±5% and Β±10%. The range of values for the parallel combination of R[1 ]and R[2] is [ Gate 2001]
a) 3.077 Ξ© to 3.636 Ξ©
b) 2.805 Ξ© to 3.371 Ξ©
c) 3.237 Ξ© to 3.678 Ξ©
d) 3.192 Ξ© to 3.435 Ξ©
Ans. Given Nominal values (True va... |
Well here is how to prove the Torque-Angular Momentum relation which is the equivalent of F=dp/dt.
We know that
L = r x p
So if we differentiate both sides, we get
dL/dt = dr/dt x p + r x dp/dt
however dr/dt is just v, and as p = mv, therefore v x p = 0. Also using Newton's second law, the second term becomes r x F = ... | 4 | Well here is how to prove the Torque-Angular Momentum relation which is the equivalent of F=dp/dt.
We know that
L = r x p
So if we differentiate both sides, we get
dL/dt = dr/dt x p + r x dp/dt
however dr/dt is just v, and as p = mv, therefore v x p = 0. Also using Newton's second law, the second term becomes r x F = T... |
How do you solve -3 + \frac{1}{x+1}=\frac{2}{x} by finding the least common multiple? | Socratic
How do you solve #-3 + \frac{1}{x+1}=\frac{2}{x}# by finding the least common multiple?
1 Answer
Explanation:
Given that
$- 3 + \frac{1}{x + 1} = \frac{2}{x}$
$- 3 + \frac{1}{x + 1} - \frac{2}{x} = 0$
$\frac{- 3 x \le... | 4 | How do you solve #-3 + \frac{1}{x+1}=\frac{2}{x}# by finding the least common multiple?
Explanation:
Given that
$- 3 + \frac{1}{x + 1} = \frac{2}{x}$
$- 3 + \frac{1}{x + 1} - \frac{2}{x} = 0$
$\frac{- 3 x \left(x + 1\right) + x - 2 \left(x + 1\right)}{x \left(x + 1\right)} = 0$
$\frac{- 3 {x}^{2} - 3 x + x - 2 x ... |
Introduction to Mathematical Physics/Electromagnetism/Exercises - Wikibooks, open books for an open world
Exercice:
Assume constitutive relations to be:
${\displaystyle D(r,t)=\epsilon (r,t)*E(r,t)}$
where ${\displaystyle *}$ represents temporal convolution\index{convolution} (value of ${\displaystyle D(r,t)}$ field... | 4 | Exercice:
Assume constitutive relations to be:
${\displaystyle D(r,t)=\epsilon (r,t)*E(r,t)}$
where ${\displaystyle *}$ represents temporal convolution\index{convolution} (value of ${\displaystyle D(r,t)}$ field at time ${\displaystyle t}$ S depends on values of ${\displaystyle E}$ at
preceeding times) and
${\displ... |
How to Calculate CARG | Sapling
CARG stands for Compound Annual Rate Growth that is more often abbreviated as CAGR. CAGR typically represents an annual rate of the investment growth calculated over several years. It is also used to
characterize the growth of other elements of business such as a number of clients or pro... | 4 | CARG stands for Compound Annual Rate Growth that is more often abbreviated as CAGR. CAGR typically represents an annual rate of the investment growth calculated over several years. It is also used to characterize the growth of other elements of business such as a number of clients or product sales. CAGR is computed wit... |
Find the zeros of the function.Enter the solutions - Asksia.ai
Answer from Sia
Posted 6 months ago
Solution by Steps
step 1
To find the zeros of the function $g(x) = -10x^2 + 490$, set the function equal to zero: $-10x^2 + 490 = 0$
step 2
Divide both sides of the equation by $-10$ to simplify: $x^2 - 49 = 0$
ste... | 4 | Find the zeros of the function.
Solution by Steps
step 1
To find the zeros of the function $g(x) = -10x^2 + 490$, set the function equal to zero: $-10x^2 + 490 = 0$
step 2
Divide both sides of the equation by $-10$ to simplify: $x^2 - 49 = 0$
step 3
Factor the left side of the equation as a difference of squares... |
AnahtarcΔ±, Berkay and Djakov, Plamen Borissov (2015) Asymptotics of spectral gaps of 1D Dirac operator whose potential is a linear combination of two exponential terms. Asymptotic Analysis, 92 (1-2).
pp. 141-160. ISSN 0921-7134 (Print) 1875-8576 (Online)
Full text not available from this repository. (
Request a copy... | 4 | The one-dimensional Dirac operator L=i((1)(0) (-1)(0))d/dx + ((0)(Q(x)) (0) P-(x)), P,Q is an element of L-2 ([0, pi]), consider on [0, pi] with periodic or antiperiodic boundary conditions, has
discrete spectra. For large enough |n|, n is an element of Z, there are two (counted with multiplicity) eigenvalues lambda(-)... |
Canadian Adventures has earnings per share of $2.86 and
dividends per share of $1.80. The total...
Canadian Adventures has earnings per share of $2.86 and dividends per share of $1.80. The total...
Canadian Adventures has earnings per share of $2.86 and dividends per share of $1.80. The total equity of the firm is $75... | 4 | Canadian Adventures has earnings per share of $2.86 and dividends per share of $1.80. The total equity of the firm is $750,000. There are 38,000 shares of stock outstanding. What is the sustainable rate of growth?
2.14 percent
3.31 percent
4.94 percent
5.37 percent
6.59 percent
The growth rate is computed as shown be... |
How do you use the definition of continuity and the properties of limits to show the function is continuous F(x)= (x^2-8)^8 on the interval (-inf, inf)? | Socratic
How do you use the definition of continuity and the properties of limits to show the function is continuous #F(x)= (x^2-8)^8# on the interval (-inf, inf)?
... | 4 | How do you use the definition of continuity and the properties of limits to show the function is continuous #F(x)= (x^2-8)^8# on the interval (-inf, inf)?
Explanation:
Let a be any number from the interval $\left(- \infty , \infty\right)$ then we need to show that $f \left(a\right) = {\lim}_{x \to a} f \left(x\right)... |
e
Find the expression of x in terms of $\xi$ when : 1) Third node R is taken at (6.0)
written 7.7 years ago by β’ modified 2.8 years ago
Coordinates of the nodes of finite element are given by P (4.0) and Q (5.0) Find the expression of x in terms of $\xi$ when :
1) Third node R is taken at (6.0)
2) Third node R is... | 5 | Find the expression of x in terms of $\xi$ when :
1) Third node R is taken at (6.0)
2) Third node R is taken at (5.0)
Comment on the result.
Quadratic element with nodes 3.
$\hspace{1cm}x=\phi, x_1+\phi_2x_2+ \phi_3 x_3 $
where, $\phi,=\frac{1}{2}\xi(\xi-1), \phi_2=\frac{1}{2}\xi (\xi+1),\phi=(1-\xi)(1+\xi)$
$x=... |
Derive Difference of Two Angles Identities (Complex Plane)
This example demonstrates how the difference of two anglesβ identities can be derived using the properties of complex numbers and Eulerβs formula. The two identities are shown below:
1. Observe that the angle (theta) forms the complex number on the unit circl... | 4 | Derive Difference of Two Angles Identities (Complex Plane)
This example demonstrates how the difference of two anglesβ identities can be derived using the properties of complex numbers and Eulerβs formula. The two identities are shown below:
1. Observe that the angle (theta) forms the complex number on the unit circle... |
What volume OF SOLVENT must we add to a 500*mL solution of 1.2*mol*L^-1 concentration to dilute the concentration to 1.0*mol*L^-1? | Socratic
What volume OF SOLVENT must we add to a #500*mL# solution of #1.2*mol*L^-1# concentration to dilute the concentration to #1.0*mol*L^-1#?
1 Answer
Look at this dimensionally....... | 4 | What volume OF SOLVENT must we add to a #500*mL# solution of #1.2*mol*L^-1# concentration to dilute the concentration to #1.0*mol*L^-1#?
Look at this dimensionally...........we must add $100 \cdot m L$ to the initial volume, to make up to a volume of $600 \cdot m L$...........
Explanation:
${C}_{1} {V}_{1} = {C}_{2}... |
Ma
Matrix Inverse
Inverse refers to a matrices multiplicitive inverse. For example 0.2 is the multiplicitive inverse of 5, 2.2 * 5 = 1. Multiplying a scalar value by it's multiplicitive inverse results in one.
Multiplying a matrix by its multiplicitive inverse results in the identity matrix.
Not all matrices have an ... | 4 | Inverse refers to a matrices multiplicitive inverse. For example 0.2 is the multiplicitive inverse of 5, 2.2 * 5 = 1. Multiplying a scalar value by it's multiplicitive inverse results in one.
Multiplying a matrix by its multiplicitive inverse results in the identity matrix.
Not all matrices have an inverse. Only squar... |
Polynomial Simplification: A Step Towards Success
What is the polynomial 3y^2(y-7)^2 - 15 after it has been fully simplified and written in standard form?
A) 4y^2 + 34
B) 3y^2 + y + 34
C) 4y^2 + 14y + 34
D) 4y^4 +34
Answer:
C) 4y^2 + 14y + 34
The polynomial 3y^2(y-7)^2 - 15 after it has been fully simplified and... | 4 | What is the polynomial 3y^2(y-7)^2 - 15 after it has been fully simplified and written in standard form?
A) 4y^2 + 34
B) 3y^2 + y + 34
C) 4y^2 + 14y + 34
D) 4y^4 +34
Answer:
C) 4y^2 + 14y + 34
The polynomial 3y^2(y-7)^2 - 15 after it has been fully simplified and written in standard form is 4y^2 + 14y + 34.
A p... |
Problems on the Sum of Angles Around a Point
PROBLEMS ON THE SUM OF ANGLES AROUND A POINT
The sum of the sizes of the angles at a point is 360Β°.
Find the unknown of the following :
Problem 1 :
Solution :
2x - 10 + 28 + x + x + 30 = 360
4x - 10 + 28 + 30 = 360
4x + 48 = 360
Subtracting 48 on both sides.
4x = 36... | 4 | The sum of the sizes of the angles at a point is 360Β°.
Find the unknown of the following :
Problem 1 :
Solution :
2x - 10 + 28 + x + x + 30 = 360
4x - 10 + 28 + 30 = 360
4x + 48 = 360
Subtracting 48 on both sides.
4x = 360 - 48
4x = 312
Dividing by 4 on both sides.
x = 312 / 4
x = 78
Problem 2 :
Solution ... |
The demand curve for potatoes is given by:
QX = 1,000 +0.3I - 300 PX +...
The demand curve for potatoes is given by: QX = 1,000 +0.3I - 300 PX +...
The demand curve for potatoes is given by:
QX = 1,000 +0.3I - 300 PX + 200 PY,where QX = Annual demand in pounds
I = Average income in dollars per year
PX = price of potat... | 5 | The demand curve for potatoes is given by:
QX = 1,000 +0.3I - 300 PX + 200 PY,where QX = Annual demand in pounds
I = Average income in dollars per year
PX = price of potatoes per pound,
PY = price of rice per pound.
(a) (1) Discuss whether potato is a normal good or an inferior good.
(b) (1) Suppose I = $10,000: What w... |
2011 AMC 8 Problems/Problem 23
Problem
How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit?
$\textbf{(A) }24\qquad\textbf{(B) }48\qquad\textbf{(C) }60\qquad\textbf{(D) }84\qquad\textbf{(E) }108$
Solution 1
We... | 4 | Problem
How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit?
$\textbf{(A) }24\qquad\textbf{(B) }48\qquad\textbf{(C) }60\qquad\textbf{(D) }84\qquad\textbf{(E) }108$
Solution 1
We can separate this into two case... |
Euler #6: Sum Square Difference
The sum of the squares of the first ten natural numbers is,
1^2+2^2+...+10^2=385
The square of the sum of the first ten natural numbers is,
(1+2+...+10)^2=55^2=3025
Hence the difference between the sum of the squares of the first ten natural numbers and the squar... | 5 | Euler #6: Sum Square Difference
The sum of the squares of the first ten natural numbers is,
1^2+2^2+...+10^2=385
The square of the sum of the first ten natural numbers is,
(1+2+...+10)^2=55^2=3025
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025... |
Zero order reaction
Posted 6 years ago by lavannya bhatia
Zero order reaction
sourceΒ : askIITians
Zero order reaction-
Reactions in which the concentrations of the reactants do not change with time and the reaction rate remains constant throughout .Those reactions are zero order reactions.
Ex.1) Photochemical re... | 4 | Zero order reaction-
Reactions in which the concentrations of the reactants do not change with time and the reaction rate remains constant throughout .Those reactions are zero order reactions.
Ex.1) Photochemical reaction between hydrogen and chlorine-
H[2] + Cl[2] ββ-> 2 HCl
Rate = K [H[2]]^0 [Cl[2]]^0 = K
Ex... |
Lecture 25
Homework 9 question 4 is subtle.
Consider this simplified version.
1. Let W, X and Y be independent identically distributed (i.i.d) random variables.
2. What is the probability that W<min(X,Y)?
3. Method 1:
1. Everything is symmetric, so each variable has 1/3 chance of being the smallest.
2. P... | 5 | Consider this simplified version.
1. Let W, X and Y be independent identically distributed (i.i.d) random variables.
2. What is the probability that W<min(X,Y)?
3. Method 1:
1. Everything is symmetric, so each variable has 1/3 chance of being the smallest.
2. P[W<min(X,Y)] = 1/3.
4. Method 2:
1. P[W<X] ... |
Pr
Lesson 5
More Graphs of Functions
Problem 1
The solution to a system of equations is \((6,\text-3)\). Choose two equations that might make up the system.
Problem 2
A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches it... | 4 | Lesson 5
More Graphs of Functions
Problem 1
The solution to a system of equations is \((6,\text-3)\). Choose two equations that might make up the system.
Problem 2
A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its d... |
A charge of 24 C passes through a circuit every 6 s. If the circuit can generate 8 W of power, what is the circuit's resistance? | Socratic
A charge of #24 C# passes through a circuit every #6 s#. If the circuit can generate #8 W# of power, what is the circuit's resistance?
2 Answers
The resistance in the circuit is ... | 4 | A charge of 24 C passes through a circuit every 6 s. If the circuit can generate 8 W of power, what is the circuit's resistance?
The resistance in the circuit is $0.5$$\Omega$
Explanation:
Data:
Charge$= Q = 2 C$
Time$= t = 6 s$
Power$= P = 8 W$
Resistance#=R=??#
We know that:
$P = {I}^{2} R$
Where $I$ is the cu... |
(7m^8-5m^3+9m^2+5)+(9m^7+3m^3-4m)=
If it's not what You are looking for type in the equation solver your own equation and let us solve it.
Simplifying (7m8 + -5m3 + 9m2 + 5) + (9m7 + 3m3 + -4m) = 0 Reorder the terms: (5 + 9m2 + -5m3 + 7m8) + (9m7 + 3m3 + -4m) = 0 Remove parenthesis around (5 + 9m2 + -5m3 + 7m8) 5 + 9... | 4 | (7m^8-5m^3+9m^2+5)+(9m^7+3m^3-4m)=
Simplifying (7m8 + -5m3 + 9m2 + 5) + (9m7 + 3m3 + -4m) = 0
Reorder the terms:
(5 + 9m2 + -5m3 + 7m8) + (9m7 + 3m3 + -4m) = 0
Remove parenthesis around (5 + 9m2 + -5m3 + 7m8)
5 + 9m2 + -5m3 + 7m8 +
(9m7 + 3m3 + -4m) = 0
Reorder the terms:
5 + 9m2 + -5m3 + 7m8 + (-4m + 3m3 + 9m7) = 0
R... |
The equation for C is ${x}^{2}+{y}^{2}={r}^{2}$ and P is a point (a, 0)
on the x-axis with a $e Β±r.$
The point on the circle C is(x, y).
Obtain the distance between (x, y) and (a, 0) as follows:
$d=\sqrt{\left(x-a{\right)}^{2}+\left(y-0{\right)}^{2}}$
$=\sqrt{\left(x-a{\right)}^{2}+{y}^{2}}$
Now, obtain the partial de... | 4 | The equation for C is ${x}^{2}+{y}^{2}={r}^{2}$ and P is a point (a, 0)
on the x-axis with a $e Β±r.$
The point on the circle C is(x, y).
Obtain the distance between (x, y) and (a, 0) as follows:
$d=\sqrt{\left(x-a{\right)}^{2}+\left(y-0{\right)}^{2}}$
$=\sqrt{\left(x-a{\right)}^{2}+{y}^{2}}$
Now, obtain the partial der... |
A circle has a diameter with endpoints of (-3, 8) and (7, 4). What is the center of the circle?
3
To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is ((x1 + x2) / 2, (y1 + y2) / 2).
Let's apply the formula to the g... | 4 | A circle has a diameter with endpoints of (-3, 8) and (7, 4). What is the center of the circle?
To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is ((x1 + x2) / 2, (y1 + y2) / 2).
Let's apply the formula to the giv... |
Laplace Transform of sin2t/t - Mathstoon
The Laplace transform of sin2t/t is equal to tan^-1(2/s). In this article, we will learn how to find the Laplace of sin2t/t. The Laplace transform formula of sin2t/t is given as follows:
L{sin2t/t} = tan^-1(2/s).
To evaluate the Laplace trasform of sin2t divided by t, we will ... | 5 | The Laplace transform of sin2t/t is equal to tan^-1(2/s). In this article, we will learn how to find the Laplace of sin2t/t. The Laplace transform formula of sin2t/t is given as follows:
L{sin2t/t} = tan^-1(2/s).
To evaluate the Laplace trasform of sin2t divided by t, we will use the two formulas listed below:
1. L... |
matrix(List) -- create a matrix from a doubly-nested list of ring elements or matrices
Description
An attempt is made to coerce the ring elements and matrices to a common ring. If the entries are ring elements, they are used as the entries of the matrix, and if the entries are matrices, then they
are used to provide b... | 4 | matrix(List) -- create a matrix from a doubly-nested list of ring elements or matrices
Description
An attempt is made to coerce the ring elements and matrices to a common ring. If the entries are ring elements, they are used as the entries of the matrix, and if the entries are matrices, then they
are used to provide b... |
The surface areas of a solid sphere and a solid hemisphere are equal to S , if their volumes are are ${V_1}$ and ${V_2}$ respectively then \
Hint : In such kinds of questions we have to use the basic formulas for volume and surface area of sphere and hemisphere . Also the relation between hemisphere and sphere has to ... | 4 | The surface areas of a solid sphere and a solid hemisphere are equal to S , if their volumes are are ${V_1}$ and ${V_2}$ respectively then \
Hint : In such kinds of questions we have to use the basic formulas for volume and surface area of sphere and hemisphere . Also the relation between hemisphere and sphere has to ... |
hap
from math import pi # given data epsilon_r=2.5 epsilon_o=8.854*10**-12 d=.2*10**-3 # in m A=20*10**-4 # in m**2 omega=2*pi*10**6 # in radians/s f=10**6 tan_delta=4*10**-4 C=epsilon_o*epsilon_r*A/d #
in F print "Capicitance is : ",(C*10**12)," miu miu F" # Formula P=V**2/R, so # R=V**2/P and P= V**2*2*pi* f * C * ta... | 5 | # given data
g=0.055 # in V-m/N
t=2*10**-3 # in m
P=1.25*10**6 # in N/m**2
epsilon=40.6*10**-12 # in F/m
V_out=g*t*P
print "Output voltage is : ",(V_out)," V"
# Formula Charge Sensivity=
epsilon_o*epsilon_r*g=epsilon*g
ChargeSensivity=epsilon*g
print "Charge Sensivity is : ",(ChargeSensivity)," C/N"
Output voltage is ... |
Intermediate Example of the Principle of Weak Mathematical Induction
Intermediate Example of the Principle of Weak Mathematical Induction
We will now look at an intermediate example of the principle of weak mathematical induction.
Example 1
Prove that $n^2 < 2^n$ for each positive integer $n \geq 5$.
Let $P(n)$ be... | 5 | We will now look at an intermediate example of the principle of weak mathematical induction.
Example 1
Prove that $n^2 < 2^n$ for each positive integer $n \geq 5$.
Let $P(n)$ be the statement that $n^2 < 2^n$.
Base Step: The statement $P(5)$ says that $5^2 = 25 < 2^5 = 32$ which is true.
Induction Step: Suppose th... |
Basic Math/Algebra
So yes, we do expect you to be able to do basic math and algebra. We will not make you do calculus or differential equations - just some plain ol' algebra. This means you might memorize an equation
with some variables in it and we tell you a few of them - then you calculate for the missing one. Her... | 4 | So yes, we do expect you to be able to do basic math and algebra. We will not make you do calculus or differential equations - just some plain ol' algebra. This means you might memorize an equation
with some variables in it and we tell you a few of them - then you calculate for the missing one. Here is an example and t... |
Which Of The Following Equations Results In No Solutions? A 3(v + 5) = 2v - 4 + V B 3(v + 5) = 2v + 15
Answer:
[tex]\boxed{\sf A) \:3(v + 5) = 2v - 4 + v}[/tex]
Step-by-step explanation:
[tex]\sf A )\:3(v + 5) = 2v - 4 + v[/tex]
Combine like terms:
[tex]\sf 3\left(v+5\right)=3v-4[/tex]
Expand:
[tex]\sf 3v+15=3v-... | 4 | Which Of The Following Equations Results In No Solutions? A 3(v + 5) = 2v - 4 + V B 3(v + 5) = 2v + 15
Answer:
$\boxed{\sf A) \:3(v + 5) = 2v - 4 + v}$
Step-by-step explanation:
$\sf A )\:3(v + 5) = 2v - 4 + v$
Combine like terms:
$\sf 3\left(v+5\right)=3v-4$
Expand:
$\sf 3v+15=3v-4$
Subtract 15 from both sides... |
. Suppose an economy is represented by the following
equations.
Consumption
function &nb
. Suppose an economy is represented by the following equations. Consumption function &nb
. Suppose an economy is represented by the following equations.
Consumption function C = 200 + 0.8Yd
Planned inv... | 5 | Suppose an economy is represented by the following equations.
Consumption function C = 200 + 0.8Yd
Planned investment I = 400
Government spending G = 600
Exports EX = 200
Imports IM = 0.1Yd
Autonomous Taxes T = 500
Marginal Tax Rate t=0.2
Planned aggregate expenditure AE = C + I + G + (EX - IM)
By using the ab... |
How do you find the intervals of increasing and decreasing using the first derivative given y=sinx+cosx? | Socratic
How do you find the intervals of increasing and decreasing using the first derivative given #y=sinx+cosx#?
1 Answer
The function is increasing on intervals of the form $\left[- \frac{3 \pi}{4} + 2 n \pi... | 5 | How do you find the intervals of increasing and decreasing using the first derivative given #y=sinx+cosx#?
The function is increasing on intervals of the form $\left[- \frac{3 \pi}{4} + 2 n \pi , \frac{\pi}{4} + 2 n \pi\right]$ and decreasing on intervals of the form $\left[\frac{\pi}{4} + 2 n \pi , \frac{5 \pi}{4} + ... |
How to create a particular initial state as a MPS?
One way is to set all qubits in this form (left half of the chain spin up, right half with spin down):
SpinHalf sites = SpinHalf(N);
auto init = InitState(sites);
for(auto n : range1(N)) {
if (n <= N/2) {
init.set(n, "Up");
} else {
init.set(n... | 5 | One way is to set all qubits in this form (left half of the chain spin up, right half with spin down):
SpinHalf sites = SpinHalf(N);
auto init = InitState(sites);
for(auto n : range1(N)) {
if (n <= N/2) {
init.set(n, "Up");
} else {
init.set(n, "Dn");
}
}
auto psi = MPS(init);
and then ap... |
What are other methods for solving equations that can be adapted to solving trigonometric equations? | Socratic
What are other methods for solving equations that can be adapted to solving trigonometric equations?
1 Answer
Solving concept. To solve a trig equation, transform it into one, or many, basic trig equations.... | 4 | Solving concept. To solve a trig equation, transform it into one, or many, basic trig equations. Solving a trig equation, finally, results in solving various basic trig equations.
There are 4 main basic trig equations:
sin x = a; cos x = a; tan x = a; cot x = a.
Exp. Solve sin 2x - 2sin x = 0
Solution. Transform the eq... |
ordinal subdivision
nLab ordinal subdivision
Idea
The most usual method of subdivision for a simplicial complex as used in elementary algebraic and geometric topology is the barycentric subdivision. There is however another very well structured
subdivision construction encountered which can be useful. The basic geome... | 4 | Idea
The most usual method of subdivision for a simplicial complex as used in elementary algebraic and geometric topology is the barycentric subdivision. There is however another very well structured
subdivision construction encountered which can be useful. The basic geometric construction involves chopping up a geome... |
no graph, but i labeled steps to draw the graph
#1
0
+1
2
1
As shown in the graph, the area of regular hexagon ABCDEF is 72, P is the midpoint of EF. What is the area of the shadow?
Graph: Step 1: Draw regular hexagon ABCDEF. Step 2: Connect AD. Step 3: Mark the midpoint of EF as P, and connect BP. Name the inter... | 4 | As shown in the graph, the area of regular hexagon ABCDEF is 72, P is the midpoint of EF. What is the area of the shadow?
Graph: Step 1: Draw regular hexagon ABCDEF. Step 2: Connect AD. Step 3: Mark the midpoint of EF as P, and connect BP. Name the intersection between these two lines as M. Find [AFPM]
Analyzing the ... |
2016 AMC 10B Problems/Problem 7
Problem
The ratio of the measures of two acute angles is $5:4$, and the complement of one of these two angles is twice as large as the complement of the other. What is the sum of the degree measures of the
two angles?
$\textbf{(A)}\ 75\qquad\textbf{(B)}\ 90\qquad\textbf{(C)}\ 135\qqua... | 4 | Problem
The ratio of the measures of two acute angles is $5:4$, and the complement of one of these two angles is twice as large as the complement of the other. What is the sum of the degree measures of the
two angles?
$\textbf{(A)}\ 75\qquad\textbf{(B)}\ 90\qquad\textbf{(C)}\ 135\qquad\textbf{(D)}\ 150\qquad\textbf{(... |
Five neighbour theorem
Every map has at least one country with five or fewer neighbours
This theorem is central to any attempted proof of the Four Colour Theorem. It relies on Euler's formula, F-E+V=2, to relate the number of countries, borders and meeting points (defined below). It is
normally associated with polyhed... | 4 | Five neighbour theorem
Every map has at least one country with five or fewer neighbours
This theorem is central to any attempted proof of the Four Colour Theorem. It relies on Euler's formula, F-E+V=2, to relate the number of countries, borders and meeting points (defined below). It is
normally associated with polyhed... |
A411/2005 - On the Asymptotics of Fast Mean-Reversion Stochastic Volatility Models.
Preprint A411/2005
On the Asymptotics of Fast Mean-Reversion Stochastic Volatility Models.
Jorge Zubelli | Souza, Max
Keywords: stochastic volatility | quantitative finances | mathematical methods in finances
We consider the asympto... | 4 | We consider the asymptotic behavior of options under stochastic volatility models for which the volatility process fluctuates on a much faster time scale than that defined by the risk-less interest
rate. We identify the distinguished asymptotic limits and, in contrast with previous studies, we deal with small volatilit... |
A Shopper Bought Shoes Marked $75, With 25%off. If The Store Also Charged 8.75% Tax. How Much Did The
75 times .25 = 18.75
75 - 18.75 = 56.25
56.25 * .0875 = 4.921875
56.25 + 4.921875 = 61.171875
Answer: $61.17
The shopper paid $61.17
Step-by-step explanation:
the motorcyclist starts x hours after the bus.
it take... | 4 | A Shopper Bought Shoes Marked $75, With 25%off. If The Store Also Charged 8.75% Tax. How Much Did The
75 times .25 = 18.75
75 - 18.75 = 56.25
56.25 * .0875 = 4.921875
56.25 + 4.921875 = 61.171875
Answer: $61.17
The shopper paid $61.17
Step-by-step explanation:
the motorcyclist starts x hours after the bus.
it take... |
Factorisation
2.2 Factorisation
Definition
β’ A process of determining the factors of an algebraic expression or algebraic terms and when multiplied together will form the original expressions.
β’ Also known as the reverse process of expansion.
Terms that related to the Product of Algebraic Expressions
... | 4 | 2.2 Factorisation
Definition
β’ A process of determining the factors of an algebraic expression or algebraic terms and when multiplied together will form the original expressions.
β’ Also known as the reverse process of expansion.
Terms that related to the Product of Algebraic Expressions
Factor
(i)
... |
How do you determine whether the function f(x) = abs(x-3) satisfies the hypotheses of the mean value theorem on the indicated interval (a,b), and if so how do you find all numbers c on [0,4] ? | Socratic
How do you determine whether the function #f(x) = abs(x-3)# satisfies the hypotheses of the mean value theorem on th... | 4 | The Mean Value Theorem has two hypotheses:
H1 : $f$ is continuous on the closed interval $\left[a , b\right]$
H2 : $f$ is differentiable on the open interval $\left(a , b\right)$.
In this question, $f \left(x\right) = \left\mid x - 3 \right\mid$ , $a = 0$ and $b = 4$.
We can apply the Mean Value Theorem if both hyp... |
How do you solve 10t^2 - 29t = -10? | Socratic
How do you solve #10t^2 - 29t = -10#?
2 Answers
$t = \frac{2}{5} \mathmr{and} \frac{5}{2}$
Explanation:
$10 {t}^{2} - 29 t + 10 = 0$
you can solve it by 2 methods, the quadratic formula or splitting the middle term.
I am doing it by the latter one.
the product of root... | 4 | How do you solve #10t^2 - 29t = -10#?
$t = \frac{2}{5} \mathmr{and} \frac{5}{2}$
Explanation:
$10 {t}^{2} - 29 t + 10 = 0$
you can solve it by 2 methods, the quadratic formula or splitting the middle term.
I am doing it by the latter one.
the product of roots is 100 and the sum is -29
the suitable pair will be -25 ... |
Solution:
Given: The base diameter of the cone is 40 cm and its height is 1m.
Since the outer side of each cone is to be painted, the area to be painted will be equal to the curved surface area of the cone.
The curved surface area of a right circular cone with base radius(r) and slant height(l) is Οrl
Slant height... | 4 | Solution:
Given: The base diameter of the cone is 40 cm and its height is 1m.
Since the outer side of each cone is to be painted, the area to be painted will be equal to the curved surface area of the cone.
The curved surface area of a right circular cone with base radius(r) and slant height(l) is Οrl
Slant height,... |
Simplifying Numerical Expressions Involving Square Roots
Question Video: Simplifying Numerical Expressions Involving Square Roots Mathematics
Express (5/2)β252 in the form πβπ where π and π are both integers and π takes the least possible value.
Video Transcript
Express five halves square root 252 in the form οΏ½... | 4 | Express (5/2)β252 in the form πβπ where π and π are both integers and π takes the least possible value.
So here, we have our expression. And we want to change it where π, which is gonna be in the five-halves spot, and π, which is on the inside of the square root, are both integers. Integers of the nice numbers.... |
ocumentation
A simple population model is fitted to abundance data to estimate the net reproductive rate for specified periods of time. The model is Nt=N0*R^t where Nt is the abundance at time t, N0 is the
estimated initial population size and R is the net reproductive rate. R can be used as an indication that the popu... | 4 | A simple population model is fitted to abundance data to estimate the net reproductive rate for specified periods of time. The model is Nt=N0*R^t where Nt is the abundance at time t, N0 is the estimated initial population size and R is the net reproductive rate. R can be used as an indication that the population is sta... |
End of preview. Expand in Data Studio
No dataset card yet
- Downloads last month
- 45