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choli [55]
3 years ago
11

5.

Mathematics
1 answer:
Gennadij [26K]3 years ago
6 0
The common ratio is 5 because each number is being multiplied/divided by 5
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Evaluate the spherical coordinate integral
expeople1 [14]

Rewrite the equations of the given boundary lines:

<em>y</em> = -<em>x</em> + 1  ==>  <em>x</em> + <em>y</em> = 1

<em>y</em> = -<em>x</em> + 4  ==>  <em>x</em> + <em>y</em> = 4

<em>y</em> = 2<em>x</em> + 2  ==>  -2<em>x</em> + <em>y</em> = 2

<em>y</em> = 2<em>x</em> + 5  ==>  -2<em>x</em> + <em>y</em> = 5

This tells us the parallelogram in the <em>x</em>-<em>y</em> plane corresponds to the rectangle in the <em>u</em>-<em>v</em> plane with 1 ≤ <em>u</em> ≤ 4 and 2 ≤ <em>v</em> ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3

Rewrite the integrand:

-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3

The integral is then

\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}

5 0
3 years ago
What is the pattern of 1.1, 2.2, 3.3, 4.4
Tanya [424]
It is adding one little percentage of increase here. or, 1.1 each time....hope that this helps.
5 0
3 years ago
Read 2 more answers
The graphs below show four functions: Graph A shows function f of x equals 4 multiplied by 3 to the power of x. Graph B shows fu
s2008m [1.1K]

Answer:

Graph B shows function f of x equals 4 multiplied by 3 to the power of negative x.

Step-by-step explanation:

f(x) = 4(3)^{-x} is the value 4 times three raised to the negative x. Graph B is the best representation.

5 0
3 years ago
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What is the distance between the points (38, 30) and (14, 20)
Brums [2.3K]
Here's a formula to slove ur problem
√(x₁-x₂) +(y₁-y₂)
=√(38-14) +(30-20)
=√24+10
=√34
6 0
3 years ago
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A population has a known standard deviation of 1.27 and a sample space contains 85 values find the margin of error needed to cre
r-ruslan [8.4K]

Answer:

The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.99}{2} = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

In this question:

\sigma = 1.27, n = 85

So

M = z*\frac{\sigma}{\sqrt{n}}

M = 2.575*\frac{1.27}{\sqrt{85}}

M = 0.3547

The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547

7 0
3 years ago
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