Find the perimeter of the figure.
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Answer 1

Answer:

Answer:

Perimeter is 56

Step-by-step explanation:

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Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 64x2 + 81y2 = 1. $ L=\iint_{R} {\color{red}9} \sin ({\color{red}384} x^{2} + {\color{red}486} y^{2})\,dA $.

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$\displaystyle\iint_R\sin(384x^2+486y^2)\,\mathrm dA$

Notice that Given that $R$ is an ellipse, consider a conversion to polar coordinates:

$\begin{cases}x(r,\theta)=\frac r8\cos\theta\ny(r,\theta)=\frac r9\sin\theta\end{cases}$

The Jacobian for this transformation is

$J=\begin{bmatrix}\frac18\cos\theta&-\frac r8\sin\theta\n\frac19\sin\theta&\frac r9\cos t\end{bmatrix}$

with determinant $\det J=\frac r{72}$

Then the integral in polar coordinates is

$\displaystyle\frac1{72}\int_0^(\pi/2)\int_0^1\sin(6r^2\cos^2t+6r^2\sin^2t)r\,\mathrm dr\,\mathrm d\theta=\int_0^(\pi/2)\int_0^1r\sin(6r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{(\pi\sin^23)/(864)}$

where you can evaluate the remaining integral by substituting $s=6r^2$ and $\mathrm ds=12r\,\mathrm dr$ .

Final answer:

To evaluate the integral, we make a change of variables using the transformation x=u/8 and y=v/9 to transform the region into a unit circle. Then we convert the integral to polar coordinates and evaluate it.

Explanation:

To evaluate the given integral, we can make the appropriate change of variables by using the transformation x = u/8 and y = v/9. This will transform the region R into a unit circle. The determinant of the Jacobian of the transformation is 1/72, which we will use to change the differential area element from dA to du dv. Substituting the new variables and limits of integration, the integral becomes:

L = \iint_{R} 9 \sin (612 u^{2} + 768 v^{2}) \cdot (1/72) \,du \,dv

Next, we can convert the integral from Cartesian coordinates(u, v) to polar coordinates (r, \theta). The integral can be rewritten as:

L = \int_{0}^{2\pi} \int_{0}^{1} 9 \sin (612 r^{2} \cos^{2}(\theta) + 768 r^{2} \sin^{2}(\theta)) \cdot (1/72) \cdot r \,dr \,d\theta

We can then evaluate this integral to find the value of L.

Learn more about Evaluation of Integrals here:

brainly.com/question/32205191

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A 224 cm rope is cut so that one part is 3/4 of the other. How long is the shorter rope? The longer rope?

Answers

Given that:

Length of a rope = 224 cm

Rope is cut so that one part is 3/4 of the other.

Solution:

Let one part of a rope be x cm.

So other part of the rope is $(3)/(4)x$ .

Total length $=x+(3)/(4)x$

Now,

$x+(3)/(4)x=224$

$(4x+3x)/(4)=224$

Multiply both sides by 4.

$7x=896$

Divide both sides by 7.

$x=(896)/(7)$

$x=128$

The value of one part 128 cm.

Second part $=(3)/(4)x$

$=(3)/(4)* 128$

$=3* 32$

$=96$

Therefore, the length of shorter rope is 96 cm and the length of longer rope is 128 cm.

Helpppp asap pleasee

Answers

Answer:

I think 1 is the right answer

Step-by-step explanation:

You need to lay communications cable around the perimeter of three offices, each 8' by 10'. How much cable do you need?

Answers

Answer:

108 units

Step-by-step explanation:

We are given that

Length of each office,l=10 units

Breadth of each office=b=8 units

Total number of office=3

We know that

Perimeter of rectangle= $2(l+b)$

Using the formula

Length of cable for 1 office= $2(10+8)=36units$

Length of cable required for 3 offices= $36* 3=108$ units

Hence, the required length of cable=108 units

PLEASE HELP

How do I solve 7,9, and 10 also what are the answers?

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7.
360 degrees- the other angles = x

Please help me i will mark brainliest

Answers

Answer:

see below

Step-by-step explanation:

The cube of something to the 1/3 power is the original something. The cube of a cube root of something is the original something. Since the cube of a cube root is the same as the cube of a 1/3 power, the 1/3 power is equivalent to the cube root.

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

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