PLEASE HELP!!! What are the cross products of the problem of the proportion 12/20=3/5

Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by

Whitepunk [10]

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

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

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

The Jacobian for this transformation is

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

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

Then the integral in polar coordinates is

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

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

5 0

3 years ago

(a) Which department accounts for approximately one-fifth of the annual budget? Select One (b) Approximately what percentage of

Goshia [24]

a. The department that accounts for approximately one-fifth of the annual budget, based on the pie chart, is the <u>Research Department</u>.

b. The percentage of the annual budget used by the Marketing and Sales departments combined is 30%.

c. If 18% of the annual budget is used for Research, approximately the percentage used for Marketing is 9%.

<h3>What is a pie chart?</h3>

A pie chart is a graphical representation of data in a circle. In this pie chart, the area or percentage of the whole circle is 100%

Thus, we can obtain the values of the different groups represented in the pie chart by systematically dividing the circle accordingly.

The rule to follow is that vertical angles are always congruent (equal) as they have two lines that intersect to form opposite angles.

<h3>Data and Calculations:</h3>

Research, Sales, and Marketing = 50% of the budget (half of the pie chart)

Research = 18%

Sales and Marketing = 32% (50% - 18%)

Research equals Media and Support and Media and Support are equal.

Therefore, Media is 9% (18%/2) and Support is also 9%.

Since opposite angles are always equal, Engineering (opposite to Sales and Marketing combined) is 32%.

This results in a total of 100% (18% + 32% + 9% + 9% +32%)

<h3>Question Completion:</h3>

The pie chart attached shows how the annual budget for Equipment Producers Incorporated is divided by department. Use this chart to answer the questions below.

c) If 18% of the annual budget is used for Research, approximately what percentage is used for Marketing?

Thus, the department that accounts for approximately one-fifth of the annual budget, based on the pie chart, is the <u>Research Department</u>.

Learn more about the pie chart at brainly.com/question/23969670

#SPJ1

5 0

2 years ago

Keith sold half of his comic books and then bought nine

Nadusha1986 [10]

Answer:

22 comic books.

Step-by-step explanation:

(20 - 9) * 2 First subtract 9 from 20

11 * 2 Multiply 11 by 2

22 is the product

3 0

3 years ago

SECOND TIMES THE CHARM.. please help

Art [367]

Answer:

y = 5x.

Step-by-step explanation:

Every y value is the corresponding x value times 5. (For example, 3 x 5 = 15, 5 x 5 =25)

<em>Hope this helps!</em>

3 0

3 years ago

Ashley deposits $1000 into an account that earns 4% interest compounded 2 times per year. How much money will Ashley have in her

vlabodo [156]

That would be C. $1218.99 :)

5 0

4 years ago

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