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3 years ago

Twice a number subtracted from four times a number, added to 15.

1 answer:

galina1969 [7]3 years ago

3 0

For twice a number we can use the variable x
For four times a number we can use the variable c

4c - 2x + 15

I believe this is correct although I'm not 100% sure

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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

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

2 years ago

What is the area, in square units, of a triangle with vertices at (-1,-1), (3,-1), (2,2) PLEASE HELP

murzikaleks [220]

Step-by-step explanation:

A=½bh

A=½(4•3)

A=½(12)

A=6 units sq

5 0

2 years ago

Need help please anybody

shepuryov [24]

The answer is 75
Explanation: 180 - 75 - 60 = 75
I sure this is true

4 0

2 years ago

You just turned 18, and you can get your own credit card. But, because you are a young person with no credit history your intere

iren [92.7K]

The answer will be D.

3 0

3 years ago

Read 2 more answers

A woman has twice as many dimes as quarters in her purse. If the dimes were quarters and the quarters were dimes, she would have

Digiron [165]

If x = # of quarters, then, the # of dimes will be equal to 2x. The total value (z) would be equal to:

z = 0.25x + 0.10(2x)

Then, since you switch the quarters and the dimes, and you have a new total, the resulting equation will be:

1.2 + z = 0.25(2x) + 0.10(x)

Plug in the values you know:

1.2 + (0.25x + 0.10(2x)) = 0.25(2x) + 0.10(x)

Solve for x:

1.2 + (0.25x + 0.20x) = 0.50x + 0.10x
1.2 + 0.45x = 0.60x
1.2 = 0.15x
x = 1.2/0.15 = 8

This means that there are 8 Quarters in her bag right now. So, the amount of dimes is just 2x which is 16. So your answer will be:

She has 8 Quarters and 16 Dimes in her bag right now. Or, $3.60.

If this doesn't make sense, then tell me. I have some resources where I got the answer from to put it into simplest terms. I have the website if you want.

4 0

3 years ago

Read 2 more answers