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3 years ago

Solve the following system of equations.

2 answers:

3 0

+8y and -8y cross out.

So the first one is 3x=15
Second one is 2x=10

x=5
Then plug x is one of the equations

2(5)-8y=10
10-8y=10

x=5
y=0

Advocard [28]3 years ago

3 0

Y=15/8 X=0.07. so that's ur answer

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What is y=7/4x+6 if the input was 53

Shkiper50 [21]

7/4(53) + 6
92.75 + 6

98.75

5 0

3 years ago

Sketch the domain D bounded by y = x^2, y = (1/2)x^2, and y=6x. Use a change of variables with the map x = uv, y = u^2 (for u ?

cluponka [151]

Under the given transformation, the Jacobian and its determinant are

$\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2$

so that

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv$

where $D'$ is the region $D$ transformed into the $u$ - $v$ plane. The remaining integral is the twice the area of $D'$ .

Now, the integral over $D$ is

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y$

but through the given transformation, the boundary of $D'$ is the set of equations,

$\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}$

We require that $u>0$ , and the last equation tells us that we would also need $v>0$ . This means $1\le v\le\sqrt2$ and $0$ , so that the integral over $D'$ is

$\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6$

4 0

3 years ago

Plz tell me the aswer and how you worked it out. A tree grows to a height of 13.75m over 5 1/2 years. What is the average annual

marin [14]

1. Take your 13.75 and 5 1/2 and put it into a dividing table
_______
5.5 I13.75

you need to get your decimal out of deviser (5.5) will now be (55) because you moved the decimal over there you also need to move the decimal that is on the inside to and it will be (137.5)

2. When you divide you would get 2.5

3. Now you would know how much the tree grew over the 5 1/2 years.

ANSWER: 2.5m a year!

Hope this helped!

:)

4 0

3 years ago

Find the slope of the line that passes through the points (-1, -2) and (-9, -2)

kodGreya [7K]

Slope = change in Y / change in x

Slope = (-2 - -2) / (-9 - -1)

Simplify:

Slope = 0/-8 = 0

Slope = 0

4 0

3 years ago

3 times the measure of an angle is 14 less than the measure of its complement. What is the measure of the angle?

Sedbober [7]

Let the measure of the angle be x and from that the measure of its complement is 90 - x. The equation that best represent the given condition above is,
3x = (90 - x) - 14
The value of x from the equation above is 19. Thus, the answer is letter A.

7 0

3 years ago