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3 years ago

How is an inverse variation similar to a linear relationship?

1 answer:

6 0

As the value of X increases, the value of y would decrease, due to this relationship being an inverse variation. ... An inverse variation would be similar to a linear relationship because in both, values can increase, as others decrease, and it would pretty much be it, because there aren't much similarities between them.

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What are the solutions to the equations x^2 + 3 = 124?

babunello [35]

X^2=121
x=11 or x=-11

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3 years ago

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stich3 [128]

Answer:

Step-by-step explanation

q bert

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3 years ago

Which set of ordered pairs does not represent a function? A. (7, 8), (-4, 4), (3, 8), (-7, -1) B.(-5, -3), (-1, -8), (-7, 0), (-

Mariana [72]

Answer:

Step-by-step explanation: 5

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4 years ago

Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2

exis [7]

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}$

with determinant $|J| = 12$ , hence the area element becomes

$dA = dx\,dy = 12 \, du\,dv$

Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

$\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1$

so that

$\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv$

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$

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2 years ago

The original cost of a lamp is $18.95 . The lamp is on sale for 75% off . How much will you pay ?

gregori [183]

18.95x0.75=14.2125

18.95-14.2125=4.73

You will pay $4.73

7 0

3 years ago

Read 2 more answers