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Marysya12 [62]
3 years ago
5

Lines C and d are perpendicular. If the slope of line c is -4, what is the slope of line d?

Mathematics
1 answer:
CaHeK987 [17]3 years ago
6 0
The slope of line D is also -4 because the lines are perpendicular.
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Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by the plane z = x and below by
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\displaystyle\iiint_R\mathrm dV=\int_{y=-7}^{y=7}\int_{x=-\sqrt{49-y^2}}^{x=0}\int_{z=x}^{z=0}\mathrm dz\,\mathrm dx\,\mathrm dy

Converting to cylindrical coordinates, the integral is equivalent to

\displaystyle\iiint_R\mathrm dV=\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}\int_{z=r\cos\theta}^{z=0}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta
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=-\displaystyle\left(\int_{\theta=\pi/2}^{3\pi/2}\cos\theta\,\mathrm d\theta\right)\left(\int_{r=0}^{r=7}r^2\,\mathrm dr\right)
=\dfrac{2\times7^3}3=\dfrac{686}3
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3 years ago
What type of System if the two linear equations have only one solution?
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a line is perpendicular to y - 5 = -1/4(x + 8) and goes through the point (-1,2). What is the lines y-intercept?
lisabon 2012 [21]

Answer:

y = 4x + 6

Step-by-step explanation:

Turn the equation we are given into slope-intercept form.

y - 5 = -1/4(x + 8)

y - 5 = -1/4x - 2

y = -1/4x + 3

The slope of a perpendicular line is the opposite reciprocal of the original line.

-1/4 -> 4/1 -> 4

Find the new y-intercept using the point given.

y = 4x + b

2 = 4(-1) + b

2 = -4 + b

6 = b

Fill in everything we solved for.

y = 4x + 6

Best of Luck!

8 0
3 years ago
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