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katen-ka-za [31]
3 years ago
13

Graph a line with a slope of -3 that contains the point (4, -2)

Mathematics
1 answer:
Crank3 years ago
5 0

Answer:

Step-by-step explanation:

Given that

Slope m=-3

A point (x, y)=(4,-2)

Equation of a line can generally be written as

y=mx+c

Where, m is the slope

And c is the intercept on y-axis

Since we are given m=-3

Then, y=mx+c becomes

y=-3x+c

To get c, let substitute the point given, i.e x=4 and y=-2

y=-3x+c

-2=-3(4)+c

-2=-12+c

-2+12=c

c=-2+12

c=10

y=mx+c, then m=-3 and c=10

Then, the equation the line becomes y = -3x + 10

This is the required line equation

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\displaystyle\int_a^b 2\pi\,x\,h(x)\,dx

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Then the integral becomes:

\displaystyle\int_0^1 2\pi\,x\,(8x-9-x^2)\,dx

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Now, solving the integral:

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=\displaystyle2\pi \int_0^19x-8x^2-x^3dx

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=\displaystyle2\pi \left[\frac{9x^2}{2}-\frac{8x^2}{3}-\frac{x^4}{4}\right|_0^1

Then evaluate the antiderivative in the limits and subtract:

=\displaystyle2\pi\left[\frac{9}{2}-\frac{8}{3}-\frac{1}{4}-0\right]=\frac{19\pi}{6}

So the volume of the solid is \displaystyle\frac{19\pi}{6}

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