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AURORKA [14]
3 years ago
11

Find the slope of the line y = -7/6x - 8/3.

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
8 0

Hello!

This equation is written in slope-intercept form.

Slope-intercept form is y = mx + b, where m is the slope and y is the y-intercept.

Since the coefficient -7/6 is multiplied with x, the slope (or m) has to equal to -7/6.

Therefore, the slope of the line is -7/6.

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V = 864\pi

Step-by-step explanation:

Since one of the boundaries is y = 0, we need to find the roots of the function f(x)=-2x^2+6x+36. Using the quadratic equation, we get

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But since the region is also bounded by x = 0, that means that our limits of integration are from x=0 (instead of -3) to x=6.

Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by

\displaystyle V = \int f(x)2\pi xdx

\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx

\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx

\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6

\:\:\:\:\:\:\:= 864\pi

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Solve for e.<br><br><br>9e − 7 = 7e − 11
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Answer:

e = -2

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3 years ago
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