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Fudgin [204]
3 years ago
5

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the

specified axis. y = x3, y = 8, x = 0; about x = 9 V =
Mathematics
1 answer:
ipn [44]3 years ago
8 0

For each x in the interval 0\le x\le2, the corresponding shell has radius x+9 (horizontal distance from x to the rotation axis) and height 8-x^3 (vertical distance between y=8 and y=x^3). A shell of radius r and height h has area 2\pi rh, so the volume is

\displaystyle2\pi\int_0^2(x+9)(8-x^3)\,\mathrm dx=2\pi\int_0^272+8x-9x^3-x^4\,\mathrm dx=\boxed{\frac{1176\pi}5}

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Is centroid and Circumcentre same?
makvit [3.9K]

No, the centroid and Circumcentre are not same but it is same in equilateral triangle.

The intersection of a triangle's perpendicular bisectors is called the circumcenter.A triangle's circumcenter is a location that is equally spaced from each of its vertices.The centroid of a triangle is the location where its medians connect.

Triangle's centroid is always within it. The centroid of a triangle is its center of gravity in physical terms. If the triangle is evenly distributed around the plane's surface and you want to balance it by supporting it at only one point, you must do it near the center of gravity.Are the circumcenter and centroid at the same location? In the case of an equilateral triangle, they will both be.

Therefore, the centroid and Circumcentre are not same but it is same in equilateral triangle.

To learn more about circumcenter click here:

brainly.com/question/16276899

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7 0
1 year ago
A line intersects the points(-22,-14) and (-18,-12). What is the slope-intercept equation for this line?
zaharov [31]

Hello there,

Well we are going to start off with the equation to find the slope based on the given points:

                                                    \frac{y_{2} - y_{1}  }{x_{2} -x_{1} }

Now using the two given points we are going to plug in and solve:

                                         \frac{(-12)-(-14)}{(-18)-(-22)} = \frac{2}{4} = \frac{1}{2}

From this you know that \frac{1}{2} is the slope of the equation. However, to find the y-intercept we are going to use y = mx+ b and plug in one of the points to solve:

                                        (-14) = \frac{1}{2} (-22) + b

                                        (-14) = (-11) + b

                                         -3 = b

That means that the y-intercept is at (0, -3). Lastly, we are just going to plug all this into the slope-intercept form:

                                       y = \frac{1}{2} - 3

Hope I helped,

Amna

6 0
3 years ago
I need to know the answer to p=4x-140
dalvyx [7]
This is not look like something that could be answered, check around the paper for a graphing box.
This looks like a formula for a line on a graph: y=Mx+b. I can help you if this is the case, 1. Put a point at -140 on the Y axis (up and down) 2. Move up 1 and over 4and put a dot there( you could multiply the 1 and 4 to cover a larger area) because it goes all the way to -140.
7 0
3 years ago
PLEASE HELP ME HURRY
Ymorist [56]

Answer:

6/5

Step-by-step explanation:

8 0
3 years ago
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY
matrenka [14]

Answer:

x=7

Step-by-step explanation:

by pythagoras, 25^2=24^2+x^2

solve for x

6 0
2 years ago
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