Answer:
9.03
Step-by-step explanation:
Just divide 63.21 by 7
Answer:
A. 1,485 cubic cm. B. 27
Step-by-step explanation:
The new prism is dilated by a factor of 3, that means it's made bigger, 3 times bigger on each side.
The dimensions of the new prism are then 12 cm by 7.5 cm by 16.5 cm.
Its volume is then of 12 x 7.5 x 16.5 = 1,485 cubic cm
To answer the second question...
Let's calculate the volume of the original prism:
The original prism's volume was 4 x 2.5 x 5.5 = 55 cubic cm
The new volume is then 1485 / 55 = 27 times bigger than the original.
Which is normal, since we increased each side (dimension) by a factor of 3, so 3x3x3 = 27.
Answer:
r = 11
Step-by-step explanation:
C = 2πr
69.08 = 2(3.14)r
69.08 = 6.28r
r = 69.08/6.28
r = 11
A decimal would be 400.0 because it is exactly 400. a fraction could be a lot but an easy one would be 400 over 1 which, if you simplify would be 400. with no remainders.
First solve x³=9x
We can ignore x = -3 because it is not in the first quadrant.
<span>So our integral is going to go from x=0 to x=3.
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<span>Now we can use the formula
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![\int\limits_{0}^{3}(\pi (9x)^2-\pi(x^3)^2)dx \\\int\limits_{0}^{3}(\pi (9x)^2-\pi(x^3)^2)dx \\\pi\int\limits_{0}^{3}(81x^2-x^6)dx \\2\times \int\limits_{0}^{3}[\pi(9x)^2-\pi(x^3)^2]dx \\\pi\left[81\frac{x^3}{3}-\frac{x^7}{7}\right]_{0}^{3} \\ \\\frac{2916\pi}{7}](https://tex.z-dn.net/?f=%5Cint%5Climits_%7B0%7D%5E%7B3%7D%28%5Cpi%20%289x%29%5E2-%5Cpi%28x%5E3%29%5E2%29dx%0A%5C%5C%5Cint%5Climits_%7B0%7D%5E%7B3%7D%28%5Cpi%20%289x%29%5E2-%5Cpi%28x%5E3%29%5E2%29dx%0A%5C%5C%5Cpi%5Cint%5Climits_%7B0%7D%5E%7B3%7D%2881x%5E2-x%5E6%29dx%0A%5C%5C2%5Ctimes%20%5Cint%5Climits_%7B0%7D%5E%7B3%7D%5B%5Cpi%289x%29%5E2-%5Cpi%28x%5E3%29%5E2%5Ddx%0A%5C%5C%5Cpi%5Cleft%5B81%5Cfrac%7Bx%5E3%7D%7B3%7D-%5Cfrac%7Bx%5E7%7D%7B7%7D%5Cright%5D_%7B0%7D%5E%7B3%7D%20%5C%5C%20%5C%5C%5Cfrac%7B2916%5Cpi%7D%7B7%7D)
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