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wolverine [178]
3 years ago
11

The volume of a sphere is given by V = (4/3)πr3 , where r is the radius. what is the formula in terms of r

Mathematics
1 answer:
guajiro [1.7K]3 years ago
7 0
 the answer is r = ∛(3V/4Π)
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Becky needs to make cookies for a school bake sale. The cookies need to be distributed evenly on 2 or more plates. If each plate
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We can take 2 plates , 3 plates or 6 plates.

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Lana71 [14]
<span>The sub-boxes will have dimensions \frac{2-0}{2} \times \frac{2-0}{2} \times \frac{2-0}{2} =1\times1\times1=1 \ cubic \ units

x sub-intervals are 0 to 1 and 1 to 2. Midpoints are at x= \frac{1}{2} and </span><span>x= \frac{3}{4}
y sub-intervals are 0 to 1 and 1 to 2. Midpoints are at </span><span>y= \frac{1}{2} and </span><span>y= \frac{3}{4}
z sub-intervals are 0 to 1 and 1 to 2. Midpoints are at </span><span>z= \frac{1}{2} and </span><span><span>z= \frac{3}{4}</span>

Let f(x,y,z)=\cos{(xyz)}

\int\limits  \int\limits  \int\limits {f(x,y,z)} \, dV \approx f\left( \frac{1}{2} , \frac{1}{2} , \frac{1}{2} \right)+f\left( \frac{1}{2} , \frac{1}{2} , \frac{3}{4} \right)+f\left( \frac{1}{2} , \frac{3}{4} , \frac{1}{2} \right)+f\left( \frac{1}{2} , \frac{3}{4} , \frac{3}{4} \right)
+f\left( \frac{3}{4} , \frac{1}{2} , \frac{1}{2} \right)+f\left( \frac{3}{4} , \frac{1}{2} , \frac{3}{4} \right)+f\left( \frac{3}{4} , \frac{3}{4} , \frac{1}{2} \right)+f\left( \frac{3}{4} , \frac{3}{4} , \frac{3}{4} \right) \\  \\ \approx\cos{ \frac{1}{8} }+\cos{ \frac{3}{16} }+\cos{ \frac{3}{16} }+\cos{ \frac{9}{32} }+\cos{ \frac{3}{16} }+\cos{ \frac{9}{32} }+\cos{ \frac{9}{32} }+\cos{ \frac{27}{64} } \\  \\ \approx0.9922+0.9825+0.9825+0.9607+0.9825+0.9607+0.9607 \\ +0.9123 \\  \\ \approx\bold{7.734}</span>
5 0
3 years ago
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