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dezoksy [38]
2 years ago
13

Find the volume of each sphere. Be sure to include appropriate units. (Show your work)

Mathematics
1 answer:
babunello [35]2 years ago
6 0

Answer:

2145.5m^3

679.2yard

Step-by-step explanation:

v

volume \: of \: a \: sphere =  \frac{4}{3}\pi \: r {}^{3}  \\ when \: r = 8 \\ volume =  \frac{4}{3}  \times  \frac{22}{7}  \times 8 {}^{3}  \\ volume =  \frac{4}{3}  \times  \frac{22}{7} \times 8 \times 8 \times 8 \\ volume =  \frac{4 \times 22 \times 512}{3 \times 7}   \\ volume =  \frac{45056}{21}  \\ volume = 2145.5m {}^{3}  \\  \\ for \: the \: second \: shape \\ volume =  \frac{4}{3}  \times  \frac{22}{7}  \times 5.5 {}^{3}  \\  =  \frac{4}{3}  \times  \frac{22}{7}  \times 166.373 \\  =  \frac{14641}{21}  \\  = 697.2yard

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In properties of exponents, if the exponent is negative then you move the variable with the negative exponent to the denominators place and it changes to positive and the numerator becomes 1.

p^-4=1/(p^4)

Also, if no exponent is present it is understood to be 1.

Keeping this in mind,
p^-4 x -5p
1/(p^4) x -5p^1            substituted p^-4 by 1/p^4 and added ^1 to -5p
-5p^1/p^4                     multiplied-5p^1 to 1 
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Apply to Row 2 : Row 2 + Row 1

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<em>Note that the matrix is in echelon form now. The next steps are for back substitution.</em>

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Apply to Row 1: Row 1 - 3 Row 3

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Apply to Row 1: Row 1 - 2 Row 2

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Simplify the rows

<u>x = -2</u>

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