Knowing that the surface area of a sphere is given by 
, complete the proof of thevolume formula for the sphere. Having separated the sphere into n pyramids ( each with the center of the sphere for its vertex), show that the volume of the sphere is 
.
What will be an ideal response?
Where the areas of the bases are 
, 
, 
, and so on through 
, the corresponding altitudes all have a length approximated by h. The the volume of the sphere is appproximated by 
. In turn, 
.
As n increases, the length h of the altitudes of the pyramids approaches r, the length of the radius of the sphere; that is, 
. As n increases, the combined base areas of the pyramids also approaches the surface area S of the sphere; that is, 
.
As n increases, we find that 
or 
, so that 
.
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Use Cramer's rule to solve the system.
x - 
y = 8
x + 
y = -12
A. 
B. 
C. 
D. ?
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.3(7 + m)
A. 21m B. 21 + m C. 21 + 7m D. 21 + 3m
Solve the application and answer with a complete sentence. Round to the nearest tenth of a percent if necessary.The price of a shirt was reduced from $92.20 to $62.23. What was the percent change in price of the shirt?
A. There was a 3.25% increase in price. B. There was a 33.5% decrease in price. C. There was a 32.5% decrease in price. D. There was a 34.5% decrease in price.
Find the length of the side of the square. If the area is not a perfect square, approximate by using a square root table or a calculator. Round to the nearest thousandth.A square with area 193 m2
A. 13.897 m B. 13.892 m C. 193.000 m D. 13.889 m