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If the radius of a sphere is doubled, the surface area is
a. multiplied by 4.
b. multiplied by 2.
c. multiplied by 3.
d. multiplied by 8.
a. The formula for the surface area of a sphere is 4πr2. If the radius is doubled, this implies that the radius is also doubled. The formula then becomes 4π(2r)2. Solve this expression, 4π(4r2) equals 16πr2. Compare 4πr2 to 16πr2; 16πr2 is 4 times greater than 4πr2. Thus, the surface area is four times as great.
For queries Q 1 and Q 2 , we say Q 1 is contained in Q 2 , denoted Q 1 ⊆ Q 2 , iff Q 1 (D) ⊆ Q 2 (D) for every database D. The container problem for a fixed Query Q 0 i
1+8
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1) let R be the triangle with vertices (0,0), (pi, pi) and (pi, -pi). using the change of variables formula u = x-y and v = x+y , compute the double integral (cos(x-y)sin(x+y) dA a
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