An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear.10x3/2(x3 + x2) - 12x5/2 - 12x3/2
A. 10x3/2(x3 - 1) + 10x3 - 2x3/2(x - 1)
B. x3/2(x - 1)[10(x2 - 1) - 2] + 10x3
C. 10x3/2(x + 1)(5x2 - 6)
D. 2x3/2(x + 1)(5x2 - 6)
Answer: D
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Find the average value of 
over the given region.
over the cube in the first octant bounded by the coordinate planes and the planes 
, 
, 
A. 
B. 
C. 243
D. 
For a certain island chain, the area A, in square miles, can be estimated by counting the number of reptile and amphibian species on the island. The following table shows the relationship.
2030405060
52519215155945619562?
A. Calculate the average rate of change in area from 30 to 40 species.B. Explain in practical terms the meaning of the number you calculated in part A.C. Use your answer from part A to estimate the area of an island in the chain which has 32 species of reptiles and amphibians.
What will be an ideal response?
Write as logarithmic equations.52 = 25
A. log2 25 = 5 B. log5 2 = 25 C. log25 5 = 2 D. log5 25 = 2
Express as a difference of logarithms.log8
A. log8 10 - log8 13 B. log8 13 ÷ log8 10 C. log8 13 - log8 10 D. log4 13 - log4 10