Solve the problem.A rectangular sheet of perimeter 39 cm and dimensions x cm by y cm is to be rolled into a cylinder as shown in part (a) of the figure. What values of x and y give the largest volume?
A. x = 15 cm; y = 
cm
B. x = 13 cm; y = 
cm
C. x = 12 cm; y = 
cm
D. x = 14 cm; y = 
cm
Answer: B
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Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.y = 4x2 - x3, y = 0
A. 
?
B. 
?
C. 
?
D. 1024?
Solve the problem.The world population of a certain species is evaluated at 2.3 × 106. By some projections, this population will be 6 times more important in 30 years. Express the population at that time in scientific notation.
A. 138 × 106 B. 13.8 × 107 C. 1.38 × 109 D. 1.38 × 107
Solve the problem.The annual population density of a species of insect after n years is modeled by a sequence. Suppose that the initial density of insects is 634 with r = 0.6. Write a recursive sequence that describes this data, where an denotes the insect density during year n.Find the terms a1 , a2 , a3 , ...., a5 . Round to two decimal places, if necessary.
A. a1 = 634, a2 = 1014.40, a3 = 1623.04, a4 = 2596.86, a5 = 4154.98 B. a1 = 634, a2 = 634, a3 = 634, a4 = 634, a5 = 634 C. a1 = 380.40, a2 = 228.24, a3 = 136.94, a4 = 82.17, a5 = 49.30 D. a1 = 634 , a2 = 380.40, a3 = 228.24, a4 = 136.94, a5 = 82.17
Given A(a, b), B(a + m, b + n), and C(a - n, b + m). Prove that AB ? AC.
What will be an ideal response?