Find the center of mass of the thin rod with the given density function.Find the center of mass of a thin rod that lies along the first-quadrant portion of the circle 
if the density of the rod is 
A. 
= 
, 
= 
B. 
= 1, 
= 1
C. 
= 
, 
= 
D. 
= 
, 
= 
Answer: B
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Solve the problem.If f(x, y) = (4000ey)/(1 + 
/2) represents the population density of a planar region on Earth, where x and y are measured in miles, find the number of people within the rectangle -9 ? x ? 9 and -2 ? y ? 0.
A. 8000(1 - e-2) ln 5 ? 16,587
B. 4000(1 - e-2) ln 
? 5896
C. 8000(1 - e-2) ln 
? 11,792
D. 16,000(1 - e-2) ln 
? 23,585
Evaluate the improper integral or state that it is divergent.
A. 
B. 0
C. - 
D. Divergent
Solve the problem.Carry's carryout doesn't deliver. Instead she gives her customers who live more than 5 miles away coupons for $1.50 off their next pizza order, and she allows customers to use up to 3 coupons at one time. If Raul orders two 16-inch pizzas at $10.99 each and uses 3 coupons, what is the price per square inch of each pizza? (Use 3.14 for ?. The size of a pizza is its diameter.)
A. $0.05 per square inch for both pizzas B. $0.04 per square inch for both pizzas C. $0.11 per square inch for both pizzas D. $0.04 per square inch for one pizza, $0.11 per square inch for the other pizza
Provide an appropriate response.Sketch a graph of f(x) = 
+ 3
What will be an ideal response?