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An aquarium is to be made in the shape of a rectangular solid with a square base and an open top. The volume of the aquarium is to be 108 cubic inches. What dimensions will minimize the amount of material needed to build it?
Show that f 5x2/(1 + x)1/3dx = 3(1 + x)2/3(5x2 - 6x + 9)/8 + C
Integral from zero to infinity of cos(x^2) dx = integral from zero to infinity of sin(x^2) dx = 1/2 * (square root of pi/2).
suppose you are an event coordinator for a large performance theater. one of the hottest new broadway musicals has
The graphical model shows the number of cars per hour that are entering or leaving a roundabout. If the portion of the roundabout between A and B has an estimated traffic flow of from 6[e] to 8[a]cars per hour, what is the estimated traffic flow b..
the length of a rectangular backyard is 13 feet longer than its width (x). what is the area of the bakyard interms of x?
Let (r,θ) be the polar coordinate, show that Δu=urr+1/r∗ur+1/r2∗uθθ. In particular, if u=f(r) is a harmonic function, show that u=c1logr+c2
a pool measuring 10 meters by 16 meters is surrounded by a path of uniform width. If the are of the pool and path combined is 272 square meters, what is the width of the path?
For this problem please state the method you used and show the work required to obtain the answer. Find the general solution for each of the systems:
Solve without graphing. Find the slope and the y-intercept for the graph of each equation in the given system. Use this information (and not the equations graph) to determine if the system has no solution or an infinite number of solutions.
The disc jockey randomly chooses the first song to play, and then she randomly chooses the second song from the remaining ones. What is the probability that both songs are country songs? Write your answer as a fraction in simplest form.
The university ACT average for entering fresh- men that year was about 21. Are the calculus students better than average, as measured by the ACT?
How fast is the radius changing at the instant when the radius is 4 inches? How fast is the surface area changing at the same instant?
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