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The volume of a cone varies jointly as the height and the square of the radius of the base. A cone height 8 cm and a base of diameter 9 cm has volume 54π. Find the constant of variation and use it to develop the general formula for the volume of a cone.
A department store wants to test the claim that 40% of its customers browse the store's website prior to visiting the store using a random sample of 100 customers. If the desired level of significance is 0.05, what are the critical values for the ..
Determine the angle of the launch to obtain the maximum length of the trajectory. Let v0 = 96 feet per second
Suppose that 560 ft of fencing is used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle. (In the blue outline represents the fencing.) Find the dimensions of the corral with maximum area.
Let N be a positive integer. Let d be an integer relatively prime to phi(N) (phi denotes the euler totient function). Prove that there exists a d' in Z (=integers) with dd'=1 mod phi(N).
A farmer plans to use 21 m of fencing to enclose a rectangular pen having an area of 55 m². Only three sides of the pen need fencing because of an existing wall. Find the dimensions of the pen.
A ceramic bowl is turned on a potter's wheel to approximate the surface obtained by revolving the curve y= (2/3)((x^2) - 1 ) from x=1 to x=2 about the y axis. What is the approximate outside area of the bowl? [assume that each unit on the x and y ..
Explain why the rules for the order of operations are necessary; give examples to back up your explanation.
A rotating light is located 19 feet from a wall. The light completes one rotation every 3 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wal..
total interest from investments was $3060. the interest from the first investment was 2 times the interest from the second. find the amounts of the three part investment.
The consultant who advised the city on this project predicted the parking revues would average $130 per day. Based on your confidence interval, do you think the consultant was correct? Why?
A rectangular swimming pool 60 ft long, 10 ft wide, and 12 ft deep is filled with water to a depth of 11 ft. Use an integral to find the work required to pump all the water out over the top. (Take as the density of water delta = 62.4 hbox{lb/ft}^3..
Let x and y be real numbers. Show that x 0 if and only if x 0 if and only if x=y.
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