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A bowl is shaped like a hemisphere with diameter 24 cm. A ball with diameter 8 cm is placed in the bowl and water is poured into the bowl to a depth of h centimeters. Find the volume V of water in the bowl. Consider two cases: one in which the ball is not completely submerged and the other in which it is.
Find the dimensions of a rectangle with area 125000 m2 whose perimeter is as small as possible. (Give your answers in increasing order, to the nearest meter.)
A plane travels 170 miles on a bearing of N 18 degrees E and then changes its course to N 49 degrees E and travels 120 mi . find the total distance traveled north and the east.
What is the least amount of wrapping paper that is needed to wrap a gift box that is 2 feet by 1 foot by 3 feet?
Suppose the objective function is changed to max 5A + 2B. Find the optimal soultion and the value of the objective function.
If 1400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
There is a line through the origin that divides the region bounded by the parabola y = 3 x - 8 x^2 and the x-axis into two regions with equal area. What is the slope of that line?
A 180 lb man carries a 20 lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 160 ft high and the man makes exactly four complete revolutions, how much work is done by the man against gravity in climbing ..
Jim Smith believes in 30 years he will need $80,000 to buy a retirement cottage. Assuming he gets an interest rate of 9% compounded annually, how much will he have to invest today to reach his retirement goal?
a boat's crew rowed 7.5 miles downstream, with the current, 1.5 hours. the return trip upstream , against the current , covered the same distance, but took 2.5 hours. find the crew's rowing rate in still water and the rate of the current.
Explain what the index of a subgroup and a coset of a group are. Also, prove that if N is a subgroup of a group G such that [G: N] = 2, and if "a" and "b" are elements of G,
The monthly incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation of $150. find the probability that a randomly selected employee earns less than $900 a month.
A landscaper wants to combine golden landscape rock with rust-colored landscape rock to make a mix. The golden rock costs $0.59 per pound and the rust-colored rock cost $0.49 per pound.
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