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A trough is 2 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x^10 from x=-1 to x=1 . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.
Use polar coordinates to evaluate the volume of the solid below the paraboloid (z= 4-x^2-y^2) and above the xy plane.
There are about 5.859x10¹² miles in 1 light-year. Estimate how many miles this star travels in one year.
To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled.
Use polar coordinates to find lim(x,y)->(0,0) [(x)(y^2)]/[(x^2)+(y^2)] note that (x,y)->(0,0) is replaced with r->0^+. explain why this is a valid replacement.
A factory produces fuses, which are packaged in boxes of 18. Six fuses are selected at random from each box for inspection. The box is rejected if at least one of these six fuses is defective. What is the probability that a box containing nine def..
Let G be a simple graph with no isolated vertex and no induced subgraph with exactly two edges. Prove that G is a complete graph. (Please read carefully the definition of an induced subgraph before you attempt to solve it!).
Let G be a group and H be a non-empty subset of G. We define H^2 as the set of elements of G which can be written in the form h_1 h_2, with h_1 ,h_2∈H.
What is the probability that two cards drawn from a deck are both aces?. Two cards are drawn at random from an ordinary deck of playing cards. The first is not replaced before the second is drawn. What is the probability that:
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 10-x^2. What are the dimensions of such a rectangle with the greatest possible area?
Your coin collection contains 53 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2063, assuming they appreciate at a 4.4 percent annual rat..
A legislative committee consists of 8 Democrats, 6 Republicans, and 1 Independent. A delegation of 3 is selected to visit a small Pacific island republic-
Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms. How many of the bulbs should she plant next fall if she would like at least 52 to bloom?
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