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Near a boy, the depth of a lake at the point with coordinates (x, y) is z = 200 + 0.02x2 - 0.001y2, where x, y, and z are measured in meters. A fisherman in a small boat starts at the point (80, 60) and moves toward the buoy, which is located at (0, 0). Is the water under the boat getting deeper or shallower when he departs?
Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.)
chocolate bars produced by a certain machine are labeled with 8.0 oz. the distribution of the actual weights of these
two truck drivers leave a cafe at the same time, traveling in different directions. one truck goes 8 mph faster thaan the other one. after 4 hr they are 408 miles apart. how fast is each truck going?
$18,700 is invested, part at 13% and the rest at 8%. If the interest earned from the amount invested at 13% exceeds the interest earned from the amount invested at 8% by $690.94, how much is invested at each rate?
If the farmer can make a profit of $140 per acre on crop A, $200 per acre on crop B and $150 per acre on crop C how many acres of each crop should be palnted to mazimize profit?
A windshield wiper that is 2 feet long sweeps through an angle of 157°. What is the distance traveled by the tip of the wiper?
the perimeter of a four sided figure is 104 inches. the lengths of the four sides are four consecutive odd integers. what are the measurements of each side?
A rectangular package with a square base to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent.
The probability that a house in an urban area will be burglarized is 5%. If 50 houses are randomly selected, what is the probability that one of the houses will be burglarized?
Let X be a subset of R, let E be a subset of X, let x_0 be an adherent point of E, and let f: X-->R, g: X-->R, h: X-->R be functions such that f(x)
Let m and n be positive integers with n dividing m. Prove that the natural surjective ring projection Z/mZ ->Z/nZ is also surjective on the units:(Z/mZ)^x ->(Z/nZ)^x
A university has 10,000 students of which 50% are male. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students.
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