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MATH 16A QUIZ 4-
(1) Find the point (x, y) on the curve y = x2 for which 2x + y is minimized, and explain why it is an absolute minimum.
(2) I have 200 feet of fencing to construct a rectangular fence for my cows. I want both the length and width of my fence to be at least 2 feet. What is the smallest area I can enclose?
(3) Find the derivative of f(x) = 4√x(2x2 - 1)3.
(4) Find the derivative of f(x) = (x3-1/x3+1) at x = 0.
A stone dropped in a still pond creates a circular ripple whose radius increases at a constant rate of 3 ft/s. At what rate is the area enclosed by the ripple increasing 8 s after the stone strikes the pond?
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.
The length of a swimming pool is 18.5 ft, and the width is 10.75 ft. Write the ratio of length to width as ratio of whole numbers.
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Let S be a set with an associative binary operation but with no identity. Choose an element 1 not belonging to S, write M = {1} or S, and define an operation on M by using the operation of S and 1s=s=s1 for all s belonging to S.
Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away. How large a radio telescope would we need to detect this signal?
the dimensions of a rectangle are such that its length is 3 in more than its width. if the length were doubled and if the width were increased by 1 in, the area would be increased by 104 in what are the length and width of the rectangle?
You are the director of communicable diseases in a city health department, responsible for a large urban community. It is early spring in 2003. For the past two years, your department has been working to control the spread of the West Nile Virus and ..
Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Give your answer correct to the nearest whole number.)
In what range of values do the proportions p from 95% of all samples fall? (c) In what range of values do the proportions p from 99.7% of all samples fall?
What is the location of someone standing on the first level in relation to someone standing on the third level?
in fiscal year 2000, the U.S. government had a budget surplus of 99 billion (99 X 10^9) dollars. How many years of such surpluses would be needed to pay off the debt, as of July 2004, of 7.26 trillion (7.26*10^12) dollars?
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