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The concentration of salt in a fluid at the point (x,y,z) is given by S(x,y,z) = x2 + y4 + x2z2 (in mg per cubic cm). You are at the point (-1, 1, 1).
(a) In which direction should you move if you want the concentration to increase the fastest?
(b) You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration (of salt) changing?
A gardener wants to create a rectangular garden with length of 9x - 5y ft. and width of x - 6y ft. What is an algebraic expression for the area of the garden? Be sure to multiply this out, express in simplest correct mathematical form, and include..
The distance from home plate to dead center firld in a certain baseball stadium is 407 feet. A baseball diamond is a square with a distance from home plate to first base is 90 feet. How far is it from first base to dead center field?
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Seven members of a group of nineteen people dislike the New Democratic Party (NDP), ten dislike the Liberals, eleven dislike the Conservatives.
Find an equation for the plane containing the line in the xy-plane where y = 1, and the line in the xz-plane where z = 2.
Find the equation of any vertical asymptotes. f(x) = (x2 - x - 6/x2 - 3x - 10)
If the water level is rising at a rate of 15000 centimeters per minute when the height of the water is 4500 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
During his first year in college, Mark Sutherland opened a checking account at the First National Bank of Arlington, Texas. His account does not have a minimum.
a retailer purchases a batch of 1000 fluorescent lightbulbs from a wholesaler at a cost of 2 per bulb. the wholesaler
the standard IQ test has a mean of 98 and the standard deviation of 14. We want to be 99% certain that we are within the 4 IQ points of the true mean. Determine the required sample size.
Two companies share the market for a new technology. They have no competition except each other. Let A(t) be the net worth of one company.
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