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1. (a) Find a vector function that represents the curve of intersection of x2 + y2 = 4 and z =x.
(b) Find the normal plane of the curve above at the point (0,2,0).2. Use the chain rule to find the indicated partial derivatives:
z = tan (x/y) with x = 2s + 3t; y = 3s - 2t
you are considering starting a walk-in clinic. your financial projections for the first year of operations are as
f(x)=xlnx find f'(e), in other words, find the derivative of f at x=e
What value would you expect the Gini Index to have for an economic system in which income is distributed evenly? What about an economic system in which almost all of the income is concentrated in the hands of a few people?
50000 people at stadium, and 40000 of them are male. if 2 people are selected at random, what is the probability that both are male?
Show that if a>0, then the convergence of the function nx/(1+n^2 x^2) is uniform on the interval [a,infinity), but is not uniform on the interval [0,infinity).
Find the level of production for each sector in order to satisfy the demand for $100 million worth of food, $40 million worth of clothing, and $250 million worth of shelter. (Round your answer to the nearest whole number.)
In recession, congress decided to stimulate the economy by providing funds to hire unemployed workers for gov. projects. Suppose the t months after the stimulus programs have begun, there are N(t) thousand people unemployed, where:
A surfboard manufacturing company has determined that the cost function c(x), in hundreds of dollars, for producing x hundreds of boards is c(x) = .2x^2 -.84x + 3.625.
A building is 50m high and its shadow on the ground is 92m long, find the angle of elevation of the building from the ground.
Fild the average rate of change of the function R(θ)= √(4θ + 1) over the interval [0, 2]. Also find the limiting value of the average rate of change when θ = 1.
Wiiand Corporation has 50,000 shares of $10 par value common stock outstanding. It declares a 10% stock dividend on december 1 when the market value per share is $16.
The sales of a small company were $27000 in its second year of operation and $63000 in its fifth year. Let y represent sales in the xth year of operation. Find the slope of the sales line.
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