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Consider an elliptic paraboloid
f(x, y) = 4 - x2 - y2/4.
a. Find the xy-, yz- and xz-traces of the graph of f(x, y) and sketch the graph.
b. Write down the equation of the level curve which passes through a point (2, 4). Sketch the level curve.
c. Find the unit vectors in the directions of the steepest descent and the steepest ascent at (2, 4). Mark these directions on the graph in (b). Verify that the gradient at (2, 4) is orthogonal to the level curve through this point.
d. Write down the equation of the tangent line to the level curve at (2, 4).
If there has beena 10 percent increase in consumer income between two periods, what was the percentage change in the demand for foreign travel? For tobacco products? For flour?
solve this equation numerically numerical methods by explicit or implicit methods or crank niclson method..find the
what is the solution of this age problem? A man, 32 years old has a son 8 years of age. In how many years will the man be twice as old as his son?
Important information about Statistics probability, Packages from packing machine have a mass, which is normally distributed with mean 200g and standard deviation 2g
Consider a bivariate normal population with u1=0,u2=2,σ11=2,σ22=1,and p12=.5, write out the bivariate normal density.
Find the median distance driven.
1.Investigate the comparative pros and cons of the mean and the median. Find examples where the mean is more appropriate than the median and vice-versa. Discuss the locations of the mean, median and mode for a normal, left-skewed and right-skewed dis..
Evaluate formulae for the coefficients -Hint: Use the linear transformation
At a price of $1.94 per bushel, the supply of corn is 9800 million bushels and the demand is 9300 million bushels. At a price of $1.82 per bushel the supply is 9400 million bushels and the demand is 9500 million bushels.
Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.
A bakery makes cakes. The bakery has daily fixed costs of $418 per day and variable costs of $7.30 per cake produced. Cakes are sold for $12.80 each.
If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade.
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