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Consider F(x,y,z)= √(x + yz), P(3,1,1,) and u= (2/7, 6/7, 3/7)
a) Find the gradient of F.
b) Evaluate the gradient at point P.
c) Find the rate of change of f at P in the direction of the vector u.
d) Find an equation of the tangent plane to √(x + yz) = 2j at the point P(3,1,1).
the manager of a paint supplystore wants to determine whether the mean amount of paint contained in 1-gallon cans
The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.44° F. What temperature represents the 95th percentile?
What is the probability that a freshman selected at random from this group is enrolled in.
A boat can travel 54 mph in still water. if it travels 236 miles with the current in the same length of time it travels 196 miles against the current what is the speed of the current?
Franklin has $2,500 in a savings account that pays interest at the rate of 4% annually. How much interest will he earn after one year?
prove that the set of natural numbers will be a ring by using ring definition.zn is a ring for all n where n stands for
Mean and Variance of a Probability distribution, A bank keeps tracks of customers coming into the bank between 12 Noon and1 PM on Monday.
Construct a polynomial equation: x7 + a1x6 + a2x5 + a3x4 + a4x3 +a5x2 + a6x + a7 ≡ 0 mod 7, with exactly 4 roots. You must specify those 4 roots
A 16 foot plank is leaning on the side of a wall and is being pulled up the wall at a rate of 1/2 ft /?sec by a worker on top of the wall. How fast is the end of the plank sliding along the ground when it is 8 feet from the wall?
During a windstorm, part of the top of a flagpole breaks off. The broken top portion touches the ground at an angle of [c]5° 1[e] feet from its base, How tall was the pole before the windstorm
the population of Atlanta, GA was 416.1 thousand in January of 2000. By January 2010, the population had grown to 540.9 thousand.
When b=2 show that the differential equation in the above figure has a solution of period k. Show that det A(t)= 1 for all t then use this to show that the floquet multipliers are roots of x2-bx+1=0 when b is the trace of A(k).
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