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Question: Show that the solution to Example may be found as follows: reflect A to the other side of the river to as shown in Figure. Draw a line connecting A' to B. Where this line intersects the horizontal line is the required point P, the location of the pumping station
Example: Towns A and B are located 3 and 6 miles respectively, from a straight river. Let C and D be the points on the river bank closest to A and B, respectively, as shown in Figure. The distance between points C and D is 9 miles. The two towns are to be supplied water from a pumping station situated on the river between them. Where on the river should the pumping station be located in order to minimize the length of piping used in connecting the towns?
Find the equation of a sphere of radius 3 which is tangent to both the planes x-2y+2z=3 and 3x+4z=8
I was one-tenth of a mile from the intersection, while she was three-twentieths of a mile from it. How fast were we approaching each other at that instant?
(a) Prove that a closed k-form w on S^k is exact if and only if int_(S^k) w = 0. [Hint: dim H^k(S^k) = 1.](b) Conclude that the linear map int_(S^k): H^k(S^k) -> R is an isomorphism.
You have a rectangular piece of cardboard that you want to fold into a box. It occurs to you that you can cut out an equal square from each corner of the rectangle, make a crease along each side and fold them up.
CRIME RATES The number of major crimes committed in Bronxville between 2000 and 2007 is approximated by the function.
Why are descriptive statistics important to understand? Please illustrate with a specific example.
at a convenience store there is a 25 chance a customer enters the store within one minute of closing time. describe the
Determine convergent or divergence. SUM from n=0 to infinity for
a simple random sample of size n is drawn from a population that is normally distributed. the sample mean is found to
How many different known sequences contain these terms? Find the specific sequence you were working with; how many different things does it count? (Can you figure out why it counts any of them?)
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level alpha.
(a) How much is in the account after the last deposit is made? (b) How much was deposited? (c) What is the amount of each withdrawal? (d) What is the total amount withdrawn?
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