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Let A = PDP-1, where P is orthogonal and D is diagonal, and let λ be an eigenvalue of A of multiplicity k. Then λ appears k times on the diagonal of D. Explain why the dimension of the eigenspace for λ is k.
Use the fact that the derivative of the function g(x)= √ x is g'(x)=1/2√x to find the equation of the tangent line to the graph of g'(x) at the point x=25.
the area of an equilateral triangle is decreasing at a rate of 4 cm^2/min. Find the rate at which the length of a side is changing when the area of the triangle is 200 cm."
the manager of 100 apartments knows that at $600 rent per month, all apartments will be rented. For each $25 increase, one apartment will not be occupied. Let x represnt the number of $25 increases to the rent. Write the revenue as function of x.
a regular pentagon with perimeter 75m , find the area of the regualr pentagon.
(Round the number that you compute and use to the nearest whole number.) According to the model, what will the enrollment be in the year 2025?
Plastic bags used for packaging are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5.6 pounds per square inch and a standard deviation of 1.8 pounds per square inch. What is the probability that the me..
Wing has different books to arrange on a shelf: 4 blue, 3 green, and 2 red. In how many ways can the books be arranged on a shelf? If books of the same color are to be grouped together, how many arrangements are possible?
What is the probability that the number 10 will not appear until the 6th number and what is the expected number of trials until a 10 appears
The length of a rectangle is 6 times the width. If the perimeter is to be at least 98 meters, what are the possible values for the width?
A body starts to move from the origin into the first quadrant along the curve y = ln(sec x) . If its speed is always 3, find x and y as functions of t .
Find the determination
the curve for xsqrtiny for 1ltylt4 is rotated around the y-axis to form a container. the container is filled with a
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