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MATH 54 QUIZ 8-
1. True/False? Justify your answer. If ||u - v||2 = ||u||2 + ||v||2, then u is orthgonal to v.
2. Find the orthogonal projection of b = onto W = Span
3. Find all least squares solutions to Ax = b where A = and b =
4. Compute an orthogonal basis of P2 where the inner product is defined by
(f, g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) .
5. Let A and B be n × n orthogonal matrices. Show that AB is orthogonal.
What is the equation with the following plot points? (10,10) (20,25)
(9) An insurance company has an obligation to pay $12,000 one year from now, and $9,000 two years from now. The insurance company purchases a combination of the followingtwo bonds (both with $ 1,000 par and redemption values) in order to exactly matc..
A box contains 10 items, of which 3 are defective and 7 are non-defective. Two items are randomly selected, one at a time, with replacement, and x is the number of defective items in the sample.
A gardener wants to create a rectangular garden with length of 9x - 5y ft. and width of x - 6y ft. What is an algebraic expression for the area of the garden? Be sure to multiply this out, express in simplest correct mathematical form, and include..
A common Stock pays an annual dividend per share of $1.60. The risk-free rate is 5 percent and the risk premium for the stock is 4 percent. If the annual dividend is expected to reemain at $1.60 per share, What is the value of the stock?
An anchor weighing 130 lb in water is attached to a chain weighing 2 lb/ft in water. Find the work done to haul the anchor and chain to the surface of the water from a depth of 35 ft.
An open-topped cylindrical pot is to have volume 125in^3. What dimensions will minimize the total amount of material used in making this pot?
Suppose that you are to make a rectangular box with a square base [B]from two different materials. The material for the top and four sides of the box costs $1/ft^2; the material for the base costs $2/ft^2.
A container in the shape of an inverted pyramid with a square base of 2 m by 2 m and height of 5 m is filled to a depth of 4 m with corn slurry. How much work is required to pump all the slurry over the top of the container?
A steep mountain is inclined 79 degree to the horizontal and rises 3100 ft above the surrounding plain. A cable car is to be installed from a point 900 ft from the base to the top of the mountain. Find the shortest length of cable needed.
The height in meters of women of a certain tribe is approximated by where t is the woman's age in years and Estimate the height (to the nearest hundredth of a meter)
find the average speed of the cyclist.
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