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If a sinC + b cosC = p
and a cosC - b sinC = q
show that a2 + b2 = p2 + q2
If the top side is black, what is the chance that the other side is white?
Apply the algorithm described in Example for finding the closest pair of points, using the Euclidean distance between points, to find the closest pair.
A designer plans the top of a rectangular workbench to be four times as long as it is wide and then determines that if the width is 2.5 ft.
Let A be a n × n orthogonal matrix.What are the possible values for det(A)?
The downstream distance, D1 is 12 miles, and the upstream distance D2 is 9miles. Substitute these values in the ratio above and solve for C. Leave answer in fraction form.
Estimate that the interest rate might increase or decrease by as much as one percentage point. Also, the price of the house might increase by as much as $10,000-it certainly won't decrease.
EXAMS An exam consists of ten true-or-false questions. Assuming that every question is answered, in how many different ways can a student complete the exam?
Paul Nagel invested some money at 3.5% simple interest and $1000 more than that amount at 5% simple interest.
Note the terms: 0% interest for ? number of years, the instant dollar discount, the retail price of the vehicle, and the interest rate of the loan. Given those figures, which is the better deal and why? Support your answer with calculations.
Use the integrating capabilities of a graphing utility to approximate the surface area of that portion of the surface z=e^x that lies over the region in the xy-plane bounded by the graphs of y=0, y=x and x=1.
How much does air pressure change as one moves from 100 meters above sea level to 1000 meters above sea level?
MATH 54 QUIZ 5. Suppose A is a 5 × 7 matrix whose rank is 3. What is the dimension of the null space of A? Justify your answer
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