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Points A and B move along the x- and y-axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing, and is it increasing or decreasing, when OB=2r and B is moving toward O at the rate of 0.3r units/sec?
Data and Probability, 1. How many variations in first-, second-, and third-place finishes are possible in a 100-yd dash with 6 runners? In a Chinese restaurant, the menu lists 8 items in Column A and 6 items in column B. To order a dinner, the dine..
Probability questions with cards and unbiased dice, Suppose that you select two cards without replacement from an ordinary deck of playing cards.
An open box is to be made from a six inch by six inch square piece of material by cutting equal squares from the corners and turning up the sides. Find the volume of the largest box that can be made
Let f be a surjection. Then f is an isomorphism iff the order of the element f(a) is equal to the order of the element a , for all a belong to G.
Verify that each of the following are equivalence relations on the plane R^2 (where R are real numbers) and describe the equivalence classes geometrically.
How many bit strings of length n are palindromes? Hint: Consider two cases n is even and n is odd. Note a palindrome is a "string" of letters or numbers which read the same frontwards and backwards.
You randomly select one card from a 52 card deck. What is the probability of selecting a black 6 or a red jack?
Check for symmetry with respect to the x and y-axis and the origin.
Standard deviation, Variance and Covariance. Calculate the standard deviation and variance of each set data, and covariance.
The resale value of a certain industrial machine decreases at a rate that depends on its age. When the machine is t years old, the rate at which its value is changing is -960e^ -t/5 dollars per year.
Find (partial z)/(partial u)( and ) (partial z)/(partial v) using the chain rule. Assume the variables are restricted to domains on which the functions are defined. Your answers should be in terms of u and v.
Find the volume of the ellipsoid generated by rotating around the x axis the region bounded by the ellipse with the equation (x/a)^2 + (y/b)^2 = 1
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