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Assume that a watermelon dropped from a tall building falls y=16t^2 in t sec. Find the watermelon's average speed during the first 3 sec of fall and the speed at the instant t=3sec.
a. 48 ft/sec; 96 ft/sec
b. 49 ft/sec; 98 ft/sec
c. 24 ft/sec; 48 ft/sec
d. 96 ft/sec; 49 ft/sec
What are the different forms of linear equations in two variables? Show an example of each form. How does the sign or value of the slope determine its type (i.e. whether it is +ve, -ve, undefined, or zero)?
Probability - independence of 2 events. Prove that if A and B are independent events in a probability space, then the events A^c and B^c are also independent.
Let A be a positive definite matrix. Show that X has a unique positive square root. That is, show that there exists a unique positive matrix X such that X^2 =A.
A pulley is suspended 13.5 m above a small bucket of cement on the ground. A rope is put over the pulley. One end of the rope is tied to the bucket and the other end dangles loosely to the ground.
Suppose that f is continuous on [a,b], f(z) 0. Set z = sup{x: f (t)
Indicate, by checking the appropriate box, whether the given points below are on line 1 , on line 2 , on both line 1 and line 2 , or on neither one of the two lines:
Calculate the mean and variance of the new observations
A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 cent stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than the number of 8 cent stamps.
An objective function is to be maximized given the following constraints: x+2y=4, x-y=1, x=0, y=0. Find the vertices of the set of feasible solutions.
Real Life Application of Linear Eqations : A mathematician has developed a model indicating a woman with x years of education can expect to earn y = 1200x + 6300 dollars a year.
Discuss a real-life situation where a straight-line graph might be applicable and explain why you think this might be true (show the equation).
Let N be a positive integer. Let d be an integer relatively prime to phi(N) (phi denotes the euler totient function). Prove that there exists a d' in Z (=integers) with dd'=1 mod phi(N).
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