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1. Consider the polynomial P(x) = x3 + 4x2 + k3x + 3, where k is some integer. Find all possible values of k such that P(x) has a rational root. (Clearly explain why there are no other values of k that work.)
2. Let u and v be two unit vectors such that u • v = 1/32.
(a) Prove that vectors u-v and 3u+3v are perpendicular.
(b) Find the angle between vectors 2u+6v and 3u-v.
Hint: Consider how dot product of a vector with itself is related to its length.
A total of 393 tickets were sold for the school play. They were either adult tickets or students tickets. There were 57 fewer student tickets sold than adult tickets. How many tickets were sold?
Car A and Car B leave the origin at noon. Car A travels north at 33 mph and car B travels east at 56 mph.
a trough is 12 ft long, 2ft high and 2ft wide at the top and has isosceles triangular ends. if water is put in at the rate of 1ft^3 per minuter, how fast is the depth increasing when it is 1.5 ft deep?
Prove that the sequence bn=(1+1/n)^(n+1) is a monotone decreasing sequence.
There are several methods used by people to organize their lives in terms of keeping track of appointments, meetings, and deadlines. Some of these include using a desk calendar, using informal notes of scrap paper, keeping them ″in your head″, usi..
let f be the function defined by f(x) = 12x^(2/3) - 4x. a) find the intervals on which f is increasing. b) Find the x and y coordinates of all relative maximum points.
Chuck, Ted, and Sally are roommates and each day one of them must wash the dishes.
Describe the four models of democracy. Tell which one you think most closely resembles today's model in America. Which model do you prefer, and why?
Suppose the scores of 500 college freshmen taking Physics 101 are normally distributed. The mean score is 60 out of 100, and the standard deviation is 10. Find the values defined by the standard deviation that is 3 standard deviations away from th..
Find the largest area of an Isosceles triangle if the two equal sides are 15cm long.
Let f be defined on the interval [0,1] by setting f(x)=0 if x is irrational, and if x=(m/n) rational where gcd(m,n)=1 set f(x)=n. Show that f is unbounded on every open interval in [0,1] and compute the Lebesgue integral of f over the interval [0,..
nick has a goal to pay his credit card balance in full by june 30.when he first wrote the goal in december his balance
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