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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.
the width of a rectangle is 7 feet less than the length the area is 120 square feet find the length and the width of the rectangle.
Calculate the expected value of having built a large plant and calculate the expected value of having built the small plant.
James is four years younger than Austin. If three times James' age is increased by the square of Agustin's age, the result is 28. Use an algebraic solution to find the ages of James and Austin.
A division of Carter Enterprises produces "Personal Income Tax" diaries. Each diary sells for $9. The monthly fixed costs incurred by the division are $20,000, and the variable cost of producing each diary is $4.
q. the carleton computer science society has a board of directors consisting of one president one vice-president one
find the vertex of the parabola defined by the function y4x22x-3 by completing the
Please answer Part 2 explaining part 2 You mentioned that looking at the p-values for each independent variable is necessary to see if they are significant, how would you determine their significance by looking at each of these values?
A company that manufactures bicycles has a fixed cost of $100,000. It costs $100 to produce each bicycle. The selling price per bike is $300.
Determine a formula for this particular aircraft that gives the takeoff roll as an exponential function of airport elevation. (Note: Use the general exponential function.)
$5900 is invested, part of it at 10% and part of it at 6%. For a certain year, the total yield is $478.00. How much was invested at each rate?
Find the absolute max and min values of f(x)=l+6x-3x^3 over the closed interval [0,4].
They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors.
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