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Mathematics
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Algebra and Trigonometry
Quiz 4: Polynomial and Rational Functions
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Question 61
Multiple Choice
Find the polynomial function of degree
whose graph is shown in the figure.
Question 62
Multiple Choice
An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below) . If
denotes the radius of a hemisphere, find a formula for the volume of the capsule.
Question 63
Multiple Choice
Find all solutions of the equation.
Question 64
Multiple Choice
Find all solutions of the equation.
Question 65
Multiple Choice
Find all values of
such that
Question 66
Multiple Choice
A flat metal plate is positioned in an xy-plane such that the temperature T (in
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 15
C, find the temperature at the point Q (9, 8) .
Question 67
Multiple Choice
Find the quotient and remainder if
is divided by
Question 68
Multiple Choice
Find all solutions of the equation.
Question 69
Multiple Choice
Show that the number is a zero of
of the given multiplicity, and express
as a product of linear factors.
Question 70
Multiple Choice
From a rectangular piece of cardboard having dimensions W = 16 and L = 30 an open box is to be made by cutting out identical squares of area x
2
from each corner and turning up the sides (see Illustration) . Find all positive values of x such that the volume of the box V ( x ) > 0. Include only allowable values of x in your answer.
Question 71
Multiple Choice
Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 40, then u = 3