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Chapter 3: Q. 9 (page 136)
If the slope m of the graph of a linear function is________, the function is increasing over its domain.
If slope of the graph of a linear function is positive then function is increasing over its domain.
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The daily revenue R achieved by selling x boxes of candy is figured to be The daily cost C of selling x boxes of candy is .
(a) How many boxes of candy must the firm sell to maximize revenue? What is the maximum revenue?
(b) Profit is given as P(x) = R(x) - C(x). What is the profit function?
(c) How many boxes of candy must the firm sell to maximize profit? What is the maximum profit?
(d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue.
Artillery A projectile fired from the point (0, 0) at an angle
to the positive x-axis has a trajectory given by
where
x = horizontal distance in meters
y = height in meters
v = initial muzzle velocity in meters per second (m/sec)
g = acceleration due to gravity = 9.81 meters per second squared
is a constant determined by the angle of elevation.
A howitzer fires an artillery round with a muzzle velocity of 897 m/sec.
(a) If the round must clear a hill 200 meters high at a distance of 2000 meters in front of the howitzer, what cvalues are permitted in the trajectory equation?
(b) If the goal in part (a) is to hit a target on the ground 75 kilometers away, is it possible to do so? If so, for what values of c? If not, what is the maximum distance the round will travel?
Height of a Ball A shot-putter throws a ball at an inclination of to the horizontal. The following data represent the height of the ball at the instant that it has traveled feet horizontally.
(a) Use a graphing utility to draw a scatter diagram of the data. Comment on the type of relationship that may exist between the two variables.
(b) Use a graphing utility to find the quadratic function of best fit that models the relation between distance and height.
(c) Use the function found in part (b) to determine how far the ball will travel before it reaches its maximum height.
(d) Use the function found in part (b) to find the maximum height of the ball.
(e) With a graphing utility, graph the quadratic function of best fit on the scatter diagram
Parabolic Arch Bridge A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the figure, what is the height h of the arch 2 feet from shore?
Enclosing the Most Area with a Fence A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. See the figure. What is the largest area that can be enclosed?
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