Alg2H Ch5 Application Problems (new’11) WK#11

HW#11 P.213 #12 Luke and Leia Problem

Luke and Leia are trapped in a room on a space station. The room is 20 meters long and 15 meters wide. But

the length is decreasing linearly with time at a rate of 2 meters per minute and the width is increasing linearly

with time at a rate of 3 meters per minute.

a)Let t be the number of minutes since the room was 20 by 15.

L(t) = the length of the room in meters = ______________________

W(t) = the width of the room in meters = _______________________

b)Let A (t) = number of sq meters of floor area in the room.

Write the particular equation for A(t) = _______________________________________ (x-intercept form)

A(x) = __________________________________________________________________(General Form)

Determine the Domain:

c)Does the area of the room reach a maximum for a positive value of t? If so, what value of t ? If not, how do

you tell? (REMEMBER: MAX OR MIN IS ____________ FOR QUAD FUNCTIONS.)

Find the maximum area:

d)When will the area of the room be zero?

REMEMBER: Setting Function = 0 IS DETERMINING THE _______________) What is the easiest form to use for this kind of

problem?____________________

e)Sketch full graph of A(x) dashed with both x-intercepts, vertex, y-intercept, symmetric pt, axis of symmetry. Solid the

part that makes sense in this problem.

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HW#11c p.226 #7

Assume that your height and your age are related by a linear function. Consulting your health records, you find

that at age A = 5 your height was H = 39 inches, and when A = 9, H = 55 inches.

a. Define the variables and express the dependent variable in terms of the independent variable.

b. Predict your height at age 16.

c. What does the H-intercept equal and what does it represent in the real world?

d. Since you are using a linear function as a model, what are you assuming about the rate at which you grow?

e. What fact in the real world sets an upper bounds on the domain in which this linear model gives reasonable

answers?

Homework #11d) Projectile Motion Problem:

The height h(t) of a projectile at any time t can be found with the quadratic function:

h(t) = -1gt2 + v0t + h0 g, the acceleration due to gravity, is: 9.8m/sec2 or 32ft/sec2

Identify independent variable:____________________________

Identify dependent variable;______________________________

You and a friend are spelunking (exploring caves) in a section of the Onondaga Cave in Missouri. From

2 feet above the floor of the cave, your friend throws a grappling hook toward a ledge above you. He

throws it upward with an initial velocity of 30 feet per second.

a. Write a function that describes the hook’s vertical motion

b. If the ledge is 17 feet above the floor of the

cave will the grappling hook reach it? Clearly defend your answer.