Question

lesson 8 practice problems

1. a girl throws a paper airplane from her treehouse. the height of the plane is a function of time and can be modeled by the equation ( h(t)=25 + 2.5t-\frac{1}{2}t^{2} ). height is measured in feet and time is measured in seconds after the airplane is thrown.

a. evaluate ( h(0) ) and explain what this value means in this situation.
b. what would a solution to ( h(t)=0 ) mean in this situation?
c. what does the equation ( h(9)=7 ) mean?
d. what does the model say about the airplane 2.5 seconds after the girl throws it if each of these statements is true?
( h(2)=28 )
( h(2.5)=28.125 )
( h(3)=28 )

1. a square picture has a frame that is 3 inches thick all the way around. the total side length of the picture and frame is ( x ) inches.

which expression represents the area of the square picture, without the frame? if you get stuck, try sketching a diagram.
a. ( (2x + 3)(2x + 3) )
b. ( (x + 6)(x + 6) )
c. ( (2x - 3)(2x - 3) )
d. ( (x - 6)(x - 6) )

Explanation:

Step1: Analyze the side length of the picture

Since the frame is 3 inches thick all around and the total side length of the picture and frame is \(x\) inches, the side length of the picture alone is \(x - 2\times3=x - 6\) inches.

Step2: Calculate the area of the picture

The area of a square is \(s^2\) (where \(s\) is the side length). So the area of the picture is \((x - 6)(x - 6)\)

Answer:

d. \((x - 6)(x - 6)\)