Intermediate Algebra (11th edition)

41.A rectangular piece of sheet metal has a length
that is 4 in. less than twice the width. A square piece
2 in. on a side is cut from each corner. The sides
are then turned up to form an uncovered box of volume
256. Find the length and width of the original
piece of metal.

42.Another rectangular piece of sheet metal is 2 in. longer than it is wide. A square piece
3 in. on a side is cut from each corner. The sides are then turned up to form an uncovered
box of volume 765. Find the dimensions of the original piece of metal.

Solve each problem. When appropriate, round answers to the nearest tenth. See Example 5.

43.An object is projected directly upward from the
ground. After tseconds its distance in feet above the
ground is

After how many seconds will the object be 128 ft

above the ground? (Hint:Look for a common factor

before solving the equation.)

44.When does the object in Exercise 43strike the ground?

s 1 t 2 = 144 t- 16 t^2.

in.^3

in.^3

SECTION 9.4 Formulas and Further Applications 529

128 ft

Ground level

s

45.A ball is projected upward from the
ground. Its distance in feet from the
ground in tseconds is given by

At what times will the ball be 213 ft

from the ground?

46.A toy rocket is launched from ground

level. Its distance in feet from the ground

in tseconds is given by

At what times will the rocket be 550 ft

from the ground?

s 1 t 2 =- 16 t^2 + 128 t. s 1 t 2 =- 16 t^2 + 208 t.

47.The function defined by

gives the distance in feet a car going approximately

68 mph will skid in tseconds. Find the time it would

take for the car to skid 180 ft.

48.The function given in Exercise 47becomes for a car going 50 mph.
Find the time it takes for this car to skid 218 ft.

A ball is projected upward from ground level, and its distance in feet from the ground in t seconds
is given by.

49.After how many seconds does the ball reach a height of 400 ft? How would you describe
in words its position at this height?

50.After how many seconds does the ball reach a height of 425 ft? How would you interpret
the mathematical result here?

s 1 t 2 =- 16 t^2 + 160 t

D 1 t 2 = 13 t^2 - 73 t

D 1 t 2 = 13 t^2 - 100 t

213 ft 550 ft

D