An astronaut on the moon throws a baseball upward

5 Math Problems

A building is

2

ft from

a

10​-ft

fence that surrounds the property. A worker wants to wash a window in the building

15

ft from the

ground.

He plans to place a ladder over the fence so it rests against the building.​ (See the​ figure.) He decides he should place the ladder

8

ft from the fence for stability. To the nearest tenth of a​ foot, how long a ladder will he​ need?

decorative image5 ft8 ft2 ft10 ft

He will need a

ft ladder.

A projectile is launched from ground level with an initial velocity of

v0

feet per second. Neglecting air​ resistance, its height in feet t seconds after launch is given by

s=−16t2+v0t.

Find the​ time(s) that the projectile will​ (a) reach a height of

240

ft and​ (b) return to the ground when

v0=128

feet per second.

​(a) Find the​ time(s) that the projectile will reach a height of

240

ft when

v0=128

feet per second. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

seconds ​(Use a comma to separate answers as​ needed.)

B.

The projectile does not reach

240

feet.

An astronaut on the moon throws a baseball upward. The astronaut is 6​ ft, 6 in.​ tall, and the initial velocity of the ball is

30

ft per sec. The height s of the ball in feet is given by the equation

s=−2.7t2+30t+6.5​,

where t is the number of seconds after the ball was thrown. Complete parts a and b.

a. After how many seconds is the ball

12

ft above the​ moon's surface?

After

seconds the ball will be

12

ft above the​ moon's surface.

​(Round to the nearest hundredth as needed. Use a comma to separate answers as​ needed.)

Sales of SUVs​ (sport utility​ vehicles) in the United States ​(in millions) for the years​ 1990-1999 can be modeled by the quadratic equation shown below.

y=0.016x2+0.124x+0.787

Here

x=0

represents​ 1990,

x=1

represents​ 1991, and so on. Use the model to approximate sales in

1996.

Sales in

1996

were approximately

million SUVs.  

​(Round to the nearest tenth as​ needed.)

In

1993​,

the sports league introduced a salary cap that limits the amount of money spent on​ players' salaries. The quadratic model

y=0.2313x2+2.600x+35.17

approximates this cap in millions of dollars for the years

1993​-2013​,

where

x=0

represents

1993​,

x=1

represents

1994​,

and so on. Complete parts a and b.

a. Approximate the sports league salary cap in

2009.

The approximate sports league salary cap in

2009

is

​$

million.

​(Round to the nearest tenth as​ needed.)