5 math problems due in 3 hours
combs
Math1.5.docx|
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.)
