26_Practice Quiz in Mathematics_College Algebra_Trigonometry_Probability and Statistics_Calculus with Answer and Solution

Refresher - MATHEMATICS Quiz 26
PROBLEM 1:


Water is leaking from a faucet at the rate of L(t) = 10e-0.5t gallons per hour, where t
is measured in hours. How many gallons of water will have leaked from the faucet
after a 24-hour period?


Solution:
Let L(x) = the no. of gallons that have leaked from the faucet after x hours


L(x) = ∫ L(t) dt
24
L(x) = ∫ 10e −0.5t dt
0



L(x) =
10
- 0.5
( )
e −0.5t - e 0

L(x) = - 20 ( e -e )
−0.5(24 ) 0




L(x) = - 20 ( e - e )
−12 0



L(x) = - 20(- 0.99999)
L(x) = 19.999 say 20 gallons

, Refresher - MATHEMATICS Quiz 26
PROBLEM 2:


On a certain day, the changes in temperature in a given house beginning at 12:00
⎛ t⎞
noon are represented by f(t) = Sin ⎜ ⎟ degrees Fahrenheit, where t is the
⎝ 2⎠
number of hours elapsed after 12 noon. If at 12:00 noon the temperature is 95˚F,
find the temperature in the green house at 5:00 PM.


Solution:
5
F(t) = 95 + ∫ f(x) dx
0

5 x
F(t) = 95 + ∫ Sin dx
0 2
5
⎡ ⎛ x⎞ ⎤
F(t) = 95 + ⎢ - 2 Cos ⎜ ⎟ ⎥
⎣ ⎝ 2 ⎠ ⎦0

⎡⎛ 5⎞ ⎤
F(t) = 95 + ⎢⎜ - 2 Cos
2 ⎟⎠
( )
- - 2 Cos 0 ⎥
⎣⎝ ⎦
F(t) = 95 + 3.602

F(t) = 98.602˚ F