Grantham WK6 Algebra Problem: Measuring Time to Fill a Pool Work Sheet

Question 17

Using the equation you wrote in the last problem, how long would it take to fill the pool if both pipes are open at the same time? Write your answer in fraction form.

Question 1
What does this mathematical symbol ∞ represent?
Zero
Infinity
Pi
Undefined
Question 2
A rational expression can be written as a ratio of two polynomial expressions.
True
False
Question 3
Asymptotes are invisible lines which a graphed function will approach very closely but not touch.
True
False
Question 4
Find the domain of the function
Domain: all real numbers x except x=6
Domain: all real numbers x except x=8
Domain: all real numbers x
Domain: all real numbers x except x = -6
Question 5
Find the domain of the function
Domain: all real numbers x except x = 7
Domain: all real numbers x except x = ±49
Domain: all real numbers x except x = -7
Domain: all real numbers x except x = ±7
Question 6
Find the domain of
all real numbers except x = -9
all real numbers except x = 81
all real numbers except x = 9
all real numbers except x = 9 and x = -9
Question 7
Find the domain of the function and identify any vertical and horizontal asymptotes.
Domain: all real numbers x except x = 2
Vertical asymptote: x = 2
Horizontal asymptote: y = -1
Domain: all real numbers x except x = 0
Vertical asymptote: x = 0
Horizontal asymptote: y = -1
Domain: all real numbers x except x = 2
Vertical asymptote: x = 0
Horizontal asympotote: y = -2
Domain: all real numbers x except x = -2
Vertical asympotote: x = 0
Horizontal asympotote: y = 2
Question 8
Select the correct graph of the function. Choose from among the graphs listed
below: 1st, 2nd, 3rd, or 4th.
Question 9
The cost C (in millions of dollars) of removing p% of the industrial and municipal
pollutants discharged into a river is given by
According to this model, it is possible to remove 100% of the pollutants.
True
False
Question 10
Based on your answer to the previous problem, explain why you chose your answer (whether it is possible or
not to remove 100% of the pollutants). Show your work
Question 11
In the following formula, S(x) is the minimum number of hours of studying required to attain a class score of
x. How many hours of study are needed to score 56? Round your answer to the nearest whole number.
Show your work
Question 12
The concentration C (in mg/dl), of a certain antibiotic in a patient’s bloodstream is
given by C(t)=50 t /(t^2 + 25) where t is the time (in hours) after taking the antibiotic.
What is the concentration 5 hours after taking the antibiotic? Show your work
Question 13
In order to join a gym, you pay a $200 annual fee, then $10 for each exercise class you attend. Indicate which
equation below would allow you to determine the average cost per class if you go to x amount of classes: 1st,
2nd, 3rd, or 4th.
Question 14
Which of the following can a graph NEVER cross?
Vertical asymptote
Horizontal asymptote
Slant asymptote
All of the above
Question 15
Select the graph of the rational function. Choose from among the graphs
below: 1st, 2nd, 3rd, or 4th.
Question 16
One pipe can fill a pool in 1.5 hours. A second pipe can fill up the pool in 2 hours. Which of the equations
below would determine how long it would take to fill the pool when both pipes are used? Select the correct
equation:1st, 2nd, 3rd, or 4th.
Question 17
Using the equation, you wrote in the last problem, how long would it take to fill the pool if both pipes are
open at the same time? Write your answer in fraction form. Show your work