Water is flowing into and being removed from a tank - Leaving Cert Mathematics - Question 10(a) - 2021
Question 10(a)
Water is flowing into and being removed from a tank.
The volume of water in the tank is measured on a daily basis, starting at day 0.
The volume of water, in litres,... show full transcript
Worked Solution & Example Answer:Water is flowing into and being removed from a tank - Leaving Cert Mathematics - Question 10(a) - 2021
Step 1
Find the value of $t$ when the tank empties.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find when the tank empties, we need to set the volume function to zero:
This simplifies to:
Factoring out t, we get:
Thus, t=0 or t=3101≈33.67 days.
Since t≥0, the tank empties when t≈33.67 days.
Step 2
Find the rate at which the volume of water in the tank is changing when $t = 5$.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find the rate of change, we need to first calculate the derivative of the volume function:
Now, substituting t=5 into the derivative:
Thus, at t=5, the volume of water in the tank is changing at a rate of 71 litres per day.
Step 3
Find the value of $t$ when the volume of water in the tank is a maximum.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find the maximum volume, we set the derivative to zero:
Rearranging gives:
Therefore, the volume of water is maximized at approximately t=16.83 days.
Step 4
Find the maximum volume of the water in the tank, correct to the nearest litre.
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find the maximum volume, substitute t≈16.83 back into the original volume function:
Calculating this gives:
≈1000.80+690.03−848.97≈841.86.
Hence, the maximum volume of the water in the tank is approximately 842 litres.
Join the Leaving Cert students using SimpleStudy...
