A partially filled pool has 10,000 liters of water in it when Finn begins to fill it with a hose on a hot, sunny day. The volume V, in liters, of water coming out of the hose in minutes is given by the function V (m) = 20m, and the volume, E, in liters, of water evaporating in minutes is given by the function E (m) = 0.1m. Let P be the total volume, in liters, of the water in the pool minutes since Finn started filling it.

A. Write a formula for P (m) in terms of V (m) and E (m).

B. Write a formula for P (m) in terms of m.

Question

Mathematics

Giana Frey

10 March, 05:00

A partially filled pool has 10,000 liters of water in it when Finn begins to fill it with a hose on a hot, sunny day. The volume V, in liters, of water coming out of the hose in minutes is given by the function V (m) = 20m, and the volume, E, in liters, of water evaporating in minutes is given by the function E (m) = 0.1m. Let P be the total volume, in liters, of the water in the pool minutes since Finn started filling it.

A. Write a formula for P (m) in terms of V (m) and E (m).

B. Write a formula for P (m) in terms of m.

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Answers (1)

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Freeway · Answer 1

(a) Total volume, P (m) = 10000 + V (m) - E (m)

(b) P (m) = 10000+19.9m

Step-by-step explanation:

The partially filled pool has 10,000 liters of water in it.

The pool is being filled with a hose, which means it adds to the volume of water. Therefore, V (m) is an addition to the total volume.

Water evaporates from the pool, which is a reduction to the volume of water. Therefore, E (m) is a subtraction from the total volume.

Therefore:

The Volume of Water in the Pool at any time, P (m) = 10000 + V (m) - E (m)

(b) Since we are given:

V (m) = 20m

E (m) = 0.1m

P=10000+20m-0.1m

The Total Volume, P (m) = 10000+19.9m