Question

An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 6 cm, and the height is 14 cm. Find the rate at which the water level is rising when the water level is 12 cm.

a) 28 cm/sec

b) 21 cm/sec

c) 14 cm/sec

d) 7 cm/sec

Answer 1

To obtain a 50% solution, you will need to add 6 gallons of pure hydrochloric acid to 10 gallons of a 20% solution.

Step-by-step explanation:

To find the amount of pure hydrochloric acid needed to obtain a 50% solution, we need to set up an equation using the concept of mass balance.

Let x be the amount of pure hydrochloric acid in gallons.

The total volume of the solution will be 10 + x gallons.

The equation will be: 0.2 * 10 + 1 * x = 0.5 * (10 + x)

Simplifying the equation, we get: 2 + x = 5 + 0.5x

Combining like terms, we get: 0.5x = 3

Dividing both sides of the equation by 0.5, we get: x = 6

Therefore, 6 gallons of pure hydrochloric acid must be added to 10 gallons of a 20% solution to obtain a 50% solution.