1. The Rock has an 88-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 6 gallons per minute. Handwritten. Show all work. Complete sentence for each question. (a) Assuming the tank was full, write a function in the form y=mx + b that represents the amount of water in the tank, Y, after X minutes. You will need to know the initial value and the rate of change. (b) How long has the tank been draining for if it has 34 gallons left?

Question

12-04-2022
Mathematics

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1. The Rock has an 88-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 6 gallons per minute. Handwritten. Show all work. Complete sentence for each question. (a) Assuming the tank was full, write a function in the form y=mx + b that represents the amount of water in the tank, Y, after X minutes. You will need to know the initial value and the rate of change. (b) How long has the tank been draining for if it has 34 gallons left?

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joaobezerra joaobezerra · Answer 1 · 2022-04-26T11:42:53+02:00

Using linear function concepts, it is found that:

a) The function is y = 88 - 6x.

b) The tank has been draining it for 9 minutes.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Item a:

The full volume of the tank is of 88 gallons, hence the y-intercept is of b = 88.

The volume can be drained at a rate of 6 gallons per minute, hence the slope is of m = -6.

Thus, the equation is given by:

y = 88 - 6x.

Item b:

This is x for which y = 34, hence:

y = 88 - 6x

34 = 88 - 6x

6x = 54

x = 9.

The tank has been draining it for 9 minutes.

More can be learned about linear function concepts at https://brainly.com/question/24808124

raphealnwobi raphealnwobi · Answer 2 · 2022-04-26T13:27:34+02:00

The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let y represent the amount of water after x minutes.

The Rock has an 88-gallon fish tank which can be drained at a rate of 6 gallons per minute. Hence:

m = -6, b = 88

y = -6x + 88

For 34 gallons:

34 = -6x + 88

x = 9

The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.

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