QuestionA pool has 603 cubic feet of water leaking at 1.5 cubic feet/hour. Explain $V(h)=-1.5h+603$ and its variables.

Studdy Solution

STEP 1

Assumptions1. The volume of water in the swimming pool is603 cubic feet. . The pool is leaking at a rate of1.5 cubic feet per hour.
3. Ruby's equation accurately represents the scenario.

STEP 2

Let's break down the equation $V(h)=-1.5 h+603$ .
In this equation, $V(h)$ is the volume of water in the pool at any given time $h$ . $h$ represents the number of hours since the pool started leaking. The coefficient of $h$ , -1.5, represents the rate at which the pool is leaking, in cubic feet per hour. The constant term,603, represents the initial volume of water in the pool, in cubic feet.

STEP 3

So, in the equation $V(h)=-1.5 h+603$ , the variable $h$ represents the number of hours since the pool started leaking. As $h$ increases, the volume of water in the pool, $V(h)$ , decreases.
$V(h) = -1.5h +603$

STEP 4

The coefficient -1. in the equation represents the rate at which the pool is leaking. This means that for each hour that passes, the volume of the pool decreases by1. cubic feet.
$V(h) = -1.h +603$

STEP 5

The constant term603 in the equation represents the initial volume of water in the pool before it started leaking. This means that when $h=0$ , i.e., at the start, the pool had603 cubic feet of water.
$V(0) = -1.5(0) +603 =603$

STEP 6

In conclusion, in the equation $V(h)=-1.5 h+603$ , $V(h)$ is the volume of water in the pool at time $h$ , $h$ is the number of hours since the pool started leaking, -1.5 is the rate at which the pool is leaking in cubic feet per hour, and603 is the initial volume of water in the pool in cubic feet. As time passes (i.e., as $h$ increases), the volume of water in the pool decreases due to the leak.

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QuestionA pool has 603 cubic feet of water leaking at 1.5 cubic feet/hour. Explain $V(h)=-1.5h+603$ and its variables.

Studdy Solution

STEP 1

Assumptions1. The volume of water in the swimming pool is603 cubic feet. . The pool is leaking at a rate of1.5 cubic feet per hour.
3. Ruby's equation accurately represents the scenario.

STEP 2

STEP 3

So, in the equation $V(h)=-1.5 h+603$ , the variable $h$ represents the number of hours since the pool started leaking. As $h$ increases, the volume of water in the pool, $V(h)$ , decreases.
$V(h) = -1.5h +603$

STEP 4

The coefficient -1. in the equation represents the rate at which the pool is leaking. This means that for each hour that passes, the volume of the pool decreases by1. cubic feet.
$V(h) = -1.h +603$

STEP 5

The constant term603 in the equation represents the initial volume of water in the pool before it started leaking. This means that when $h=0$ , i.e., at the start, the pool had603 cubic feet of water.
$V(0) = -1.5(0) +603 =603$

STEP 6

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QuestionA pool has 603 cubic feet of water leaking at 1.5 cubic feet/hour. Explain V(h)=−1.5h+603V(h)=-1.5h+603V(h)=−1.5h+603 and its variables.

Studdy Solution

STEP 1

Assumptions1. The volume of water in the swimming pool is603 cubic feet. . The pool is leaking at a rate of1.5 cubic feet per hour.3. Ruby's equation accurately represents the scenario.

STEP 2

STEP 3

So, in the equation V(h)=−1.5h+603V(h)=-1.5 h+603V(h)=−1.5h+603, the variable hhh represents the number of hours since the pool started leaking. As hhh increases, the volume of water in the pool, V(h)V(h)V(h), decreases.V(h)=−1.5h+603V(h) = -1.5h +603V(h)=−1.5h+603

STEP 4

The coefficient -1. in the equation represents the rate at which the pool is leaking. This means that for each hour that passes, the volume of the pool decreases by1. cubic feet.V(h)=−1.h+603V(h) = -1.h +603V(h)=−1.h+603

STEP 5

The constant term603 in the equation represents the initial volume of water in the pool before it started leaking. This means that when h=0h=0h=0, i.e., at the start, the pool had603 cubic feet of water.V(0)=−1.5(0)+603=603V(0) = -1.5(0) +603 =603V(0)=−1.5(0)+603=603

STEP 6

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QuestionA pool has 603 cubic feet of water leaking at 1.5 cubic feet/hour. Explain $V(h)=-1.5h+603$ and its variables.

Assumptions1. The volume of water in the swimming pool is603 cubic feet. . The pool is leaking at a rate of1.5 cubic feet per hour.
3. Ruby's equation accurately represents the scenario.

So, in the equation $V(h)=-1.5 h+603$ , the variable $h$ represents the number of hours since the pool started leaking. As $h$ increases, the volume of water in the pool, $V(h)$ , decreases.
$V(h) = -1.5h +603$

The coefficient -1. in the equation represents the rate at which the pool is leaking. This means that for each hour that passes, the volume of the pool decreases by1. cubic feet.
$V(h) = -1.h +603$

The constant term603 in the equation represents the initial volume of water in the pool before it started leaking. This means that when $h=0$ , i.e., at the start, the pool had603 cubic feet of water.
$V(0) = -1.5(0) +603 =603$