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In one hour, the distance, $d(s)$ , in kilometers that a ferry can travel up and down a river flowing with a constant speed, $s$ , in meters per second is: $d(s) = 10.7 - 1.2s^2$ where $s$ and $d(s)$ are positive. $\newline$ Which of the following equivalent expressions for $d(s)$ contains the speed of the river in meters per second, as a constant or coefficient, for which the ferry can travel a distance of $8$ kilometers in one hour?

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Identify independent and dependent variables

Full solution

Q. In one hour, the distance,

d(s)

, in kilometers that a ferry can travel up and down a river flowing with a constant speed,

s

, in meters per second is:

d(s) = 10.7 - 1.2s^2

where

s

and

d(s)

are positive.

\newline

Which of the following equivalent expressions for

d(s)

contains the speed of the river in meters per second, as a constant or coefficient, for which the ferry can travel a distance of

8

kilometers in one hour?

Set Distance Equal to $8$ km: Set the given distance equal to $8$ km. $\newline$ $d(s) = 10.7 - 1.2s^2$ $\newline$ $8 = 10.7 - 1.2s^2$
Solve for s: Solve for $s$ . $\newline$ $8 = 10.7 - 1.2s^2$ $\newline$ Subtract $10$ . $7$ from both sides: $\newline$ $8 - 10.7 = -1.2s^2$ $\newline$ $-2.7 = -1.2s^2$
Divide by $-1$ . $2$ : Divide both sides by $-1$ . $2$ . $\newline$ $\frac{-2.7}{-1.2} = s^2$ $\newline$ $s^2 = 2.25$
Take Square Root: Take the square root of both sides. $\newline$ $s = \sqrt{2.25}$ $\newline$ $s = 1.5$
Verify Solution: Verify the solution. $\newline$ Substitute $s = 1.5$ back into the original equation: $\newline$ $d(1.5) = 10.7 - 1.2(1.5)^2$ $\newline$ $d(1.5) = 10.7 - 1.2(2.25)$ $\newline$ $d(1.5) = 10.7 - 2.7$ $\newline$ $d(1.5) = 8$

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