Math  /  Algebra

QuestionSpecialists can determine the speed a vehicle was traveling from the length of its skid marks d and the coefficient of friction f . The formula for calculating the speed s is s=15.9df\mathrm{s}=15.9 \sqrt{\mathrm{df}}. Rewrite the formula to solve for the length of the skid marks. d=d= (Simplify your answer. Use integers or decimals for any numbers in the expression.)

Studdy Solution

STEP 1

What is this asking? We're given a formula that tells us how fast a car was going based on its skid marks and friction, and we need to rewrite it to tell us how long the skid marks are based on the speed and friction. Watch out! Don't forget to keep track of what you're solving for!
It's easy to get mixed up when rearranging formulas.

STEP 2

1. Isolate the square root
2. Isolate dd

STEP 3

We start with our speed formula: s=15.9dfs = 15.9 \cdot \sqrt{d \cdot f}

STEP 4

To **isolate** the square root term, we **divide** both sides by **15.9**: s15.9=15.9df15.9\frac{s}{15.9} = \frac{15.9 \cdot \sqrt{d \cdot f}}{15.9} s15.9=df\frac{s}{15.9} = \sqrt{d \cdot f}Remember, we're doing this because we want to get dd by itself!

STEP 5

To get rid of the square root, we **square** both sides of the equation: (s15.9)2=(df)2\left(\frac{s}{15.9}\right)^2 = (\sqrt{d \cdot f})^2 s215.92=df\frac{s^2}{15.9^2} = d \cdot f

STEP 6

Now, we **divide** both sides by ff to finally **isolate** dd: s215.92f=dff\frac{s^2}{15.9^2 \cdot f} = \frac{d \cdot f}{f} s215.92f=d\frac{s^2}{15.9^2 \cdot f} = d

STEP 7

Let's **calculate** 15.9215.9^2: 15.92=252.8115.9^2 = 252.81 So, our formula becomes: d=s2252.81fd = \frac{s^2}{252.81 \cdot f}

STEP 8

Our final formula for the length of the skid marks is: d=s2252.81fd = \frac{s^2}{252.81 \cdot f}

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