Exercise 13 Page 60

To find the speed of the car, we will use the given formula. 1/24 s^2= d Here, s is the vehicle's speed in miles per hour and d is the length of the skid marks in feet. We need to substitute 54 for d into this formula.

1/24s^2=d

Substitute

d= 54

1/24s^2= 54

MultEqn

LHS * 24=RHS* 24

s^2=1296

Notice that 1296 is the square of 36. Let's rewrite it so all terms are on the left-hand side and then factor it.

s^2=1296

WritePow

Write as a power

s^2=36^2

SubEqn

LHS-36^2=RHS-36^2

s^2-36^2=0

FacDiffSquares

a^2-b^2=(a+b)(a-b)

(s-36)(s+36)=0

To solve this equation, we will apply the Zero Product Property.

(s-36)(s+36)=0

ZeroProdProp

Use the Zero Product Property

lcs-36=0 & (I) s+36=0 & (II)

AddEqn

(I): LHS+36=RHS+36

ls=36 s+36=0

SubEqn

(II): LHS-36=RHS-36

ls_1=36 s_2=- 36

Since speed cannot be negative, we ignore the negative solution. The speed of the car is 36 mph.