Exercise 35 Page 248

Practice makes perfect

a We are given an equation for the velocity v of a roller coaster at the bottom of a hill with height h.

v=sqrt(64h) To simplify this expression, we will first split the radicand into factors and then we will use the Product Property of Square Roots.

v=sqrt(64h)

SplitIntoFactors

Split into factors

v=sqrt(8*8* h)

ProdToPowTwoFac

a* a=a^2

v=sqrt(8^2* h)

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

v=sqrt(8^2)* sqrt(h)

SqrtPowToNumber

sqrt(a^2)=a

v=8sqrt(h)

b We want to determine the velocity of the roller coaster at the bottom of a 134-foot hill. To do so, we will substitute h= 134 into the simplified form of the equation.

v=8sqrt(h)

Substitute

h= 134

v=8sqrt(134)

UseCalc

Use a calculator

v=92.606695...

RoundDec

Round to 1 decimal place(s)

v≈ 92.6

Therefore, the velocity is about 92.6 feet per second.

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Exercises p.248-250

Exercise 35 Page 248

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