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McGraw Hill Glencoe Algebra 2, 2012 View details

1. Multiplying and Dividing Rational Expressions

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Exercise 75 Page 537

Use the formula L=10log( I10^(- 12)), where L is the loudness of the sound and I is its intensity to calculate the intensity of each sound.

About 50 times.

Practice makes perfect

Recall the following formula. L=10log(I/10^(- 12)) Here L is the loudness of the sound expressed in decibels, and I is its intensity. Note that if the base of a logarithm is not stated, it means it is ten. We will use this formula to calculate the intensities of the noise allowed during the day and the noise allowed at night.

Noise During the Day

We know that the noise during the day cannot exceed 72 decibels. Let's find the intensity corresponding to this loudness.

L=10log(I/10^(- 12))

Substitute

L= 72

72=10log(I/10^(- 12))

▼

Solve for I

RearrangeEqn

Rearrange equation

10log(I/10^(- 12))=72

DivEqn

.LHS /10.=.RHS /10.

log(I/10^(- 12))=7.2

10^(LHS)=10^(RHS)

10^(log( I10^(- 12)))=10^(7.2)

10^(log(m))=m

I/10^(- 12)=10^(7.2)

MultEqn

LHS * 10^(- 12)=RHS* 10^(- 12)

I=10^(7.2)* 10^(- 12)

MultPow

a^m*a^n=a^(m+n)

I=10^(- 4.8)

The intensity of the maximum noise allowed during the day is 10^(- 4.8).

Noise at Night

We know that the noise at night cannot exceed 55 decibels. Again, let's find the intensity corresponding to this loudness.

L=10log(I/10^(- 12))

Substitute

L= 55

55=10log(I/10^(- 12))

▼

Solve for I

RearrangeEqn

Rearrange equation

10log(I/10^(- 12))=55

DivEqn

.LHS /10.=.RHS /10.

log(I/10^(- 12))=5.5

10^(LHS)=10^(RHS)

10^(log( I10^(- 12)))=10^(5.5)

10^(log(m))=m

I/10^(- 12)=10^(5.5)

MultEqn

LHS * 10^(- 12)=RHS* 10^(- 12)

I=10^(5.5)* 10^(- 12)

MultPow

a^m*a^n=a^(m+n)

I=10^(- 6.5)

The intensity of the maximum noise allowed at night is 10^(- 6.5).

Comparison of the Intensities

The noise level allowed during the day has an intensity of 10^(- 4.8). The noise level allowed at night has an intensity of 10^(- 6.5). We want to know how many times as intense is the noise level allowed during the day than at night. 10^(- 4.8)/10^(- 6.5) Let's simplify the above expression.

10^(- 4.8)/10^(- 6.5)

DivPow

a^m/a^n= a^(m-n)

10^(- 4.8-(- 6.5))

SubNeg

a-(- b)=a+b

10^(- 4.8+6.5)

AddTerms

Add terms

10^(1.7)

UseCalc

Use a calculator