# The depth of the well if the total time is 3 s. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.5, Problem 119E
To determine

## The depth of the well if the total time is 3 s.

Expert Solution

The depth of the well if the total time is 3 s is 132.6ft_.

### Explanation of Solution

Given:

The total time elapsed between dropping the stone and hearing the splash is t1+t2=d4+d1090 where, t1 is the time takes for the stone to fall, t2 is the time takes for the sound to travel back up and d is the depth of the well.

Formula used:

The solution of a quadratic equation of the form ax2+bx+c=0,a0 can be obtained by using the quadratic formula x=b±b24ac2a.

Calculation:

Total time elapsed between dropping the stone and hearing the splash is 3s.

Substitute 3 for t1+t2 in the above t1+t2=d4+d1090 to obtain the depth of the well if the total time is 3 s.

3=d4+d10903=545d+2d21802d+545d=3×21802d+545d=65402(d)2+545d=6540

Let x=d.Substitute x for d in the above equation

2(x)2+545x=65402x2+545x6540=0

Use Quadratic formula to find value of x.

Substitute 2 for a, 545 for b and 6540 for c in the quadratic formula.

x=545±(545)24×2×(6540)2×2=545±297025+523204=545±3493454x=545±591.054

Simplify the above equation as follows.

x=545+591.054or x=545591.054x=46.054or x=1136.054x=11.512or x=284.01

Note that, the distance can’t be negative.

Therefore, x is equal to 11.512.

Substitute d for x in x=11.512 and solve for x.

d=11.512(d)2=(11.512)2d=132.6

Thus, the depth of the well if the total time is 3 s is 132.6ft_.

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