SOLUTION: Speed of sound through water caries by temperature s=-0.0276t^2 + 9.1558t + 4354.7 (between freezing and boiling) s= speed in feet/second, t= temperature Fahrenheit I dropped

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Question 632564: Speed of sound through water caries by temperature
s=-0.0276t^2 + 9.1558t + 4354.7 (between freezing and boiling)
s= speed in feet/second, t= temperature Fahrenheit
I dropped a loud waterproof buzzer in the ocean. My friend who was 4700 feet away heard it 1 second later. What is the temperature of the water? (nearest degree fahrenheit)
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Speed of sound through water caries by temperature
s=-0.0276t^2 + 9.1558t + 4354.7 (between freezing and boiling)
s= speed in feet/second, t= temperature Fahrenheit
I dropped a loud waterproof buzzer in the ocean. My friend who was 4700 feet away heard it 1 second later. What is the temperature of the water? (nearest degree fahrenheit)
.
Set s to 4700/1 and solve for t:
4700 = -0.0276t^2 + 9.1558t + 4354.7
0 = -0.0276t^2 + 9.1558t - 345.3
Using the "quadratic equation" we get:
x = {43.4, 288.3}
Throw out the 288 because it is outside the boiling point leaving:
x = 43 degrees
.
Details of quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=45.70755364 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 43.3888373932807, 288.34304666469. Here's your graph:
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