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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case -0.0276x%5E2%2B9.1558x%2B-345.3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%289.1558%29%5E2-4%2A-0.0276%2A-345.3=45.70755364.

Discriminant d=45.70755364 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9.1558%2B-sqrt%28+45.70755364+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289.1558%29%2Bsqrt%28+45.70755364+%29%29%2F2%5C-0.0276+=+43.3888373932807
x%5B2%5D+=+%28-%289.1558%29-sqrt%28+45.70755364+%29%29%2F2%5C-0.0276+=+288.34304666469

Quadratic expression -0.0276x%5E2%2B9.1558x%2B-345.3 can be factored:
-0.0276x%5E2%2B9.1558x%2B-345.3+=+-0.0276%28x-43.3888373932807%29%2A%28x-288.34304666469%29
Again, the answer is: 43.3888373932807, 288.34304666469. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.0276%2Ax%5E2%2B9.1558%2Ax%2B-345.3+%29