SOLUTION: When a stone is dropped into a deep well, the number of seconds until the sound of a splash is heard is given by the formula t= sqrt (x)/4+x/1100, where x is the depth of the well
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Question 1113670: When a stone is dropped into a deep well, the number of seconds until the sound of a splash is heard is given by the formula t= sqrt (x)/4+x/1100, where x is the depth of the well in feet. For one particular well, the splash is heard 14 seconds after the stone is released. How deep (to the nearest foot) is the well? Answer by ikleyn(52787) (Show Source):
14 = +
Let y = be new variable. Then the equation takes the form
14 = + .
Multiply both sides by 1100 to get
= 0
= = .
Only positive root works y = = 47.7.
Then x = = 2275.3 ft.
Check. + = 14.
Answer. The depth of the well is equal to 2275.3 ft.
