anonymous
  • anonymous
A trough is 14 ft long and its ends have the shape of isosceles triangles that are 2 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 8 ft3/min, how fast is the water level rising when the water is 9 inches deep?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
hello
anonymous
  • anonymous
let x be length of water filled from bottem. so length of water surface at cross section =2x(using similar triangle) now volume of water filled V=(1/2)(x)(2x).14=14x^2 dV/dx=28x (dV/dt).(dt/dx)=28x dt/dx=28x.(dt/dV) now put the values from question dt/dx=28(9/12).1/8 dx/dt=24/63. ans .... water level increases at the rate of 24/63 ft /min
anonymous
  • anonymous
Thanks

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