![]() ![]() The rate of change for height is 1/6 cubic feet/min at 2 min. ![]() Take derivative of volume with respect to time to find equation for rate of filling the trough. Using properties of isosceles right triangle and tan: ![]() This part would be a lot easier with a diagram, but unfortunately I can't upload one. We're interested in height so we will substitute out base with height. Length or l is a constant at 9, so we can sub it in the equation.īase and height of the filled trough at any time is related by trigonometry. All units match so I will work with numbers only. Find the volume of this solid.First let's find the Volume of the trough, I assume it's an inverted triangle where the sides are equal since the diagram is not shown. This solid, each cross section perpendicular to the y-axis is a rectangle with height four times the
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