3.9. (12, 1) This question has several pons that must be completed sequentially.

Question

3.9. (12, 1)

This question has several pons that must be completed sequentially. If you skip a part or the Question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate or 14 ft^3/min, how fast is the water level rising when the water is 7 inches deep? Let h be the water's height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h. 3/1 =

Explanation / Answer

3/1 =b/h

=>b =3h

volume of water in trough V=(1/2)*b*h*10

V=5bh

V=5(3h)h

V=15h2

differentiate with respect to time

dV/dt =15*2h*dh/dt

dV/dt =30hdh/dt

volume of water added at 14ft3/min => dV/dt =14

water is 7inches deep =>h=7/12 ft

14=30(7/12)dh/dt

dh/dt=14*12/(30*7)

dh/dt=0.8

water level rising at 0.8 ft /min

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.