A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 f

Question

A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at is deepest point. A cross-section is shown in the figure. If the pool is being filled at a rate of 1.2 ft3/min, how fast is the water level rising when the depth at the deepest point is 5 ft? (Round your answer to five decimal places.) ft/min Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 5 ft high? (Round your answer to two decimal places.) ft/min A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? rad/s

Explanation / Answer

1>rate=1.2/(20*(12+5*6/6+5*12/6)=0.0022 ft/min
2>v=1/3 pi r^2*h,h=2r

dh/dv=1/pi*h2

dh=40/(3.14*5^2)=0.50955

3>theta=arccos(100/200)

x=r*sin(theta)

dx/d=r*cos(theta)=200*100/200=100

d=8/100=0.08

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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