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(Solution Library) (a) A cylindrical tank (standing upright with the circular base on the ground) of radius 2 ~m and height 10 ~m is empty. It is then filled

Question: (a) A cylindrical tank (standing upright with the circular base on the ground) of radius \(2 \mathrm{~m}\) and height \(10 \mathrm{~m}\) is empty. It is then filled with water at the rate of \(\sqrt{x} \mathrm{~m}^{3} / \mathrm{min}\), where \(x\) metres is the depth of the water in the tank.

  1. Find an expression for \(x(t)\) of the amount of water in the tank at any
    time \(t\).
  2. How long will it take to fill the tank completely?

(b) Solve the initial value problem

\[\frac{d y}{d x}+\frac{y}{x}=\frac{\sin x}{x}, \text { for } x>0 \text { and } y\left(\frac{\pi}{2}\right)=1\]

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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