# SOLUTION: 1. Oil is dripping from a pipe at a constant rate and forms a circular pool. The area of the pool is increasing at 15cm^2/s. Find, to 3 significant figures, the rate of increase of

Algebra ->  Algebra  -> Test  -> Lessons -> SOLUTION: 1. Oil is dripping from a pipe at a constant rate and forms a circular pool. The area of the pool is increasing at 15cm^2/s. Find, to 3 significant figures, the rate of increase of      Log On

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 Click here to see ALL problems on test Question 163286: 1. Oil is dripping from a pipe at a constant rate and forms a circular pool. The area of the pool is increasing at 15cm^2/s. Find, to 3 significant figures, the rate of increase of the radius of the pool when the area is 50cm^2. 2. The region enclosed by the curve with equation y^2=16x, the x-axis and the lines x=2 and x=4 is rotated through 360º about the x-axis. Find, in terms of π, the volume of the solid generated. 3. A particle P moves in a straight line. At time t seconds, the displacement, s metres, of P from a fixed point O of the line is given by s=2tcost+t^2. Find, in m/s to 3 significant figures, the velocity of P when t=3.Answer by Edwin McCravy(8906)   (Show Source): You can put this solution on YOUR website! 1. Oil is dripping from a pipe at a constant rate and forms a circular pool. The area of the pool is increasing at 15cm^2/s. Find, to 3 significant figures, the rate of increase of the radius of the pool when the area is 50cm^2. ``` >>...The area of the pool is increasing at 15cm^2/s...<< That says . So we substitute that and we have: But we also have to substitute when So we have to calculate from when to find out what is then. So we substitute that in: Answer: ``` 2. The region enclosed by the curve with equation , the x-axis and the lines x=2 and x=4 is rotated through 360º about the x-axis. Find, in terms of π, the volume of the solid generated. ``` First we draw the graph of the parabola . Taking square roots, we see this is really two graphs and Next we'll draw in the vertical lines and : Now we'll erase everything that is not involved in the rotation about the x-axis. That leaves only the graph of between and and the x-axis. We draw a slender rectangle as an element of area . Label the top point of the element (x,y), and the height of it y: The formula for the volume of a vertically rotated function using the disk method is: The height of that tiny rectangle is y and its width is dx. It is the height of that rectangle that will rotate about the x-axis, so the radius of rotation is y. The leftmost value of x is 2 and the rightmost value of x is 4. Then we replace y by ``` 3. A particle P moves in a straight line. At time t seconds, the displacement, s metres, of P from a fixed point O of the line is given by . Find, in m/s to 3 significant figures, the velocity of P when t=3. ``` The velocity of P is the derivative of the displacement s with respect to time t, that is, . When When calculating that be sure your calculator is in radian mode, not degree mode. Explanation of the negative sign: Suppose the line on which P is moving is horizontal. If a positive velocity means that P is moving to the right, then a negative velocity means that P is moving to the left. So this negative velocity only indicates that at the exact instant when 3 seconds have passed, P is moving left. Edwin```