To adeebnafees: A solid cone is taken out of a solid hemisphere. The radius of the hemisphere is 7cm. The radius of the cone is 4cm and the height of the cone is 3.5cm. Calculate the volume of the remaining solid. (π = 22/7)
AdeebNafees: True, tnk.
AdeebNafees: Volume of hemisphere is half that of a sphere of same radius   (reply)
AdeebNafees: Volume of hemisphere = 0.5*4/3*π*7^3  (reply)
AdeebNafees: Volume of cone is 1/3*π*16*3.5  (reply)
AdeebNafees: Subtract 1/3*π*16*3.5 from 0.5*4/3*π*7^3  (reply)
AdeebNafees: That's 650 something  (reply)
AdeebNafees: 659.73  (reply)
AdeebNafees: Probably.  (reply)

To AdeebNafees: Given the function y = (x^3)/3 + (1/2)x^2 - 6x + 4. Find the coordinates of the maximum and minimum points of the function.
AdeebNafees: We find the first derivative first because why not  (reply)
AdeebNafees: y' = x^2 + x - 6  (reply)
AdeebNafees: The value of this should be zero at both the maximum and minimum points  (reply)
AdeebNafees: So now we need to see when this becomes 0  (reply)
AdeebNafees: x^2 + x - 6 = 0  (reply)
AdeebNafees: Roots will be x = -3 and 2, acully  (reply)
AdeebNafees: I've seen this equation tons of times  (reply)
AdeebNafees: So at x = -3 and 2, we have the maxima and minima  (reply)
AdeebNafees: To figure out which is which, we find the second derivative of y  (reply)
AdeebNafees: y'' = 2x + 1  (reply)
AdeebNafees: Value at x = -3 is -5 < 0  (reply)
AdeebNafees: Less than zero means we have lower values on either side  (reply)
AdeebNafees: Hmm  (reply)
AdeebNafees: So x = -3 is the maximum  (reply)
AdeebNafees: Since the question states both a maximum and a minimum, the remaining point must be a minimum  (reply)
CalmWaters: WHAT THE LITERAL ****
AdeebNafees: So the minima is x = 2  (reply)
AdeebNafees: Now, we need y for these two points  (reply)
AdeebNafees: These are obtained by plugging in values in y  (reply)
AdeebNafees: y = 35/2 when x = -3  (reply)
AdeebNafees: y = -10/3 when x = 2  (reply)
AdeebNafees: Therefore required coords: (-3, 35/2), (2, -10/2)  (reply)