Calculus Answers

Bottled water costs $0.72 for a 0.5 liter bottle. What would it cost to fill a bathtub with bottled water. The bathtub holds 7.28 cubic feet of water. (Recall that 1.00 inch = 2.54 cm, and that a liter is exactly 1000 cm3).

if a,b,c,d,e,f are non negative real numbers and a+b+c+d+e+f=1 then maximum value of ab+bc+cd+de+ef

If you travel 320miles in 1.6hrs calculate speed in: milometers hr, feet per second, kilometer per hour, centimeters per second

What is the limit, as h approaches 2,of (1/3-2/3h)/ (h-2)?

Solve for each of the following completely:

1. A water tank is in the form of an inverted right circular cone of height 12 m. and the radius of its circular opening is 6 m. If water enters the tank at a rate of 8 m3/hr, how fast is the water level rising when the water is 4m deep?

2. A spherical balloon is being made so that its volume is increasing at the rate of 8 ft3/min. Find the rate at which the radius is increasing when the balloon is 4 ft. in diameter.

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Sketch the region R bounded by the curves y = x, x = 2 y^2 and y = 0.
b. Indicate the method you use to set up the integrals (do not integrate) that give
the volume of the solid generated by rotating the region R around
i. the x-axis
ii. the y-axis
iii. the line x = 2
iv. the line y = 1.

minimum number of unequal vectors whose sum is equal to zero is what? and how?

Log I = Log 10^-16 + 9....Im having trouble solving for I. I understand Log 10 to any power is that number (in this case, -16). But I still am having trouble solving for I

Draw the graph of y=1-(x^3)/2
a) Choose a point S1 on the graph at which the tangent at S1 meets the graph again at another point T1 . Use the graph to estimate the coordinates of T1.
b) using differentiation , find the gradients of the graph at S1 and T1.
c) find the ratio of the gradient of the graph at S1 to the gradient of the graph at T1.
d) repeat the steps (a) to (c) , choosing another three point S2 , S3 , S4 .
e) make a conclusion about the ratio of the gradient of the gradient of the graph at any point S to the gradient of the graph at T where T is another point of intersection of the graph and its tangent at S.