Parametric Equation of a Ferris Wheel

A ferris wheel with radius of 70 feet takes 420 seconds to rotate once. Center is (0,70). Write a parametric equation to satisfy this ferris wheel.

Derivatives: Minimizing Time and Distance

A lighthouse is 30 miles off a straight coast and a town is located 25 miles down the sea coast. Supplies are to be moved from the town to the lighthouse on a regular basis and at a minimum time. If the supplies can be moved at a rate of 4 miles per hour on water and 40 miles per hour on land, how far from the town should the do ...continues

Stable and Unstable Equilibria

Which equilibria is stable and which is unstable? Please see attached file for full problem description.

Linearization

Find the linearization, L(x) of f(x) at x = -7 f(x) = sqrt(x^2 + 15).

Percentage Error of an Estimation

How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?

Lower Estimate, Upper Estimate?

Please see the attached file for the fully formatted problems. 14) A power plant generates electricity by burning oil. Pollutants produced as a result of the burning process are removed by scrubbers in the smokestacks, Over time, the scrubbers become less efficient and eventually they must be replaced when the amount of pol ...continues

Area of Region

Find the area of the region bounded by the following graphs: y=x^2 ; y=8-x^2 ; and y=x^2+6. I first figured out the area of (8-x^2) minus (x^2) using integral from -2 to 2 and found 64/3 . Then I figured out the area of (8-x^2) minus (x^2+6) using integral -1 to 1 and found 4. I then just subtracted these two regions fr ...continues

Volume of Revolution about X-axis

Given the region bounded by y=x^2 and y=-4x+12 and y=0 , find the volume of the solid generated by rotating this region about the x axis. I found a volume of 477pi/5 or approx. 300, does this sound right?

The Length of a Curve

Using the curve y=2x^(3/2) +3 (3/2 is the power on x) from x=0 to x=4 : A.) estimate the length of the curve by computing the straight line distance between the endpoints. *I found the answer to be sq root of 272 or approx. 16.4924. Sound correct? B.) Compute exact length of the curve. *I'm using S = The Integral ...continues

Work Done to Pump Water out of a Tank

A tank is in the shape of an inverted cone (pointy at the top) 6 feet high and 8 feet across at the base. The tank is filled to a depth of 3 feet. How much work is done in emptying the tank through a hole at the top? (Weight density of water is 62.4 lb/ft^3). *I found the distance to be 6-y and used the disk method to solve ...continues