1) A right triangular plate of base 8.0 m and height 4.0 m is submerged vertically, find the force on one side of the plate. (W = 9800N/m^3)?

2) The cable of a bridge can be described by the equation y = 0.06x^(3/2) from x = 0 to x = 200 ft. find the length of the cable?

3) A conical tank is resting on its apex. The height of the tank is 10 ft, and the radius of its top is 7 ft. the tank is full of gasoline weighing 45 lb/ft. how much work will it take to pump the gasoline to the top? Give your answer to the nearest ft . lb?

4) a tank truck hauls oil in a 12-ft- diameter horizontal right circular cylindrical tank. If the density of the oil is 60 lb/ft^3, how much farce does the oil exert on each end of the tank when the tank is half full?

5)a rectangular sea aquarium observation window is 16.0 ft wide and 4.00 ft high. What is the force on this window if the upper edge is 5.00 ft below the surface of the water? The density of sea water is 64.0 lb/ft^3.

Thank you for help

Solution Summary

There are five calculus problems here: the force on one side of the plate, the length of the cable, work pumping gasoline, force of oil at a given density, and force on a window below water level

Question 4
Find the work done by the force
F (x,y,z) = -x^2y^3 i + 4j + xk
on moving charged electric particle along the path given by the equation
r (t) = 2cos t i + 2sintj + 4k,
where the parameter t varies from pi/4 to 7pi/4.
Question 5
Displacement of the spring system with friction is described by the differenti

Using the Fundamental Theorem of Calculus I need to find the solution of the following problems. Can you explain how?
Please see the attached file for the fully formatted problems.

Please see the attached file for full problem description.
Please use work concepts for solution. The solution should involve integration from 2 to 0 distance block travel.
Please detail any calculus involved - if the response doesn't involve calculus, I would still like to see it, but please explain why since I am fairl

Please see the attached file for the fully formatted problems.
1. Use an iterated integral to find the area of a region...
2. Evaluate the double integral...
3. Use double integral to find the volume of a solid...
4. Verify moments of inertia...
5. Limit of double integral...
6. Surface area...
7. Triple integral...

This solution shows how to solve for various calculus problems, including differentiation of functions using the product rule, the quotient rule, and the chain rule, as well as how to calculate integrals.

A person removes a 10.5 kg stereo amplifier from a shelf that is 1.82 m high. The amplifier is lowered at a constant speed to a height of 0.75 m. What is the work done by
(a) the person
(b) the gravitational force that acts on the amplifier