Fluid Force on an Isoceles Trapezoid

A vertical gate in a dam has the shape of an isoceles trapezoid. The top of the gate measures 10 feet across, the gate is 11 feet below the surface of the water, the gate is 7 feet high, the bottom of the gate is 8 feet across. Find the fluid force on the gate.

Coordinates of a centroid of a plane region

NOTE: I need to see how to find the centroid coordinates by using integrals and moments. I have attached a word document w/ the formulas we are supposed to use to find the centroid. Now here is the problem: Given: y = 9 - x^2, y = 2 Find the coordinates of the centroid of the above plane region.

Fluid force - Applications of Integration

NOTE: We are supposed to find the fluid force using integrals. I have attached a word document with the fluid force formula we are supposed to use. Please use the US system of measurement (i.e. pounds) Now here is the problem: A vertcial gate in a dam has the shape of an isoceles trapezoid. The top of the gate measures 10 ...continues

spring compression using hooke's law

NOTE: we are supposed to find the work using integrals and Hooke's Law. I have attached the formula and Hooke's Law in a word document. The problem: A 1,000 lb force compresses a spring 5 inches from its natural length of 20 inches. Find the work done by compressing the spring an additional 2 inches. The answer I got is ...continues

Area of a surface of revolution

NOTE: we are supposed to use the definition of the Area of a Surface of Revolution to solve this problem. I have attached this formula in a word document. The problem: Given: y = -x^2 + 4x defined on the closed domain [0,4] Revolve the graph about the x-axis. Find the area of the surface obtained.

center of mass for a plane region

I need to see how to find the centroid coordinates by using integrals and moments. I have attached the formulas to use and the answers I received in a word document. The answer I keep getting is (0,4.79) Here is the problem: Given: y = 9 - x^2, y = 2 Find the coordinates of the centroid of the above plane region. Th ...continues

Surface of the area of revolution

We are supposed to use the definition of the Area of a Surface of Revolution to solve this problem. I have attached this formula and the answers I received in a word document. The problem: Given: y = -x^2 + 4x defined on the closed domain [0,4] Revolve the graph about the x-axis. Find the area of the surface obtained ...continues

How to write line equation knowing the points

Write an equation and sketch a graph of the line through the points (-4,-3) and 3,12)

Solving trigonometric identities.

Solve for x: a) sin(^2)x=cosx-1 b) sin2x=cosx c) sin2x=2sinx

Calculating the limits of a sequence.

Use two methods to calculate the limit of the following sequence. x(n)=1/n^3+2^2/n^3+...+n^2/n^3