Math Answers

The displacement, 

y(m), of a body in damped oscillation is y=2e^-t sin sin 3t . 

The task is to:

1.  Use the Product Rule to find an equation for the velocity of the object if v=dy/dt.

The width of rectangle is 25% shorter than the length. If the perimeter is 21. Find the are of the rectangle

Prove that integral of 0 to pie √x e^-x3 dx = √pie/3

Initial 100 milligram of a radio active substance was present.After 6 hour the mass has been decreased by 3%. If the rate of decay is proportional to the amount of the substance present at time t,find the amount remaining after 24hours.

y'''+4y'=e^x cos2x write the given differential equation in the form pf L(y)=g(x),where L is a linear differential operator with constant .IF possible , factor L.

Two industrial plants, 𝐴𝐴 and 𝐵𝐵, are located 15 miles per apart and emit 75 ppm (parts per

million) and 300 ppm of particular matter, respectively. Each part is surrounded by a restricted

area of radius 1 mile in which no housing is allowed, and the concentration of pollutant arriving

at any other point 𝑄𝑄 from each plant decreases with the reciprocal of the distance between that

plant and 𝑄𝑄. Where should a house be located on a road joining the two plants to minimize the

total pollution arriving from both plants?

A cylindrical can is to be constructed to hold a fixed volume of liquid. The cost of the

material used for the top and bottom of the can is 3 cents per square inch, and the cost of the

material used for the curved side is 2 cents per square inch. Use calculus to derive a simple

relationship between the radius and height of the can that is the least costly to construct.

y''-8y'+20y=100x²-26xe^x solve the given differential equation by undetermined cofficient

Find the solutions of the equation if 0≤𝑡<2𝜋

tan^2 𝑡−1=0

A pendulum of length 10 cm has swung so that θ is the radian measure of the angle formed by the pendulum and a vertical line. Find h in terms of θ