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Use the Laplace transform to solve the following differential equations:
1. y'+6y=2*t+3, y(0)=1
2. y'-2*y=exp(-t)*cos(t) , y(0)=-2
3. y''-y=2*t , y(0)=0, y'(0)=-1
Show every single steps, must use Laplace transform to solve the problems
Express the area of the triangle in terms of x only. Find A '(x). Find the critical point for x > 0. Find the maximum area of the triangle. Give an exact answer.
1. What circumstances might you need to conduct qualitative market research data on behalf of your organisation or an organisation for which you consult? 2. Why would you choose to conduct qualitative rather than quantitative research?
Please outline the specific problem, your solution and how the specific problem solving guidelines were applied. Be sure to carefully tell us how you applied each of the guidelines to your problem.
If an open box has a square base and a volume of 110 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. (Round your answers to two decimal places.)
the mean of a normal distribution is 400 pounds.nbsp the standard deviation is 10 pounds.a. what is the area between
Explain using the Mean Value Theorem how you know that this operator did in fact exceed the safe speed of 70 mph between the two checkpoints.
Use the Lagrange-method to calculate the maximal production given that the cost is $128. How many units of capital and labor will the company use?
The opening of the cannon pictured at the left is 16 feet above the ground. The daredevil, who is shot out of the cannon, reaches a maximum height of 55 feet after about 1.56 seconds and hits a net that is 9.5 feet off the ground after 3.25 second..
Convert the rectangular point (x, y, z) = (3√3, 3, 4) into cylindrical (r, θ, z). Convert the spherical point (ρ, θ, Φ) = (10, π/2, π/6) into rectangular (x, y, z).
Sound intensity, known as decibels, d, is calculated using:d = 9.8log IaI is the intensity per unit of area. a is faintest audible sound of the average human ear.
Use the Internet to obtain recent crash-safety ratings for passenger vehicles. Then answer these 4 questions:
Two weather tracking stations are on the equator 146 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and on a bearing of N 23°E from the eastern station. How far is the balloon from the western station?
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