### Inverse Laplace Transformation : g(t) = L^-1(G)(t) when G(s)=(1-e^-s)/(s+2)

Find the Laplace transform of g(t) = L^-1(G)(t) when G(s)=(1-e^-s)/(s+2) and create a piecewise definition of the solution.

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Find the Laplace transform of g(t) = L^-1(G)(t) when G(s)=(1-e^-s)/(s+2) and create a piecewise definition of the solution.

I think the solution is probably a simple modification to the predation equations: dN/dt = rN - cNP is the growth rate for the prey population and dP/dt = -dp + gcNP is the growth rate for predator population, where: N= prey density P = predator density d= death rate g = conversion efficiency of prey to predators r = p

For time t between 2 and 3 hours the radius of circle c is 5t-t^2-6 feet. at time t=2.6 hours the area of the circle is changing at a rate of ------. at time 2.6 hours the area of the circle is-----. a(t) = pie(5t-t^2-6)squared

Theorem 8.3. Assume P and Q are continuous on an open interval I. Choose any point a in I and let b be any real number. Then there is one and only one function y = f(x) which satisfies the initial value problem y' + P(x)y = Q(x), with f(a) = b on the interval I. This function is given by the formula f (x) = be- A( x) + e-A( x

1960 88 1970 121 1980 152 1990 205 1997 217 a) Model the data with two linear function. Let the independendt variable represent the number of years after 1960. b) With each function found in part a), predict the amount of maunicipal solid waste in 2005. c) Which of the two models

Using uniqueness theorem, what can you conclude about the solution to the equation with the given inital conditions? dy/dt = f(y) y1(t) = 4 for all t is a solution y2(t) = 2 for all t is a solution y3(t) = 0 for all t is a solution inital condition y(0) = 1

DVc/dt = ( V(t) - Vc ) / ( RC) Supposed V(t) = 2cos(3t). If R = 4 and C = 0.5, use Eulers method to compute values of the solutions with the given inital conditions over the interval 0 <= t <= 10 for Vc(0) = -1

Sand falls from an overhead hopper to form a right circular cone. If the cone formed has an angle theta find the rate of change of volume with respect to height? If the height is changing at 2cms per minute, what volume of sand is falling from the hopper when the height of the cone is 3 meters? (The volume of a cone is (1/3)pir2

You are standing on a cliff 200 feet high. How long will it take a rock to reach the ground if a) you drop it? b) you throw it downward at an initial velocity of 40 feet per second? c) How far does the rock fall in 2 seconds if you throw it downward with an initial velocity of 40 feet per second?

To get to work Sam jogs 3 Kilometers to the train, then rides the remaining 5 kilometers. If the train goes 14 kilometers per hour faster than Sam's constant rate of jogging and the entire trip takes 45 minutes, how fast does Sam jog?

Find the volume of the solid generated when the region y=x^-1/2 on the interval [1,4] is revolved about a)x-axis b) y-axis c) the line y=-2

Please see the attached file for the fully formatted problems.

Several questions: 1. If a ball is thrown straight up in the air with an initial velocity of 90 ft/s... (See attached file for full problem description)

The derivative of 1/sqrt(x) is -1/2(x^3/2), Give the equation of the NORMAL line at x=1

1. Find the intersection point of the line (x-1)/2=(y+1)/3=z-2 and the plane 2x+y-z=17. 2. Find the distance from point Q(1,-2,3) to the plane 2x-y-z=6. Need steps and solutions.....Thanks!

1. Find an equation for the line passing through the points P(1,-1,1) and Q(3,1,-2). 2. Find an equation for the plane containing points P(1,0,0), Q(0,-1,0), and R(0,0,-1). Need steps and solutions. Thanks a bunch!

Please help...this is a revision question very likely to appear in my exam next month but I do not understand it! (See attached file for full problem description)

A radiator contains 10 quarts of fluid, 30% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 40% antifreeze?

If you borrow $500 from a credit union at 12% annual interest and $250 from a bank at 18% annual interest, what is the effective annual interest rate (that is, what single rate of interest on $750 would result in th same total amount of interest)?

A merchant has 5 pounds of mixed nuts that cost $30. He wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. How many pounds of peanuts are needed?

I already solved the homogeneous portion, and I need help solving the particular solution and of course combining the two to get the entire solution to the differential equation. Not too difficult - see attachment. Please use equation editor if possible. Thank you. --- Given that: dMS/dt = m(MN - MS) - pMS¬

(See attached file for full problem description) --- Find the radius of convergence of the following series...(see attachment for equation) ---

1). Define T : C[0,1] --> C[,1] by (Tx)(t) = 1 + integral from 0 to 1 x(s)ds. Is T a contraction? ( Please justify every step and claim, I want a proof not a yes or no only). P. S. I believe C[0,1] is the set of all the continuous functions on [0,1]. 2). Consider the operator in C[0,1], Ty(t) = integral from 0 to t (t-s)*

This question relates to a section that deals with basic vector calculus and introduces partial derivatives. Here is the question: Consider the scalar field (pressure field) given by f(x,y,)=9x^2 +4y^2. Q: Find the isobars (curves of constant pressure) and sketch some of them.

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.

Consider the graph of f(x): a)Can you draw a graph of F(x), the antiderivative of f(x), where F(0) = 1. b) Draw a graph of f(x).

Need to find the antiderivatives. (See attached file for full problem description)

F(t) = 10,000 / 10 + 50e ^-0.5t HOW do I obtain the derivative? What is the "e" portion of the problem? I know the derivative = 250,000e^-0.5t/ (10+50e ^-0.5t)^2 Please describe in detail the steps taken to arrive at this answer. For example, Why is the top of the equation 250,000e^-0.5t? Why is the bottom (10+50e^-0

Consider the heat equation delta(u)/delta(t) = (delta^2)(u)/delta(x^2) Show that if u(c, t) = (t^alpha)psi(E) where E = x/sqrt(t) and alpha is a constant, then psi(E) satisfies the ordinary differential equation alpha(psi) = 1/2 E(psi) = psi, where ' = d/dE is independent of t only if alpha = - 1/2. Further, show th

Please see the attached file for the fully formatted problems.