8. a. Let y(t) be the amount of a radiactive material with relative decay rate k. Let Q(t) be the decay rate. Use the differential equation for y (not the solution formula) to show that the quantity Q also undergoes exponential decay with rate constant k. b. It is sometimes easier to measure the rate of radioactive decay t
Question (1) What is the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = 5 - x^2 around the X-axis. Question (2) Find the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = Tan x about the x-axis from x = 0 to x = pi/4. See attached file
Using the method of undetermined coefficients to find the particular solution of the nonhomogeneous equation, find the solution of the following d.e. satisfying the given initial conditions y"+4y=x^2+3e^x y(0)=0 y'(0)=2
Q1(c) (ii) Use the Cauchy-Riemann Equations to show that the function f (x + iy) = x2 + 4y + y2 + i3xy + i4x is differentiable only at 8i/5.
Please see the attached file for the fully formatted problems.
Given that y1(x)=e^-x is a solution of y'' + 2y' + y =0, find second solution using the method of reduction of order. I substituted y =ve^-x so y' = v'e^-x - v^-x; y''= v''e^-x -v'e^-x +v e^-x I came out of that with v''e^-x + v'e^-x =0 I think the next step is to seperate variables. Looking for help to finish the pro
Determine the number of units x for which marginal revenue is equal to marginal cost. R(x) = 240x - 0.02x2 C(x) = 210x
In April 1990, the population of Phoenix was 983,403. In April 2000, the population of Phoenix was 1,321,045. What was the average rate of increase in population per year?
Use implicit differentiation to find an equation of the line tangent to the curve x^3+2xy+y^3 = 13 at the point (1,2).
Show that: lim (x+y)=o as x and y approach zero; using the epsilon-delta definition Also, show that: lim f(x)=1 as x approaches zero; using the epsilon-delta definition. **Note: x is a vector in this case, with a right arrow going over it. It is not just "x".
Let G(x) = Int(0..x, (Int(0..s, f(t)dt)) , ds), where f is continuous for all real t. Find a) G(0) b) G'(0) c) G''(x) d) G''(0)
Problem states " if L[y] =ay'' +by' +cy, where a,b,and c are constants, compute L[e^rx], where "r" is constant. Is this just a matter of substituting for "y"? Please work out, thanks!
Please see the attached document to view this problem formatted properly. Evaluate the limit: lim 1/(x - 2) x --> 2
Please see the attached file for the fully formatted problems.
Please see the attached file for the fully formatted problems. Evaluate the limit lim _x2 + 3x - 1__ x ∞ x2 - 5x + 2
Please see the attached file for proper formatting. Evaluate the limit: lim 1/x x --> - inf. Include all steps required for solving.
Two springs are attached in series as shown in Figure 5.42. If the mass of each spring is ignored, show that the effective spring constant k ot the system is defined by I/k = I/k + I/k2. A mass weighing W pounds stretches a spring 1/2 foot and stretches a different spring 1/4 foot. The two springs are attached, and the mass is
(See attached file for full problem description)
Question 4 (30 marks) Clauser's experiment II is the background to this question. The objective is to find an approximate analytical solution for an equilibrium ( = constant) turbulent flow. The free stream velocity at the edge of the boundary layer and the measured values of friction coefficient, Cf are given against di
(See attached file for full problem description).
D2y/dx2 + x^2 y =0
In Problem 42 solve the given initial-value problem in which the input function gx) is discontinuous. (Hint: Solve each problem on two intervals, and then find a solution so that v and y' are continuous at x = pi (Problem 42).) 42. y" ? 2y' + 10y= g(x), y(O) = 0, y'(0) = 0, where g(x)={20 0<x<pi {0 x>pi
(See attached file for full problem description) f(x)=x+[|x^2|]-[|x|]
Please see attached file for full problem description. As you can see I understand the format but not how to substitute the values from the original equation and then simplify.
(e^x+1) dy/dx=y-ye^x Problem is separable, solve for "y".
(See attached file for full problem description) I have one question and I am looking for an accurate answer with full working (and diagrams if necessary).
(x+e^y)dy-dx=0 This is linear in "x". Can you show how it is integrated to the proper answer?
D2y/dt2 - 4 dy/dt = 6 e^3t -3e^-t y(0)=1 y'(0)-1
(See attached file for full problem description) Solve initial value problem y(0)= -3
(See attached file for full problem description)