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Use the differential equation for y (not the solution formula) to show that the quantity Q also undergoes exponential decay with rate constant k.
Find the length of the graph of y = 1/3 x3/2 - x1/2 from (1, - 2/3) to (4, 2/3).
Find a function f(x) = x^k and a function g such that f(g(x)) = h(x) = v(3x+ x2)
Consider two tanks, labeled Tank A and Tank B. Tank A contains 100 gallons of solution in which is dissolved 20 lbs of salt.
Find the present value and future value of an income stream of $1000 a year, for a period of 5 years, if the interest rate is 8%.
Determine the shape assumed by the surface of a liquid being spun in a circular bowl at constant angular velocity, W.
What dimensions will maximize the enclosed area? Be sure to verify that you have found the maximum enclosed area.
An object having a mass of 1 kg. is suspended from a spring with a spring constant (k) of 24 Newtons/meter.
Suppose that the cost of preventive maintenance increases as the weeks between the preventive maintenance increases.
The second way, find the inverse LaPlace transform of 1 / s2 using the integration theorem, and then apply the s-shift theorem.
Write the Taylor series with center zero for the function f(x) = In(1 + x2). Compute the first-order partial derivatives of f(x, y) = 2x/ x - y
Find the zero of the linear function f(x)=3x-12 , find the zeros and state the multiplicity of each.
A box with its base in the xy-plane has its four upper vertices on the surface with equation z = 48 - 3x^2 - 4y^2 . What is the maximum possible volume.
A spring with a 4-kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N.
How do you find the x, y, and z-intercepts of a 3-Dimensional graph step by step?
Last week's profits from a dry cleaners was $2000. Suppose the $2000 is invested at interest rate k, compounded continuously, and grows to $2983.65 in 5 years.
y’’ + k*y = 0 BC: y’(0) = 0 y’(L) = 0 Provide complete and step by step solution for the question and show calculations and use formulas.
Find the zeros and state the multiplicity of each for f(x)=x^2(x+3)(x+1)^4. Find the axis of symmetry of f(x)=x^2-2x+4
For the problem given below use the convolution theorem to write a formula for the solution of the I.V. problem in terms of f(t).
First find the general solution of the differential equation dy/dx = 3y. Then find the particular solution the satisfies the initial condition that y(1) = 4.
Use the method of Lagrange multipliers to find the extreme valus of 3x - 4y +12z on the spherical surface with equation x^2+y^2+z^2=1.
America creates more garbage than any other nation. According to Denis Hayes, president of Seattle’s nonprofit Bullitt Foundations and a founder of Earth Day.
Consider the limit state function L = X1 - X2. Compute the probability of failure Pf = P[L > 0]. Is your computed answer exact or approximate?
Consider the following very simple model of blood cholesterol levels based on the fact that cholesterol is manufactured by the body for use in the construction.
Use Runge-Kutta method of order four to approximate the solution to the given initial value problem and compare the results to the actual values.