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A mass of clay of volume 432 in^3 is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the maximum?
Find the mass M (in grams) of a rod coinciding with the interval [0,4] which has the density function ? (x)=5sin(p/4)x
Compare your answer with the one given by the Poisson Integral Formula to compute the definite integral.
Substitution Methods and Exact Equations.Provide complete and step by step solution for the question and show calculations and use formulas.
Find two linearly independent power series solutions of the given differential equation. Determine the radius of the convergence of each series.
Show the function y = e^-t cos 3t satisfies the differential equation y" = -10y - 2y'.
Use PhaseLines to investigate the bifurcation diagram for the differential equation, where a is a parameter.
The rate of production of X varies directly as the product of the instantaneous amounts of A and B present.
The number of bacteria in a Petri dish was initially determined to be 200. After one hour, the number had increased to 500 and after another hour to 1,000.
When, to the nearest minute, will the water leaving the tank contain 4/3 pounds of salt per gallon?
Determine the maximum current that can be obtained in the simple circuit described.
If the initial charge on the capacitor is 3 coulombs, find a general formula for the charge at any time t.
Does f(x) have a limit as x approaches infinity? Explain you answer.Let f(x) {o if x is a natural odd number.
Consider a harmonic oscillator with mass m = 1, spring constant k = 1, and damping coefficient b = 4.
At time t=0 what proportion of the whole cable is on the left side of the peg and what proportion is on the right side?
Write the equation in terms of a rotated x'y'-system using q, the angle of rotation. Write the equation involving x' and y' in standard form.
Set up but do not solve a differential equation that models the amount of salt in the tank for the following: A tank, having a capacity of 700 liters
Compare this value with the analytical value and discuss how the approximate value obtained by Euler’s method may be improved.
Find the volume of the solid generated by revolving R around the y-axis by the method of cylindrical shells.
A small town has 1100 inhabitants . At 8am , 100 people have heard a rumor. By noon half the town has heard it.
Use one-sided limits to find the limit or determine that the limit does not exist.Provide complete and step by step solution .
Consider a projectile of mass m which is shot vertically upward from the surface of the earth with initial velocity V.
Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
Prove that if y1 and y2 achieve a maximum or a minimum at the same point in I, then they cannot form a fundamental set of solutions on this interval.
An object moves along the x-axis with initial position x(0)=2. The velocity of the object at time t is greater than or equal to 0 is given by v(t)=sin((p/3)t).