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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).
They need to know how much material will be required to construct the main support cables and what sort of cable they need to buy.
Water is the most important substance on Earth. One reason for its usefulness is that it exists as a liquid over a wide range of temperatures.
Determine the (x,y) coordinates and the value of the parameter at the point(s) where the slope of the tangent line to the curve is 4.
If f(x) is concave up for all x and g(x) is concave down for all x, what can you say about the concavity of f(x) + g(x)?
As an epidemic spreads through a population, the number of infected people, I, is expressed as a function of the number of susceptible people.
The total cost of producing q units of product is given by C(q) = q3 - 60q2 +1400q + 1000 for 0 < q <= 50; the product sells for $788 per unit.