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Consider the following ODE:
y"= - 4y
where y is the dependent variable which is a function of the independent variable x.
The general solution for this ODE is: y = c1cos(2x + c2sin(2x)
where c1 and c2 are constants.
Find the particular solution for the Initial Value Problem (IVP) defined by these initial conditions:
y(0) = 1 and y'(0) = 3
At what rate is the water level rising when the level is 5 m high? As time passes, what happens to the rate at which the water level rises
In this Show You Know Assignment, you will explore the derivatives of the sine and cosine functions but when the angle is measured in degrees. Will the derivative rules stay the same? If so, why? Will the derivative rules change, if so how and why..
An entrepreneur has the following cost and revenue functions: TC = 30 + 3Q and TR = 4Q. calculate the equilibrium quantity algebraically and graphically at the break-even point.
Find the interest rate needed for an investment of $3600 to double in 6 yr if interest is compounded continuously. (Round your answer to two decimal places.)
Given f (x, y) = xy / (x - y). Find all the second partial derivatives of this function. Find the tangent plane to the graph of this function at (2,1, 2).
laboratory designed a radio telescope with a diameter of 280 feet and a maximum depth of 40 feet. Find the equation of this parabola.
the distance from a college to a students home follows a right skewed distribution with a mean if 15 miles and a
Use the library or Internet to find another example of a function. Explain how it works with a three sets of inputs for your example. What is the output of your data? What is the practical use of your function?
Explain the correspondence between straight lines and linear equations.
suppose that a body with temp. 85F is discovered at midnight, and that the ambient temp. is 70F. the body is removed quickly to the morgue where the ambient temp. is 40F. after 1 hour the body temp. is found to be 60F. estimate time of death.
An industrial tank (a solid formed by adjoining two hemispheres to the ends of a right circular cylinder) must have a volume of 4000 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimen..
Clear glass costs $3 per square foot and stained glass costs $10 per square foot. Express the cost of the window as a function of the radius of the stained glass pane.
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