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Suppose consumers' demand function a commodity D(q)=50-3q-q2 dollars per unit. Find the number of units that will be bought if the market price is $32 per unit.
Write down the equation of a sinusoidal function f with the mean value: -1, amplitude 5, the period 4 pi and f(0) = -1
A truck is traveling away from the transmitter along the highway at a speed of 80 km per hour. How fast is the distance between the truck.
Find an expression for the tax revenue (e.g. tQ) maximizing t in terms of the parameters of the model.
Find the interval on which the function f is increasing and or is decreasing and label the local maxima and minima if there is a global extrema.
How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 40% antifreeze?
Compute the elasticity of demand for the given demand function D(p) and determine whether the demand is elastic, inelastic.
Find the values of a and b for the polynomial f(x) = 2x^3 + ax^2 - 4x + b, given that f(x) is divisible by x+1 and x-3. Write f(x) in a factorised form.
Compute the derivative of the given function and find the equation of the line that is tangent to its graph for the specified value x = c.
It takes 8.4 minutes to make one revolution. Assuming it starts on the positive x-axis, what are the coordinates of the point in 7.4 minutes?
Find the volume of the unbounded solid generated by rotating the unbounded region around the x axis.
Find the intersection point of the line (x-1)/2=(y+1)/3=z-2 and the plane 2x+y-z=17.
Find the volume of the solid generated when the region y=x^-1/2 on the interval [1,4] is revolved about x-axis.
How far does the rock fall in 2 seconds if you throw it downward with an initial velocity of 40 feet per second?
Sand falls from an overhead hopper to form a right circular cone. If the cone formed has an angle a find the rate of change of volume with respect to height?
Supposed V(t) = 2cos(3t). If R = 4 and C = 0.5, use Eulers method to compute values of the solutions with the given inital conditions.
Model the data with two linear function. Let the independendt variable represent the number of years after 1960.
Prove that the spheres x2 + y2 +z2 = 16 and x2 + (y-5)2 + z2 = 9 intersect orthogonally.
Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.
Find the volume of the solid generated when the region R bounded by the geven curves is revolved about the indicated axis.
Let A be any constant. Write down a differential equation satisfied by g(x)=f(A)f(x), and also give the value of g(0).
There is a type of differential equation which will always be solvable by two different methods.
For the following problems a function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one to one.
For the following graph the given functions on a computer screen, how are these graphs related?
X'' + 2x' + x = 5exp(-t) + t for t greater/equal to zero; x(0)=2; x'(0)=1 and identify critically damp, over-damped or under-damped (overdamped or underdamped)