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The vertical height in feet of a ball thrown upward from a cliff is given by s(t)=-16t^2+64t+200, where t is measured in seconds
If the functions f and g are defines for all real numbers and f is an antiderivative of g, which statements are not true?
Find the absolute maximum and the absolute minimum on the interval (1,4]. f(x) = x3 - 7x2 + 12x -6 / x - 1.
A skydiver, weighing 70kg, jumps from an aeroplane at an altitude of 700 metres and falls for (T) seconds before pulling the rip cord of his parachute.
Locate the critical points of f(x,y) and determine if they are local maxima, minima, or neither.
The birth rate in a state is 2% per year and the rate is 1.3% per year. The population of the state is now 8,000,000.
Use the method of undetermined coefficients to solve the following differential equation.
If Rolle’s Theorem can be applied, find all the values, c, in the interval such that f'(c) = 0 . If Rolle’s Theorem cannot be applied, state why.
What are the domain and range and x intercepts of the function? Approximate to two decimal places.
By decomposing the triangle into six right triangles having the incenter as a common vertex, express the area A of the triangle in term of a, b , c.
Find the maximum and the minim values of the directional derivative (df/ds)]u at ( 1 , 3/2 ) as u varies.
If the trough is being filled with water at a rate of 12 ft^3/min, how fast is the water level rising when the water is 6 inches deep?
A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point.
Write a short paragraph comparing and contrasting the method of undetermined coefficients and variation of parameters.
Mercury pollution in a lake (revisited): As an environmental engineer, you have been asked to analyze mercury levels in nearby Lake Arrowhead.
Calculate the curl of F=r^n*(xi+yj). For each n for which curlF=0 , find a potential g such that F=grad(g).
Find a particular solution to the differential equation: y'' - 2y' -15y = 450t3
Make a continuous model of her economic situation, i.e. write a differential equation together with initial condition for the balance B(t) .
A ping-pong ball is caught in a vertical plexiglass column in which the air flow alternates sinusoidally with a period of 60 seconds.
A water bucket is shaped like the frustum of a cone with height 24 inches, base radius of 6 inches and top radius of 12 inches.
Evaluate at least two seperate designs both of which are concave outward. The graph should be a parabolic with floating cans could be cone shapes.
Where and how do you begin to set this problem up to be solved using the Laplace transform? The value y(4)(t) is the fourth derivative of function y(t).
The rate of change of the population of a town in Pennsylvania at any time t is proportional to the population at that time.
The particle's position at time t = 0 is at the origin, and its initial velocity is 1 cm/sec. What is the position of the particle, in cm. at time t seconds?
Show that u (x, y) is harmonic in some domain and find a harmonic conjugate v (x, y) when u (x, y) = 2x (1 - y)