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A tank is in the shape of an inverted cone (pointy at the top) 6 feet high and 8 feet across at the base. The tank is filled to a depth of 3 feet.
At 8am on Saturday, a man begins running up the side of a mountain to his weekend campsite. On Sunday at 8am, he runs back down the mountain.
Show that the rate of change of the volume of water in the container due to evaporation is directly proportional to the exposed surface area of the water.
The graph of g passes through each of the points (x,f(x)) given in the table above. Is it possible that f and g are the same function?
An ant is walking around the outside of the cube in "straight" paths (where we define a straight path in this case as one formed by the edges.
Find the volume of the solid generated when the enclosed region of f and g between x = ½ and x = 1, is revolved about the line y = 4.
Make a conjecture, on the basis of physical reasoning, as to whether you expect the amount of salt in the tank to reach a constant equilibrium value.
Most drugs are eliminated from the body according to a strict exponential decay law. Here are two problems that illustrate the process.
If 2 subintervals of equal length are used, what is the midpoint Reimann sum approximation of integral with 5 on top and 1 on bottom f(x)dx?
Let f be a differentibale function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that.
Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)
A portion of a river has the shape of the equation y=1-x^2/4, where distances are measured in tens of kilometres, and the positive y-axis represents due north.
What is the terminal velocity vT=lim as t approaches infinity of a 100-kilogram object (a small linebacker or a large flower pot) subject to air resistance.
Find the critical points and use your test of choice to give local maximum and minimum values. Give those values.
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.