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If the rope is pulled in at a rate of 1m/s, how fast is the boat approaching the dock when it is 8m from the dock?
If the trough is being filled with water at a rate of 0.2m3/min, how fast is the water level rising when the water is 30cm deep?
Write the equations. Provide complete and step by step solution for the question and show calculations and use formulas.
Find if the planes are parallel, perpendicular or neither. If they are not parallel then find the equation for the line of intersection.
Find the angle between a cube's diagonal and one of its sides. (use the vector calculus to get your answer) give detailed response.
Find the Taylor polynomial of degree 4 at c=1 for the equation and determine the accuracy of this polynomial at x=2.
The quarterback of a football team releases a pass at a height of 7feet above the playing field, and the football is caught by a receiver 30 yrds .
Find the points at which the function has a horizontal tangent line. f(x)=x^2+4x+5
The inverse cosine function has domain [-1,1] and range [0, pi]. Prove that (cos^-1)'(x) = -1 / sqrt(1-x^2)
If I be an open interval containing the point x. (x0) and suppose that the function f:I->R has two derivatives.
Let I be an open interval and n be a natural number. Suppose that both f:I->R and g:I->R have n derivatives.
The equation x2 - 3x + 1 = 0 has a solution for x = 0. Give the third approximationby using Newton's method. Your first approximation is to be 1.
Let f: I ?R where I is an open interval containing the point c, and let k ? R. Prove the following.
Differentiate to derive the equation for instantaneous velocity, which would be represented by the gradient of a graph.
Determine whether the function is homogenous. If it is, state the degree.Provide complete and step by step solution for the question and show calculations.
Find the mass and centroid of the plane lamina with the indicated shape and density.
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?