Basic Math question and answers for November 08, 2024
- Q 8 A radioactive isotope is decaying at a rate of 18% every hour. Currently there are 100 grams of the substance.Part B: How much will be left one day from...
- Q Use Newton's method to approximate a root of the equation3 sin(x) = x as follows.Let x1 = 2 be the initial approximation.The second approximation 2 isand the third approximation is
- Q Suppose h" is continuous at x = 5.h' (5)= 0, and h" (5) > 0.What can you say about the behavior of h at x = 5?Inflection pointInflection point at...
- Q Use Newton's Method to estimate a root of the functionf(x) = 5x + 2 - exUse the initial estimate x1 = 0.5:x1 = 0.5x2x3X4X5 =x6X7
- Q The function f(x) = 2x ? 27x +84x + 3 has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema.This function...
- Q Suppose a hiker finds himself in a forest 3 miles from the nearest point on a straight road. He wants to walk to his car which is parked 10 miles...
- Q Suppose h" is continuous at x = 2.h' (2) = 0, and h" (2) < 0.What can you say about the behavior of h at x = 2?Inflection pointInflection point...
- Q Use linear approximation, i.e. the tangent line, to approximate 1/0.103 as follows: Let f(x) = 1/x and find the equation of the tangent line to f(x) at a "nice" point...
- Q Let f(x) = (3x - 1) (3x - 7) on [1,3]. Answer the following.(a) Find all critical numbers of f.(b) Find the intervals on which f is increasing.(c) Find absolute...
- Q A toy manufacturing company's monthly profit in its first two months of operation is given by the profit functionP(x) = x -6x2 +9x+6, where is the number of toys sold...
- Q Use Newton's method to approximate a root of the equation4x7 + 5x4 + 2 = 0 as follows.Let x1=2 be the initial approximation.The second approximation x2 isand the third approximation...
- Q A cube is expanding, with the length of an edge decreasing 2 cm every minute. At the moment the cube has a volume of 343 cm, the rate at which...
- Q If you have 240 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area =...
- Q A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along...
- Q An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per second. The pyramid, at the top, has the shape of a square with...
- Q A circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per day and the sides of the square are increasing at...
- Q Between two telephone poles that are 40 feet apart, there is a wiresuspended in the shape of a catenary y = 25 cosh (x/25) - 5, whereand y are measured...
- Q Fermium-257 has a half-life of 100 days. A sample has a mass of 60 mg initially.I) What is the formula for finding the amount remaining after t days.II) When will...
- Q Find the coordinates of the vertex of the graph of the function. Tell whether the vertex is a maximum or a minimum. y = -2x -12x - 6 (3,-60); minimum...
- Q Between two telephone poles that are 44 feet apart, there is a wire suspended in the shape of a catenary y = 15 cosh (x/15) - 8, where x and...
- Q At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship B is sailing north at 24 knots....
- Q The ideal gas law states that for an ideal gas PV=nRT, where P,V, and T are the pressure, volume, and absolute temperature, n is the number of moles of gas,...
- Q If 1400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume= (include...
- Q Let C(x) = 2x + 550 and R(x) = 28x.(a) Write the profit function P(x).P(x) =(b) What is the slope m of the profit function?m=(c) What is the marginal profit...
- Q There are currently 300 cells in a culture and it grows at a rateproportional to its size. After one hour the population has increased to430.How much time will have passed...
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