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- Prove the conjecture made in the previous exercise.Use Simpson's 3/8 rule to compute the approximated solution where f (x) = 1/Cosx + 4 defined at the interval (1,4.5) and n = 7A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π. What are the dimensions of the rectangle with largest area, and what is the largest area?
- Consider a χ2-curve with df = 16. Obtain the χ2-value that has area a. 0.025 to its left. b. 0.975 to its left.Consider a Lorenz curve given by f(x)=x^n for 0≤x≤1 and n≥1. What happens to the Gini index G.I as n→1, and what's the interpretation of that result?A stone, projected vertically upward with initial velocity 112ft/sec, moves according to s=112t−16t2, where s is the distance from the ground. What is the maximum height reached by the stone?
- Suppose that the position of one particle at time t is given by x1 = 3 sin(t), y1 = 2 cos(t), 0 ≤ t ≤ 2? and the position of a second particle is given by x2 = −3 + cos(t), y2 = 1 + sin(t), 0 ≤ t ≤ 2?. (a) Graph the paths of both particles. How many points of intersection are there? __ points of intersection (b) Are any of these points of intersection collision points? That is, are the particles ever at the same place at the same time? If so, find the collision points. (Enter your answers as a comma-separated list of ordered pairs of the form (x, y). If there are no collision points, enter DNE.) (x, y) =__ (c) Describe what happens if the path of the second particle is given by x2 = 3 + cos(t), y2 = 1 + sin(t), 0 ≤ t ≤ 2?. The circle is centered at (x, y) = __ There are _ intersection point(s), and there are _ collision point(s).Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin. Estimate the error in the approximation if | x| ≤ 0.1 and | y | ≤ 0.1.Consider an F-curve with df = (6, 8). Determine the F-value that has area a. 0.01 to its left. b. 0.95 to its left.
