To help get in shape, Zahra gets a new pair of running shoes. If she runs 1 kilometer each day in week 1 and then adds 1/8.9 of a kilometer each week to her routine, how many kilometers has she run after 19 weeks? Round your answer to five decimal places. If n = 262, and f(x) = 8100 - x, what is the absolute difference between the left and right endpoint Riemann sums on [-90, 90]? Round your answer to 4 decimal places. When creating a Riemann sum, what is the width of an approximating rectangle on [31.6, 249.6], if we are using 4 rectangles? When creating a left-endpoint Riemann sum on the interval [80.2, 424.9] using 47 rectangles, the 9th endpoint used to calculate the height of the approximating rectangle would be When creating a right-endpoint Riemann sum on the interval [15.8, 230.4] using 31 rectangles, the 8th endpoint used to calculate the height of the approximating rectangle would be 100 Suppose that1 = 39.9 and 100 i=1 b = = 8.1. Then what is 100 3; - 4b i=1 If f(1) = -10.1, f'(x) is continuous, and S '(x)dx = -18, what is the value of f(4)? Answer: An icosahedron is a Platonic solid with a surface that consists of 20 equilateral triangles. By what factor does the surface area of an icosahedron increase as the side length of each triangle doubles from a unit to 2a units, if a = 7.9? Round your answer to three decimal places. Answer: As a car accelerates, it does not accelerate at a constant rate; rather, the acceleration is variable. The quadratic function a(t) = 0.70t + 1.44t + 10.44 describes the acceleration in seconds. Compute the average value of a(t) to estimate the average acceleration between t = 0 and t = 24.7 seconds. Round your answer to five decimal places. Answer: Let A be the area under y = e* and above the x-axis, on [0,a]. Let B be the area under y = e* and above the x-axis, on [0,b]. B is 25.7 times A. What is b in terms of a? a. b = In(e^a + -23.70) b. b = In(25.7e^a + 25.7) - c. a In(25.7e^b + 1) d. b = In(25.7e^a + -24.7000) e. b = In(25.7 -24.70) Suppose that for each i such that 1 i N one has What is if N = 39? Answer: i f(t)dt = i Lo N f(t)dt 4 4 Suppose that f(x)dx = 17.6, f f(x)dx = 2.8, fo* g(x)dx = -6.9, and fo g(x)dx = 8.1. Then what is 4 [* f(x) + g(x)dx If a 18.3, what is = La d -a ax dx If a = 40.4, what value does b have to be to make a [b-xd b xdx = 0 Consider the parabola p(x) = 6.3x + 9.4x + 12.3. For which interval [A, B] is as large as possible? B L p(x)dx A note about the choices: for some incomprehensible reason eClass sometimes switches the position of A and B. Read each option very carefully, as your interval might be a backwards version of what eClass is showing as an option.