Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range rof the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle 0 above the horizontal at which it is thrown. SPEED v (ft/s) 85 188 212 75 80 90 35 165 238 197 222 249 40 173 45 176 200 226 253 50 173 197 222 249 Use the accompanying table and the equations below to estimate the partial derivatives. f (xo + Ax, yo) – f (xo, yo) f (xo. yo + Ay) – f (xo. yo) (xo. Yo) = lim ,(xo. Yo) = lim- Ar 4y-0 Ay Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of rwith respect to v when v = 80ft/s and 0 = 40°. dr (b) Estimate the partial derivative of rwith respect to 0 when v = 80ft/s and 0 = 40°. dr ANGLE O (degrees)

Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range rof the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle 0 above the horizontal at which it is thrown. SPEED v (ft/s) 85 188 212 75 80 90 35 165 238 197 222 249 40 173 45 176 200 226 253 50 173 197 222 249 Use the accompanying table and the equations below to estimate the partial derivatives. f (xo + Ax, yo) – f (xo, yo) f (xo. yo + Ay) – f (xo. yo) (xo. Yo) = lim ,(xo. Yo) = lim- Ar 4y-0 Ay Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of rwith respect to v when v = 80ft/s and 0 = 40°. dr (b) Estimate the partial derivative of rwith respect to 0 when v = 80ft/s and 0 = 40°. dr ANGLE O (degrees)

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter9: Solving Quadratic Functions

Section: Chapter Questions

Problem 2CA

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