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Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at whichit is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseballis a function of the initial speed v of the ball when it leaves Nolan's hand and the angle o above the horizontal at which it is thrown. SPEED U (f/s) 80 85 90 95 188 212 238 35 266 40 197 222 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. 1.(Xo. Yo) = lim f(xo + Ax, Yo) – f(x0. Yo). S(x0, yo + 4y) – f(x0, Yo) lim Ay-0 (x0, Yo) Ax-0 Ax 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 r with respect to vwhen y = 85ft/s and 0 = 45°. dr (b) Estimate the partial derivative of r with respect too when y = 85f/s and 0 = 45'. dr ANGLE 0 (degrees)

Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at whichit is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseballis a function of the initial speed v of the ball when it leaves Nolan's hand and the angle o above the horizontal at which it is thrown. SPEED U (f/s) 80 85 90 95 188 212 238 35 266 40 197 222 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. 1.(Xo. Yo) = lim f(xo + Ax, Yo) – f(x0. Yo). S(x0, yo + 4y) – f(x0, Yo) lim Ay-0 (x0, Yo) Ax-0 Ax 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 r with respect to vwhen y = 85ft/s and 0 = 45°. dr (b) Estimate the partial derivative of r with respect too when y = 85f/s and 0 = 45'. dr ANGLE 0 (degrees)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at whichit is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseballis a function of the initial speed v of the ball when it leaves Nolan's hand and the angle o above the horizontal at which it is thrown. SPEED U (f/s) 80 85 90 95 188 212 238 35 266 40 197 222 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. 1.(Xo. Yo) = lim f(xo + Ax, Yo) – f(x0. Yo). S(x0, yo + 4y) – f(x0, Yo) lim Ay-0 (x0, Yo) Ax-0 Ax 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 r with respect to vwhen y = 85ft/s and 0 = 45°. dr (b) Estimate the partial derivative of r with respect too when y = 85f/s and 0 = 45'. dr ANGLE 0 (degrees)
Transcribed Image Text:Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at whichit is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseballis a function of the initial speed v of the ball when it leaves Nolan's hand and the angle o above the horizontal at which it is thrown. SPEED U (f/s) 80 85 90 95 188 212 238 35 266 40 197 222 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. 1.(Xo. Yo) = lim f(xo + Ax, Yo) – f(x0. Yo). S(x0, yo + 4y) – f(x0, Yo) lim Ay-0 (x0, Yo) Ax-0 Ax 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 r with respect to vwhen y = 85ft/s and 0 = 45°. dr (b) Estimate the partial derivative of r with respect too when y = 85f/s and 0 = 45'. dr ANGLE 0 (degrees)
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