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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 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 ) above the horizontal at which it is thrown. SPEED v (ft/s) 80 85 06 95 35 188 212 238 266 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. f(Xo+Ax, yo)-f(xo. yo) f(xo. Yo+4y)-f(xo. Yo) f(xo. yo) = lim 5(xo.Yo) = lim7 (xo. Yo +4y) -f(xp. V,) 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. (al Estimate the nartial derivative of rwith respect to when y = 90ft/s and A = 40'. 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 ) above the horizontal at which it is thrown. SPEED v (ft/s) 80 85 06 95 35 188 212 238 266 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. f(Xo+Ax, yo)-f(xo. yo) f(xo. Yo+4y)-f(xo. Yo) f(xo. yo) = lim 5(xo.Yo) = lim7 (xo. Yo +4y) -f(xp. V,) 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. (al Estimate the nartial derivative of rwith respect to when y = 90ft/s and A = 40'. ANGLE O (degrees)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.5: Trigonometric Graphs
Problem 57E
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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 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 () above the horizontal at which it is thrown. SPEED v (ft/s) 80 85 188 212 238 266 90 95 35 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. f(xo+Ax. yo)-f(Xo. yo) f(xo.Yo+4y)-f (xo.Yo) f(xo. yo) = lim -,(Xo.Yo) = lim 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. (al Estimate the partial derivative of rwith respect to when y = 90ft/s and A = 40'. ANGLE O (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 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 () above the horizontal at which it is thrown. SPEED v (ft/s) 80 85 188 212 238 266 90 95 35 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. f(xo+Ax. yo)-f(Xo. yo) f(xo.Yo+4y)-f (xo.Yo) f(xo. yo) = lim -,(Xo.Yo) = lim 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. (al Estimate the partial derivative of rwith respect to when y = 90ft/s and A = 40'. ANGLE O (degrees)
f. (Xo. Yo) = lim Ar-0 f, (xo. Yo) = lim Ay-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 v when v = 90ft/s and 0 = 40'. dr dv i (b) Estimate the partial derivative of r with respect to @when v = 90ft/s and 0 = 40'. dr i
Transcribed Image Text:f. (Xo. Yo) = lim Ar-0 f, (xo. Yo) = lim Ay-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 v when v = 90ft/s and 0 = 40'. dr dv i (b) Estimate the partial derivative of r with respect to @when v = 90ft/s and 0 = 40'. dr i
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