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(b) Suppose that the base 6 and height a (and therefore the hypotenuse c) of the right triangle shown are changing with time. By differentiating the relation a? + b² = c² with respect to time t, derive a relation between a, b, c, da/dt, db/dt and dc/dt. a b (c) In the scenario from part (b), suppose that at a certain moment, a = 6 cm, 6 = 8 cm, da/dt = 1.5 cm/sec and dc/dt = -1 cm/sec. At what rate is the length of the base changing at this same moment?

(b) Suppose that the base 6 and height a (and therefore the hypotenuse c) of the right triangle shown are changing with time. By differentiating the relation a? + b² = c² with respect to time t, derive a relation between a, b, c, da/dt, db/dt and dc/dt. a b (c) In the scenario from part (b), suppose that at a certain moment, a = 6 cm, 6 = 8 cm, da/dt = 1.5 cm/sec and dc/dt = -1 cm/sec. At what rate is the length of the base changing at this same moment?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 56E
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(b) Suppose that the base 6 and height a (and therefore the hypotenuse c) of the right triangle shown are changing with time. By differentiating the relation a? + b² = c² with respect to time t, derive a relation between a, b, c, da/dt, db/dt and dc/dt. a b (c) In the scenario from part (b), suppose that at a certain moment, a = 6 cm, 6 = 8 cm, da/dt = 1.5 cm/sec and dc/dt = -1 cm/sec. At what rate is the length of the base changing at this same moment?
Transcribed Image Text:(b) Suppose that the base 6 and height a (and therefore the hypotenuse c) of the right triangle shown are changing with time. By differentiating the relation a? + b² = c² with respect to time t, derive a relation between a, b, c, da/dt, db/dt and dc/dt. a b (c) In the scenario from part (b), suppose that at a certain moment, a = 6 cm, 6 = 8 cm, da/dt = 1.5 cm/sec and dc/dt = -1 cm/sec. At what rate is the length of the base changing at this same moment?
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