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The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is the area of the triangle changing when the legs are 4 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 4 m long? c. At what rate is the length of the hypotenuse changing?

The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is the area of the triangle changing when the legs are 4 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 4 m long? c. At what rate is the length of the hypotenuse changing?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
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The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is the area of the triangle changing when the legs are 4 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 4 m long? c. At what rate is the length of the hypotenuse changing? a. Write an equation relating the area of an isosceles right triangle, A, and the length of the legs of the triangle, x. 1 A = -x2 2 Differentiate both sides of the equation with respect to t. dA dx dt dt When the legs are 4 m long, the area of the triangle is changing at a rate of 20 m2 /s. (Type an exact answer, using radicals as needed.) b. When the hypotenuse is 4 m long, the area of the triangle is changing at a rate of m² /s. (Type an exact answer, using radicals as needed.)
Transcribed Image Text:The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is the area of the triangle changing when the legs are 4 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 4 m long? c. At what rate is the length of the hypotenuse changing? a. Write an equation relating the area of an isosceles right triangle, A, and the length of the legs of the triangle, x. 1 A = -x2 2 Differentiate both sides of the equation with respect to t. dA dx dt dt When the legs are 4 m long, the area of the triangle is changing at a rate of 20 m2 /s. (Type an exact answer, using radicals as needed.) b. When the hypotenuse is 4 m long, the area of the triangle is changing at a rate of m² /s. (Type an exact answer, using radicals as needed.)
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