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The legs of an isosceles right triangle increase in length at a rate of 4 m/s. a. At what rate is the area of the triangle changing when the legs are 2 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 2 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. A = Differentiate both sides of the equation with respect to t. dA dx dt dt When the legs are 2 m long, the area of the triangle is changing at a rate of 8 m2 /s. (Type an exact answer, using radicals as needed.) b. When the hypotenuse is 2 m long, the area of the triangle is changing at a rate of 4/2 m2 /s. (Type an exact answer, using radicals as needed.) c. Write an equation relating the length of the legs of an isosceles triangle, x, to the length of the hypotenuse of the triangle, h. 2x2 = n2 The length of the hypotenuse is changing at a rate of 4/2 m/s. (Type an exact answer, using radicals as needed.)

The legs of an isosceles right triangle increase in length at a rate of 4 m/s. a. At what rate is the area of the triangle changing when the legs are 2 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 2 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. A = Differentiate both sides of the equation with respect to t. dA dx dt dt When the legs are 2 m long, the area of the triangle is changing at a rate of 8 m2 /s. (Type an exact answer, using radicals as needed.) b. When the hypotenuse is 2 m long, the area of the triangle is changing at a rate of 4/2 m2 /s. (Type an exact answer, using radicals as needed.) c. Write an equation relating the length of the legs of an isosceles triangle, x, to the length of the hypotenuse of the triangle, h. 2x2 = n2 The length of the hypotenuse is changing at a rate of 4/2 m/s. (Type an exact answer, using radicals as needed.)

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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The legs of an isosceles right triangle increase in length at a rate of 4 m /s. a. At what rate is the area of the triangle changing when the legs are 2 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 2 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. A = Differentiate both sides of the equation with respect to t. dA dx dt dt When the legs are 2 m long, the area of the triangle is changing at a rate of 8 m2 /s. (Type an exact answer, using radicals as needed.) b. When the hypotenuse is 2 m long, the area of the triangle is changing at a rate of 42 m2 /s. (Type an exact answer, using radicals as needed.) c. Write an equation relating the length of the legs of an isosceles triangle, x, to the length of the hypotenuse of the triangle, h. 2x? = h2 The length of the hypotenuse is changing at a rate of 4/2 m/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 4 m /s. a. At what rate is the area of the triangle changing when the legs are 2 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 2 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. A = Differentiate both sides of the equation with respect to t. dA dx dt dt When the legs are 2 m long, the area of the triangle is changing at a rate of 8 m2 /s. (Type an exact answer, using radicals as needed.) b. When the hypotenuse is 2 m long, the area of the triangle is changing at a rate of 42 m2 /s. (Type an exact answer, using radicals as needed.) c. Write an equation relating the length of the legs of an isosceles triangle, x, to the length of the hypotenuse of the triangle, h. 2x? = h2 The length of the hypotenuse is changing at a rate of 4/2 m/s. (Type an exact answer, using radicals as needed.)
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