The legs of an isosceles right triangle increase in length at a rate of 3 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 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. 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 (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 (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. The length of the hypotenuse is changing at a rate of (Type an exact answer, using radicals as needed.)
The legs of an isosceles right triangle increase in length at a rate of 3 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 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. 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 (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 (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. The length of the hypotenuse is changing at a rate of (Type an exact answer, using radicals as needed.)
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
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Transcribed Image Text:The legs of an isosceles right triangle increase in length at a rate of 3 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 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.
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
(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
(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.
The length of the hypotenuse is changing at a rate of
(Type an exact answer, using radicals as needed.)
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