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The area of a circle increases at a rate of 6 cm? / s. a. How fast is the radius changing when the radius is 4 cm? b. How fast is the radius changing when the circumference is 3 cm? a. Write an equation relating the area of a circle, A, and the radius of the circle, r. (Type an exact answer, using t as needed.) Differentiate both sides of the equation with respect to t. dA dr dt dt (Type an exact answer, using a as needed.) When the radius is 4 cm, the radius is changing at a rate of (Type an exact answer, using t as needed.) b. When the circumference is 3 cm, the radius is changing at a rate of (Type an exact answer, using t as needed.)

The area of a circle increases at a rate of 6 cm? / s. a. How fast is the radius changing when the radius is 4 cm? b. How fast is the radius changing when the circumference is 3 cm? a. Write an equation relating the area of a circle, A, and the radius of the circle, r. (Type an exact answer, using t as needed.) Differentiate both sides of the equation with respect to t. dA dr dt dt (Type an exact answer, using a as needed.) When the radius is 4 cm, the radius is changing at a rate of (Type an exact answer, using t as needed.) b. When the circumference is 3 cm, the radius is changing at a rate of (Type an exact answer, using t as needed.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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The area of a circle increases at a rate of 6 cm2/s. a. How fast is the radius changing when the radius is 4 cm? b. How fast is the radius changing when the circumference is 3 cm? a. Write an equation relating the area of a circle, A, and the radius of the circle, r. (Type an exact answer, using t as needed.) Differentiate both sides of the equation with respect to t. dA dr dt dt (Type an exact answer, using t as needed.) When the radius is 4 cm, the radius is changing at a rate of (Type an exact answer, using a as needed.) b. When the circumference is 3 cm, the radius is changing at a rate of (Type an exact answer, using a as needed.)
Transcribed Image Text:The area of a circle increases at a rate of 6 cm2/s. a. How fast is the radius changing when the radius is 4 cm? b. How fast is the radius changing when the circumference is 3 cm? a. Write an equation relating the area of a circle, A, and the radius of the circle, r. (Type an exact answer, using t as needed.) Differentiate both sides of the equation with respect to t. dA dr dt dt (Type an exact answer, using t as needed.) When the radius is 4 cm, the radius is changing at a rate of (Type an exact answer, using a as needed.) b. When the circumference is 3 cm, the radius is changing at a rate of (Type an exact answer, using a 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 4 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 6 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 4 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 6 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.)
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 4 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 6 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 4 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 6 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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