The legs of an isosceles right triangle increase in length at ...

Question

The legs of an isosceles right triangle increase in length at a rate of 2 m/s.

c. At what rate is the length of the hypotenuse changing?

Accepted Answer

Welcome back, everyone. The radius of a circle is increasing at a rate of 4 centimeters per second. At what rate is the circumference of the circle changing? We're given 4 answer choices A says 85 centimeters per second, B 45 centimeters per second, C 16 5 centimeters per second, and D 2 centimeters per second. So first of all, let's relate the circumference of a circle to its radius. We have to recall that circumference. C is equal to 2 pi multiplied by radius R. and what we want to do is simply differentiate this equation, right? We have to understand that circumference is going to be. A function of time, right, so C is C of T, and also our radius is changing relative to time. So R is R of T. So what we want to do is differentiate the left hand sides. We're going to get D C divided by DT, which is the first derivative of circumference with respect to time. Now, 2 pi is a constant, and then we multiply 2 pi by DR divided by DT, right, where differentiating R. And that's it. We have our equation that we want to use. It shows us that the rate of change of circumference with respect to time is equal to 2 pi multiplied by. The derivative of radius relative to time. So what are we given? Well, we're given the radius of a circle is increasing at the rate of 4 centimeters per second. So that's dr divided by the T. It is 4 centimeters per second, and we want to find the rate of change of circumference. So we want to find the C divided by D T. Which is equal to 2 multiplied by dr divided by dT. So we're multiplying by 4 centimeters per second. It is increasing, so we're using the positive quantity, and now we can multiply to get 8 centimeters per second, which corresponds to the answer choice A. Thank you for watching.

The legs of an isosceles right triangle increase in length at a rate of 2 m/s.c. At what rate is the length of the hypotenuse changing?

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The legs of an isosceles right triangle increase in length at a rate of 2 m/s.
c. At what rate is the length of the hypotenuse changing?