# calculus problem

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the thin lens equation in physics is 1/s+1/S=1/f where s is the object distance from the lens,S is the image distance from the lens,and f is the focal length of the lens.Suppose that a certain lens has a focal length of 6cm and that an object is moving toward the lens at the rate of 2cm/s .How fast is the image distance changing at the instant when the object is 10cm from the lens?Is the image moving away from the lens or towards the lens?

• calculus problem -

I like it in this form:
1/o + 1/i = 1/f for object, image, and focal length.

take the derivative:
-do/dt* 1/o^2 -di/dt 1/i^2= 0 (f is a constant0

do di/dt= -(i/o)^2 do/dt

Can you take it from here?

• calculus problem -

Suppose and object is traveling directly from the earth to moon. The mass of the earth is 5.9742 x10^24 kg, the mass of the moon is 7.349 x 10^22 kg, and the mean distance from the earth to the moon is 384,000km. For an object between the earth and the moon, how far from earth is the force of the object due to the moon greater than the force on the object due to earth?

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