the depth of a rain puddle d(t) is given in inches, and t is given in minutes. if the depth is changing with respect to time, wh

Question

10 months ago

7

ich expression gives the rate of change at which the depth is changing at 3 minutes?

1 answer:

garik1379 [7] · Answer 1 · 2024-01-03T10:46:51+03:00

The required expression gives the rate of change will be d'(3) at which the depth is changing at 3 minutes.

Let d(t) represent the depth of the rain puddle at any time t,

⇒ d(t) ....(i)

The depth is changing with respect to time, which is given in the question

Differentiate equation (i) with respect to t and we get

⇒ δd(t)/δt = d'(t) ....(ii)

This is the rate of change in depth unit time

As per the question, the depth is changing at 3 minutes

Substitute the value of t = 3 in equation (ii), and we get

⇒ d'(3)

Therefore, the required expression gives the rate of change will be d'(3).

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