Question

Let $\theta$ (in radians) be an acute angle in a right triangle and let $x$ and $y$, respectively, be the lengths of the sides adjacent to and opposite $\theta$. Suppose also that $x$ and $y$ vary with time. At a certain instant $x = 9$ units and is increasing at $8$ unit/s, while $y = 6$ and is decreasing at $\frac{1}{5}$ units/s. How fast is $\theta$ changing at that instant?

Name: let theta in radians be an acute angle in a right triangle and let x and y respectively be the lengths of the sides adjacent to and opposite theta suppose also that x and y vary with time at 28385
Uploaded: 2022-04-13T11:56:48-08:00
Duration: 3 min 39 s
Channel: Suman Saurav Thakur
Description: let theta in radians be an acute angle in a right triangle and let x and y respectively be the lengths of the sides adjacent to and opposite theta suppose also that x and y vary with time at 28385

          Let $\theta$ (in radians) be an acute angle in a right triangle and let $x$ and $y$, respectively, be the lengths of the sides adjacent to and opposite $\theta$. Suppose also that $x$ and $y$ vary with time.
At a certain instant $x = 9$ units and is increasing at $8$ unit/s, while $y = 6$ and is decreasing at $\frac{1}{5}$ units/s.
How fast is $\theta$ changing at that instant?

let theta in radians be an acute angle in a right triangle and let x and y respectively be the lengths of the sides adjacent to and opposite theta suppose also that x and y vary with time at 28385

Added by Jeffrey B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

04/13/2022

Step 1

We are given that $\frac{dx}{dt} = 8$ and $\frac{dy}{dt} = -\frac{1}{5}$ at the instant when $x = 9$ and $y = 6$. We want to find $\frac{d\theta}{dt}$ at that instant. Show more…

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Let $\theta$ (in radians) be an acute angle in a right triangle and let $x$ and $y$, respectively, be the lengths of the sides adjacent to and opposite $\theta$. Suppose also that $x$ and $y$ vary with time. At a certain instant $x = 9$ units and is increasing at $8$ unit/s, while $y = 6$ and is decreasing at $\frac{1}{5}$ units/s. How fast is $\theta$ changing at that instant?