“1 2 3” are all part of the same problem that all refer to the info at the top. **Problem 2:**The moment the batmobile passes through the point \((-1, \sqrt{3})\), the angle \(\theta\) is changing at a rate given by\[\frac{d\theta}{dt} = 3 \, \text{rad/hr}.\]Find the rate at which the batmobile’s horizontal velocity, \(\frac{dx}{dt}\), is changing at this time.---**Problem 3:**Find the rate at which the distance between the batmobile and the origin \((0, 0)\) is changing the moment the batmobile passes through the point \((-2, 0)\). **Title: Calculating Rates of Change in Circular Motion**Batman is at it again, driving his vehicle frantically around Wayne Manor (luckily avoiding Alfred’s freshly planted patch of dwarf cypress and gardenia). This time, the Batmobile moves counterclockwise along a circular path given by the equation:\[ x^2 + y^2 = 4. \]Let \(\theta\) denote the angle formed between the Batmobile and the positive x-axis at time \(t\).**1. Problem 1**At the moment the Batmobile passes through the point \((\sqrt{2}, \sqrt{2})\), its vertical velocity (in miles per hour) is given by:\[ \frac{dy}{dt} = 30 \text{ mi/hr}. \]Find the rate (in radians per hour) at which the angle \(\theta\) is moving at this time.**2. Problem 2**At the moment the Batmobile passes through the point \((-1, \sqrt{3})\), the angle \(\theta\) is changing at a rate given by:\[ \frac{d\theta}{dt} = 3 \text{ rad/hr}. \]Find the rate at which the Batmobile’s horizontal velocity, \(\frac{dx}{dt}\), is changing at this time.

Name: “1 2 3” are all part of the same problem that all refer to the info at
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: “1 2 3” are all part of the same problem that all refer to the info at the top. **Problem 2:**The moment the batmobile passes through the point \((-1, \sqrt{3})\), the angle \(\theta\) is changing at a rate given by\[\frac{d\theta}{dt} = 3 \, \text{r