A road is shaped in the shape of the cardioid r = 1000(1 + cos(theta)) (polar coordinate form of...

Question:

A road is shaped in the shape of the cardioid {eq}r = 1000(1 + \cos\theta) {/eq} (polar coordinate form of the curve), where {eq}r {/eq} is in meters. When a car is traveling on the road at the point represented by {eq}\theta = \frac{\pi}{6} {/eq}, the car is traveling at a speed of 30 meters per second. Determine {eq}\frac{d\theta}{dt} {/eq}. The car is traveling counter-clockwise along the road.

Cardioids:

Cardioids is defined as the shape attained by the traces of the circle that looks very similar to the shape of the heart. There are two types of the cardioids, one is vertical cardioids and another is horizontal cardioids.

Answer and Explanation: 1

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Given Data:

  • The shape is given as {eq}r = 1000\left( {1 + \cos \theta } \right) {/eq}
  • The direction at an instant is given as {eq}\theta =...

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Cardioid in Math: Definition, Equation & Examples

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Chapter 1 / Lesson 13
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This lesson will cover a neat shape studied in upper-level mathematics called a cardioid. We will look at the basic shape, how it is constructed, its equation in polar form, and various examples of these equations and corresponding cardioids.


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