Calculating Rate of Change of Distance to Origin

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Homework Help Overview

The problem involves a particle moving along the curve defined by the equation y = 3√(4x + 4). The specific scenario examines the rate of change of the distance from the particle to the origin as it passes through the point (3, 12) with a given rate of change of the x-coordinate.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss starting with a formula for the distance from the particle to the origin and suggest differentiating it with respect to time. Questions arise regarding the specific formula for distance being referenced.

Discussion Status

The discussion is ongoing, with some participants providing guidance on how to approach the problem, while others seek clarification on the distance formula. Multiple interpretations of the problem setup are being explored.

Contextual Notes

There is a lack of clarity regarding the distance formula and its application to the problem, which may be contributing to the confusion among participants.

Weave
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Homework Statement


A particle is moving along the curve [tex]y= 3 \sqrt(4 x + 4)[/tex]. As the particle passes through the point (3, 12), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

Homework Equations


1.[tex]y= 3* \sqrt(4 x + 4)[/tex]


The Attempt at a Solution


Not too sure how to start.
 
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Begin with a formula for the distance(D) from (x,y) to the origin. Then you can plug in what you know about y. Finally differentiate (implicitly) the formula with respect to time. You should get an equation involving dD/dt, x, and dx/dt. You know x, and dx/dt. Find dD/dt.
 
What formula for distance are you talking about?
 
Weave said:
What formula for distance are you talking about?

No wonder you are having a problem! When dealing with "distance to the origin", you really need to know that the distance from a point (x,y) to the origin, (0,0), is [itex]\sqrt{x^2+ y^2}[/itex]!:approve:
 

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