Solved

Another Related Rate question

Posted on 2014-10-19
8
158 Views
Last Modified: 2014-10-20
A particle p moves on the curve y = x pow(2) + 1 in such a way that dx / dt = 4.  If s is the distance of P from the point ( 0, 6 ), find ds / dt :  ( a ) in general as a function of x and ( b ) when P is at ( 2, 5).

Please explain how to get started with this problem.  

This is University calculus I  related rate problem.
0
Comment
Question by:naseeam
  • 3
  • 3
  • 2
8 Comments
 
LVL 32

Accepted Solution

by:
phoffric earned 400 total points
ID: 40390942
To get started with this problem, draw a line from a point (x,y) on the curve to (0,6). Then, s = f(x,y), and you are given that y = g(x).
0
 
LVL 1

Author Comment

by:naseeam
ID: 40391176
What do they mean by particle p moves on the curve y = x pow(2) + 1 in such a way that dx / dt = 4?
0
 
LVL 84

Expert Comment

by:ozo
ID: 40391186
Solving
dx / dt = 4
we get
x = 4t +C
Given that, can you find y(t)?
0
Gigs: Get Your Project Delivered by an Expert

Select from freelancers specializing in everything from database administration to programming, who have proven themselves as experts in their field. Hire the best, collaborate easily, pay securely and get projects done right.

 
LVL 32

Assisted Solution

by:phoffric
phoffric earned 400 total points
ID: 40391194
>> What do they mean by particle p moves on the curve y = x^2 + 1 in such a way that dx / dt = 4?
You have a parabola and a particle is moving on it in such a way that its speed in the x-direction is always 4 length-units/second.
0
 
LVL 1

Author Comment

by:naseeam
ID: 40391244
dx / dt = 4
 we get
 x = 4t +C
 Given that, can you find y(t)?

I believe this is integration.  Students haven't learned integration in this class yet.
0
 
LVL 32

Assisted Solution

by:phoffric
phoffric earned 400 total points
ID: 40391269
You don't need integration to compute the derivative ds/dt.

I already mentioned that you can determine s = f(x,y).
And you know that the particle p moves on the curve y = x^2 + 1
So, y = g(x).

So, implicitly, s = h(x), right?
And dx/dt = 4 from your OP.

So, now you can take derivative of s --> ds/dt using what rule?
0
 
LVL 84

Assisted Solution

by:ozo
ozo earned 100 total points
ID: 40391276
If you have x(t) and y(x), can you get y(t)?
From y(t) and x(t) can you get s(t)?
0
 
LVL 1

Author Closing Comment

by:naseeam
ID: 40391903
Great answers!  Not too much help, not too little help.  Perfect balance!
0

Featured Post

Live: Real-Time Solutions, Start Here

Receive instant 1:1 support from technology experts, using our real-time conversation and whiteboard interface. Your first 5 minutes are always free.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Need help with programming in R stats software 6 34
Exam question 48 121
Calculating Percentile Value inside Excel. 2 76
How to write an English digest paper 6 48
This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…

774 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question