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anonymous
 one year ago
A particle moves along the curve y=√(1+x^3). As it reaches the point (2,3), the ycoordinate is increasing at the rate of 4cm/s. How fast is the xcoordinate of the point changing at this instant?
anonymous
 one year ago
A particle moves along the curve y=√(1+x^3). As it reaches the point (2,3), the ycoordinate is increasing at the rate of 4cm/s. How fast is the xcoordinate of the point changing at this instant?

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2this looks like a related rates question... \[\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah it is :) hmm... so what are you doing there?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2ok... so you need to find \[\frac{dy}{dx} ~~~given~~~~ y = (1 + x^3)^{\frac{1}{2}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok... thats \[\frac{ 3x^2 }{ 2\sqrt(1+x^3) }\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2looks good to me... now the point is (2, 3) so substitute x = 2 and get a value

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's all i gotta do? :O

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0i think we need to find \(\dfrac{dx}{dt}\), the rate of change of x coordinate

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2well that is just a step

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The answer is correct @campbell_st, it's 2

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2so remember its \[\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx}\] so you need a numeric value for dy/dx so use the x value at the point

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmm... how do you get that? Is it just something i have to memorize?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2well I'm using the chain rule I got \[\frac{dy}{dx} = \frac{6}{\sqrt{9}}\] so then if I use the chain rule \[\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx} ~~~~then~~~~\frac{6}{\sqrt{9}} = 4 \times \frac{dt}{dx}\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2then I'd say \[\frac{6}{4\sqrt{9}} = \frac{dt}{dx}\] take the reciprocal of both sides \[\frac{dx}{dt} = \frac{4\sqrt{9}}{6}\] you can simplify it...

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.2that would be my approach to this question... other more learned people may have different views...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That makes a lot of sense now! Thanks so much @campbell_st :) I appreciate it!
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