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# ocr mathematics core 3 a2

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1. Given that x=(4t+9)^1/2 and y=6e^1/2x+1, find expressions for dx/dt and dy/dx

I've got dx/dt= 2(4t+9)^-1/2 and dy/dt= 3e^1/2x+1

dt/dx= 1/2(4t+9)^1/2

dy/dx= 3e^1/2x+1/2(4t+9)^1/2

(ii) Hence find the value of dy/dt when t=4, giving your answer correct to 3 significant figures.

but I don't understand how to find dy/dt?

thanks
2. (Original post by nerdygeek123)
Given that x=(4t+9)^1/2 and y=6e^1/2x+1, find expressions for dx/dt and dy/dx

I've got dx/dt= 2(4t+9)^-1/2 and dy/dt= 3e^1/2x+1

dt/dx= 1/2(4t+9)^1/2

dy/dx= 3e^1/2x+1/2(4t+9)^1/2

(ii) Hence find the value of dy/dt when t=4, giving your answer correct to 3 significant figures.

but I don't understand how to find dy/dt?

thanks
Well you've already got the equation of dy/dt so just plug your value of t = 4 into that equation.

Okay I'm actually gonna assumed you typed it wrong cause no question asks to find dy/dt. To find dy/dx you need to divide dy/dt by dx/dt, that way the dt cancel out and it becomes dy/dx. Then you've got an equation of dy/dx to plug the value of t=4 into.

Hope that makes sense
3. (Original post by nerdygeek123)
Given that x=(4t+9)^1/2 and y=6e^1/2x+1, find expressions for dx/dt and dy/dx

I've got dx/dt= 2(4t+9)^-1/2 and dy/dt= 3e^1/2x+1

dt/dx= 1/2(4t+9)^1/2

dy/dx= 3e^1/2x+1/2(4t+9)^1/2

(ii) Hence find the value of dy/dt when t=4, giving your answer correct to 3 significant figures.

but I don't understand how to find dy/dt?

thanks
In part (i) you told us that dy/dt is equal to 3e^1/2x+1.
So, you can substitute your equation of x in terms of t into y, in order to get y in terms of t. Then differentiate, and substitute t=4.

Alternatively, you know that dy/dt = dy/dx • dx /dt.
You already have dy/dx in terms of t and already have dx/dt. So multiply them, and substitute t=4.

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