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AP CAL AB HELP!!!!!!!!!!!

AP CAL AB HELP!!!!!!!!!!!-example-1
User Esty
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2 Answers

3 votes

Answer:With what does though

Explanation:

User Siliarus
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5.5k points
2 votes

Answer:


(dx)/(dt)=0

Explanation:

We have:


y^2+xy-3x=8

Where both x and y are functions of t.

To find our solution, let's first take the derivative of both sides with respect to t:


(d)/(dt)[y^2+xy-3x]=(d)/(dt)[8]

Expand:


(d)/(dt)[y^2]+(d)/(dt)[xy]+(d)/(dt)[-3x]=(d)/(dt)[8]

Differentiate. We must differentiate implicitly. Also, for the second term, we must use the product rule. So:


(2y(dy)/(dt))+((dx)/(dt)y+x(dy)/(dt))-(3(dx)/(dt))=0

Simplify:


2y(dy)/(dt)+(dx)/(dt)y+x(dy)/(dt)-3(dx)/(dt)=0

We know that dy/dt is 3 when x is -4 and y is 2.

So, to find dx/dt, substitute 3 for dy/dt, -4 for x, and 2 for y. This yields:


2(2)(3)+(dx)/(dt)(2)+(-4)(3)-3(dx)/(dt)=0

Simplify:


12+2(dx)/(dt)-12-3(dx)/(dt)=0

Simplify:


-(dx)/(dt)=0

Divide both sides by -1:


(dx)/(dt)=0

最终答案是零 :)

User Gaston
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4.9k points