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A particle is moving along the parabola x2=4(y+3). As the particle passes through the point (4,1), the rate of change of its y-coordinate is 6 units per second. How fast, in units per second, is the x-coordinate changing at this instant?a) 4b) 13c) 32d) 6e) 3

Respuesta :

LammettHash

[tex]x^2=4(y+3)[/tex]

Differentiate both sides with respect to time [tex]t[/tex]:

[tex]2x\dfrac{\mathrm dx}{\mathrm dt}=4\dfrac{\mathrm dy}{\mathrm dt}[/tex]

We're given that [tex]\frac{\mathrm dy}{\mathrm dt}=6[/tex] at the moment [tex](x,y)=(4,1)[/tex], so that

[tex]2\cdot4\dfrac{\mathrm dx}{\mathrm dt}=4\cdot6\implies\dfrac{\mathrm dx}{\mathrm dt}=3[/tex]

units per second (D).

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