SOLUTION: A particle travels along the parabola y = 5x^2 + x + 3. At what point do its abscissa and ordinate change at the same rate.

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Question 1082943: A particle travels along the parabola y = 5x^2 + x + 3. At what point do its abscissa and ordinate change at the same rate.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+5x%5E2+%2B+x+%2B+3

The abscissa and ordinate change at the same rate when 

dx%2Fdt=dy%2Fdt

Differentiate 

y+=+5x%5E2+%2B+x+%2B+3

with respect to t (use the chain rule) 

dy%2Fdt=10x%2Aexpr%28dx%2Fdt%29+%2B+dx%2Fdt

Since dx%2Fdt=dy%2Fdt, we divide equals by equals by dividing
the left side by dy%2Fdt and the right side through by dx%2Fdt

1=10x+%2B+1

0=10x

0=x

So the abscissa and ordinate change at the same rate when x=0,
and that is when  

y+=+5%280%29%5E2+%2B+%280%29+%2B+3

y=3

So the abscissa and ordinate change at the same rate at the
point (0,3)

Edwin