Question

a point moves on the parabola y^2=8 in such a way that the rate of change of the ordinate is always 5 units/second. how fast is the abscissa changing when the ordinate is 4?

Answer 1

Thanks you for showing up D:

Answer 2

shouldnt there be an x term in the parabola?

Answer 3

Oh yea

Answer 4

so in general what you should do is differentiate the equation wrt to time. For example if the equation is \(x = f(y)\)
\[\frac {dx}{dt} = \frac{df(y)}{dt}\]
which further can be represented as,
\[\frac{dx}{dt} = \frac{df(y)}{dy}\frac{dy}{dt}\]
so when \(y=4\) find the \(\frac{dx}{dt}\)
\[\left[\frac{dx}{dt} \right]_{y=4} = \left[\frac{df(y)}{dy}\right]_{y=4} \left[\frac{dy}{dt}\right]_{y=4} \]

Answer 5

okay, so I have to find that?

Answer 6

yeah find the values of the expressions in the r.h.s

Answer 7

kk one second

Answer 8

\[ \frac{ ds }{ dt }=5?\]

Answer 9

but according to your given problem, the question itself contradicts. since it is stated that \(y^2=8\implies y = \pm \sqrt 8\) which is a constant and later it talks about a rate of change in the value of y wrt time..

Can you state the equation correctly

Answer 10

I have no clue about this :/

Answer 11

are you sure that the question given to is like that?

Answer 12

I think i may be able to figure it out, but thank you soooo much man! :D

Answer 13

medal for you ;)

Answer 14

u are welcome ;)

Answer 15

=D