A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle is at the point (3,4), dx/dt=6. What is the value of dy/dt at this time?

The movement of the particle on the circle is its displacement

The value of dy/dt at this time is -9/2

The equation of the circle is given as:

Differentiate with respect to time

Divide through by 2

At point (3,4);

x =3 and y = 4.

So, we have:

Also: dx/dt = 6

So, we have:

Multiply

Subtract 18 from both sides

Divide through by 4

Simplify

Hence, the value of dy/dt at this time is -9/2

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Step-by-step explanation:

Differentiation

We have a relationship between x and y as follows:

Both variables depend on time t for t≥0.

Differentiating with respect to time:

Applying the derivative of a power function:

Recall the derivative of a constant is 0.

Dividing by 2:

Solving for y':

At some specific time, we have:

x=3, y=4, dx/dt = x' = 6. Substituting:

Operating:

Simplifying:

what are ur choices?

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is