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:

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation:

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.