Question

Need help #1. The answer is shown, but I don’t know how to get to the answer. Please teach and show steps.

Answer 1

Answer:

Let x and y be functions of time t such that the sum of x and y is constant.

(B) is the right answer

Answer 2

Answer:

B

Step-by-step explanation:

We are given that x and y are functions of time t such that x and y is a constant. So, we can write the following equation:

$x(t)+y(t)=k,\text{ where k is some constant}$

The rate of change of x and the rate of change of y with respect to time t is simply dx/dt and dy/dt, respectively. So, we will differentiate both sides with respect to t:

$\displaystyle \frac{d}{dt}\Big[x(t)+y(t)\Big]=\frac{d}{dt}[k]$

Remember that the derivative of a constant is always 0. Therefore:

$\displaystyle \frac{dx}{dt}+\frac{dy}{dt}=0$

And by subtracting dy/dt from both sides, we acquire:

$\displaystyle \frac{dx}{dt}=-\frac{dy}{dt}$

Hence, our answer is B.