Let x and y be functions of time t such that the sum of x and twice y is constant. Which of the following equations describes the relationship between the rate of change of x with respect to time and the rate of change of y with respect to time?

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  b)  dx/dt = -2dy/dt

Step-by-step explanation:

We are given that ...

  x(t) +2y(t) = k

for some functions x(t) and y(t) and some constant k.

Differentiating with respect to time gives ...

  x'(t) +2y'(t) = 0

  x'(t) = -2y'(t) . . . . . subtract the y term

In the form used in the answer choices:

  dx/dt = -2dy/dt . . . . . matches choice B

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

d) 48

step-by-step explanation:

16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,304,320,336