A man 6 ft tall walks at a rate of 7 ft/sec away from a lamppost that is 14 ft high. At what rate is the length of his shadow changing when he is 60 ft away from the lamppost? g

Let be the distance between the lamppost and the man, and the length of the man's shadow cast by light. Then the man and lamppost form a set of similar right triangles (see image) in which

We can solve for :

Differentiating both sides with respect to time :

Since is changing at a rate of 7 ft/sec, it follows that is changing at a 25% slow rate, or 7*3/4 = 21/4 = 5.25 ft/sec.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.