Show your work and explain your work. Simplify the answers. All calculator value

Question

Show your work and explain your work. Simplify the answers. All calculator values MUST be preceded by a true, exact values (for example, you can use 1.41 as an approximation of root 2,ONLY after root 2 have been used in the previous step). Use separate paper for the solutions. 1. A spotlight on the ground shines on a wall 12m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6m/s, how fast is the length of his shadow on the building decreasing when he is 4m from the building?

Explanation / Answer

Let y = length of shadow on the building
We can form similar triangles here so that we have,
y/2 = 12/x, where x = distance of man from the spotlight
or y = 2(12)/x
y = 24/x

taking the derivative of y with respect to time t:
dy/dt = - 24(dx/dt)/x^2

From the given conditions of the problem, dx/dt = 1.6 m/s and
x = 12m - 4m = 8m.

Therefore,
dy/dt = -24(1.6 m/s)/(8 m)^2
dy/dt = -0.6 m/s answer

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.