Mathematics, 18.05.2021 19:20 719563mercy

A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tallman is walking towards the wall at the rate of 30 feet per second. How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall

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Answer from: hbked23

The rate at which the tip of his shadow is moving down is $\frac{24}{15} ft/sec$

Step-by-step explanation:

Given - A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tall man is walking towards the wall at the rate of 30 feet per second.

To find - How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall ?

Proof -

From the given information, the figure becomes

Triangle ABC and Triangle DBE are similar triangle

AC/DE = BC/BE

⇒h/6 = 200/(200-x)

⇒h = 1200/(200 -x)

Now,

Differentiate h with respect to t, we get

$\frac{dh}{dt} = 1200(-\frac{1}{(200-x)^{2} } )(-1)\frac{dx}{dt}$

⇒ $\frac{dh}{dt} = (\frac{1200}{(200-x)^{2} } )\frac{dx}{dt}$

Now,

If the rate of the tip is moving down the wall

At x = 50 feet, dx/dt = 30 feet per second

So,

⇒ $\frac{dh}{dt} = (\frac{1200}{(200-50)^{2} } )(30)$

⇒ $\frac{dh}{dt} = \frac{1200}{(150)^{2} } (30)$

⇒ $\frac{dh}{dt} = \frac{1200}{(150)(150) } (30)$

⇒ $\frac{dh}{dt} = \frac{24}{15 }$

So, we get

The rate at which the tip of his shadow is moving down is $\frac{24}{15} ft/sec$

A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tallman is walking

Answer from: Quest

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i

Answer from: Quest

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

Bwill make the inequalities y < 2x + 1 and y> -x- 2 true. o a. region b o b. region c o c. r

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