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A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6

Burka [1]

Answer:

Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

Step-by-step explanation:

Given : In the figure attached, Length of girl EC = 4 ft

Length of street light AB = 25 ft

Girl is moving away from the light with a speed = 6 ft per sec.

To Find : Rate ( $\frac{dw}{dt}$ ) of the tip (D) of the girl's shadow (BD) moving away from th

light.

Solution : Let the distance of the girl from the street light is = x feet

Length of the shadow CD is = y feet

Therefore, $\frac{dx}{dt}=6$ feet per sec. [Given]

In the figure attached, ΔAFE and ΔADE are similar.

By the property of similar triangles,

$\frac{x}{21}=\frac{x+y}{25}$

25x = 21(x + y)

25x = 21x + 21y

25x - 21x = 21y

4x = 21y

y = $\frac{4x}{21}$

Now we take the derivative on both the sides,

$\frac{dy}{dt}=\frac{4}{21}\times \frac{dx}{dt}$

= $\frac{4}{21}\times 6$

= $\frac{8}{7}$

≈ 1.14 ft per sec.

Since w = x + y

Therefore, $\frac{dw}{dt}= \frac{dx}{dt}+\frac{dy}{dt}$

$\frac{dw}{dt}=6+1.14$

= 7.14 ft per sec.

Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

3 0

3 years ago

Write a 3-digit number that can be divided by 3 but not by 10.

NARA [144]

Answer:

Hi

999

Step-by-step explanation:

8 0

3 years ago

Will mark brainliest

faust18 [17]

$x^3$ is strictly increasing on [0, 5], so

$\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125$

and

$\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0$

so the integral is bounded between

$\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}$

8 0

2 years ago

Find each percent change. Round to the nearest tenth of a percent. State if it is an increase or decrease. From 79 miles to 84 m

PolarNik [594]

Answer:

the answer is d.

Step-by-step explanation:

first, you want to use the formula,

new value - original value

____________________

original value * 100

you see that 84 is the new value and 79 would be the original value. substitute the numbers in. this is a increase since you will get a positive value.

84 - 79

______

79 * 100

now we solve it.

5

__

79 * 100

you can either solve the fraction first then multiply that by 100 or multiply the numerator by 100 first then divide that by 79, each way works.

500

____

79 = approximately 6.3% increase (this is not a exact value, just rounded)

or

5

__

79 = approximately 0.063 (this is not a exact value, just rounded)

0.063 * 100 = 6.3% increase

7 0

3 years ago

The oblique pyramid has a square base.

Brums [2.3K]

Good evening ,

______

Answer:

the volume of the pyramid = 5cm³

___________________

Step-by-step explanation:

the volume of the pyramid = (b×h)/3 = (2²×3,75)/3 = (4×3,75)/3 = 15/3 = 5.

:)

6 0

3 years ago