MATHEMATICS COLLEGE

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.4 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Answers

Answer 1

Answer:

Answer:

the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Step-by-step explanation:

From the diagram attached below;

the man is standing at point D with his head at point E

During that time, his shadow on the wall is y = BC

ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e

$(AD)/(AB) = (DE)/(BC)$

$(8)/(12) = (2)/(y)$

8y = 24

y = 24/8

y = 3 meters

Let take an integral look at the distance of the man from the building as x, therefore the distance from the spotlight to the man is 12 - x

∴

$(12-x)/(12)=(2)/(y)$

$1- (1)/(12)x = 2* (1)/(y)$

To find the derivatives of both sides ;we have:

$- (1)/(12)dx = 2* (1)/(y^2)dy$

$- (1)/(12) (dx)/(dt) = 2* (1)/(y^2) (dy)/(dt)$

During that time ;

$(dx)/(dt )= 1.4 \ m/s$ and y = 3

So; replacing the value into above ; we have:

$-(1)/(12)(1.4) = - (2)/(9) (dy)/(dt)$

$(dy)/(dt) = \frac{\frac{ 1.4} {12 } }{ (2)/(9)}$

$(dy)/(dt) = {\frac{ 1.4} {12 } }*{ (9)/(2)}$

$(dy)/(dt) =0.525 \ m/s$

Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s

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For spirit week at a local high school, students were encouraged to wear their school colors of green and white. 1,500 students wore their school colors while 300 students did not wear green and white. What percent of the school population did not wear their school colors?

Answers

Answer:

17%

Step-by-step explanation:

1,500 + 300 = 1,800

300/1,800 ≈ 17%

What is the y-intercept of the line your equation X-1/2Y = -6A.-6

B.-3

C.0

D.12

Answers

9514 1404 393

Answer:

D. 12

Step-by-step explanation:

Set x=0 and solve for y.

0 -1/2y = -6

y = (-2)(-6) = 12 . . . . . . multiply by -2 to clear the fraction

The y-intercept is 12.

A standard 52-card deck has four 13-card suits: diamonds, hearts, clubs, and spades. the diamonds and hearts are red, and the clubs and spades are black. each 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king, and an ace. an experiment consists of drawing 1 card from the standard deck. find the probability of drawing a black king of heartsblack king of hearts.

Answers

The probability of getting a black king of hearts is 1/52

From the question, we have:

The number of cards in a standard deck, n = 52

Black king of heart, r = 1

The probability of getting a black king of hearts is the quotient of the number of black king of heart and the total number of cards in the deck.

So, we have:

p = 1/52

Hence, the probability of getting a black king of hearts is 1/52

Answers

here what i got
3
12
48
192

-2[(4y+1)-(2y-2)]=6(7-y)-6

Answers

Answer:

y=9

Step-by-step explanation:

-2[(4y+1)-(2y-2)]=6(7-y)-6

-2[4y+1-2y-2]=6(7-y)-6

-2[2y-1]=6(7-y)-6

-2y+2=6(7-y)-6

-2y+2=42-6y-6

Add 6y to both sides

4y+2=42-6

4y+2=38

Subtract 2 from both sides

4y=36

Divide both sides by 4

y=9

There are two different music download companies that offer a monthly plan for downloading songs. S-Jams charges $1.29 per song plus $10 monthly fee. C-tunes charges $0.99 per song plus $16 monthly fee. When will the company’s plans cost the same? Write an expression for the cost of S-Jams.

Answers

Answer:

Thus, when both S-jams and C-tunes have 20 songs downloaded in a month , the cost will be same.

an expression for the cost of S-Jams $0.99n + $16

Step-by-step explanation:

For

S-Jams

cost of 1 song = $1.29

let there be n songs downloaded in a month

then

cost of n songs = n*cost of 1 song = $1.29n

monthly fee = $10

Total cost of S-Jams = $1.29n+$10

________________________________________

For

C-Tunes

cost of 1 song = $0.99

let there be n songs downloaded in a month

then

cost of n songs = n*cost of 1 song = $0.99n

monthly fee = $16

Total cost for C-Tunes= $0.99n + $16

we have to find When will the company’s plans cost the same.

Total cost of S-Jams = Total cost of C- Tunes

1.29n+10 = 0.99n + 16

=> 1.29n - 0.99n = 16-10

=> 0.30n = 6

=> n = 6/0.3 = 20

Thus, when both S-jams and C-tunes have 20 songs downloaded in a month , the cost will be same.

an expression for the cost of S-Jams $0.99n + $16

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