1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
posledela
3 years ago
5

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along

a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?

Mathematics
1 answer:
mina [271]3 years ago
7 0

Answer:

The tip of the man shadow moves at the rate of \frac{20}{3} ft.sec

Step-by-step explanation:

Let's draw a figure that describes the given situation.

Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.

Here it forms two similar triangles.

Let's find the distance "y" using proportion.

From the figure, we can form a proportion.

\frac{y - x}{y} = \frac{6}{15}

Cross multiplying, we get

15(y -x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

y = \frac{15x}{9\\} y = \frac{5x}{3}

We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).

\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt} ----(1)

We are given \frac{dx}{dt} = 4 ft/sec. Plug in the equation (1), we get

\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec

Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.

You might be interested in
L = $20 r = 4% t = 2 years
Annette [7]
I'm guessing this is a question about interest rates? If you have $20 that increases by 4% in one year, you need to multiply 20 by 1.04. This gets you $20.8.

If you are talking about compound interest, we will take this number and multiply it again by 1.04 for the second year. 20.8 x 1.04 = $21.632. 

If it is instead simple interest, we will simply add another .8 dollars for each year, instead of getting 4% interest compounded every year onto the new value. This gets you $21.6.
7 0
2 years ago
Quincy's retirement party will cost $30 if he invites 10 guests. If there are 16 guests, how much will Quincy's retirement party
3241004551 [841]

Answer:

$48

30/10 is equal to 3/1, 16 x 3 equals to 48.

8 0
2 years ago
Read 2 more answers
At fairvie middle school 75 band members need to raise a total of 8250 for a trip. So far they have raised 3120. How much money
galina1969 [7]
$8250 - $3120 = $5130

$5130/75 = $68.40

Each band member must raise $68.40
8 0
2 years ago
Which graph represents a reflection of f(x) = One-tenth(10)x across the y-axis? On a coordinate plane, an exponential function a
Ira Lisetskai [31]

Answer:

Step-by-step explanation:

The answer is D

8 0
3 years ago
Read 2 more answers
Members of a lacrosse team raised $1352.50 to go to a tournament. They rented a bus for $802.50 and budgeted $25 per player for
Alecsey [184]

Answer: 22

Step-by-step explanation:

From the question the, we are informed that members of a lacrosse team raised $1352.50 to go to a tournament and that they rented a bus for $802.50 and budgeted $25 per player for meals.

The equation which can be used to determine p, the number of players the team can bring to the tournament would be calculated as:

802.50 + 25p = 1352.50

25p = 1352.50 - 802.50

25p = 550

p = 550/25

p = 22

They can bring 22 players to the tournament

3 0
3 years ago
Read 2 more answers
Other questions:
  • Pie stands for 3.14 but need to know the answer
    12·1 answer
  • Mauro has 140 ft of rope. He will cut it into two pieces so that the length of the longer piece is 3 times the length of the sho
    10·2 answers
  • What’s the correct answer for this question?
    9·1 answer
  • A pack of pencils contains 20 pencils. If Trish uses 3/4 of the pack, how many pencils will she use?
    5·1 answer
  • How does a "for every" statement show a ratio comparison? (Example of a for every statement: There a 5 strawberries for every 6
    10·2 answers
  • What was the purpose of the Peace Corps?
    10·2 answers
  • Solve for x and show work<br> PLEASE HELP!!!
    14·2 answers
  • Find the approximate area of a semicircle with a radius of 6 centimeters.
    8·1 answer
  • The leg of a right triangle is 3 units and the hypotenuse is 11 units. What is the length, in units, of the other leg of the tri
    15·1 answer
  • Help<br> Me ? I’m marking brainlist
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!