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
a_sh-v [17]
2 years ago
12

A 4-foot tall child walks directly away from a 12-foot tall lamppost at 2 mph. How quickly is the length of her shadow increasin

g when she is 6 feet away from the lamppost (rounded to the nearest tenth of a foot per second)

Mathematics
1 answer:
xz_007 [3.2K]2 years ago
3 0

Answer:

The length of the shadow is increasing with the rate of 1.5 feet per sec

Step-by-step explanation:

Let AB and CD represents the height of the lamppost and child respectively ( shown below )

Also, let E be a point represents the position of child.

In triangles ABE and CDE,

\angle ABE\cong \angle CDE    ( right angles )

\angle AEB\cong \angle CED  ( common angles )

By AA similarity postulate,

\triangle ABE\sim \triangle CDE

∵ Corresponding sides of similar triangles are in same proportion,

\implies \frac{AB}{CD}=\frac{BE}{DE}

We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,

\implies \frac{12}{4}=\frac{6+DE}{DE}

12DE = 24 + 4DE

8DE = 24

DE=3

Now, the speed of walking = 2 mph = \frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}

Note: 1 mile = 5280 ft, 1 hour = 3600 sec

Thus, the time taken by child to reach at E  

= \frac{\text{Walked distance}}{\text{Walking speed}}

=\frac{6}{2.933}

= 2.045 hours

Hence, the change rate in the length of shadow

= \frac{\text{Length of shadow}}{\text{Time taken}}

=\frac{3}{2.045}

= 1.5 ft per sec.

You might be interested in
Use Product sue<br>solve<br>to<br>5x sino<br>23<br>tana​
Naily [24]

Step-by-step explanation: You dumb b*** I loved you i loved you iloved you its true. I wanted to be you and do what you

7 0
3 years ago
Please find the surface area of the prism... I will mark you brainliest
Oksi-84 [34.3K]
the surface area is 548 in^2
4 0
2 years ago
Read 2 more answers
Evaluate best answer for brainliest
Nadya [2.5K]
4/5 is the answer unless you need it in decimal

5 0
2 years ago
Read 2 more answers
Strawberry smoothie
Katen [24]
The milk is the greatest quantity
8 0
3 years ago
PLEASE HELP IM STUCK
SpyIntel [72]

Step-by-step explanation:

\frac{y2 - y1 }{x2 - x1}  =  \frac{3 -  - 2}{5 - 0}  =  \frac{5}{5}  = 1

4 0
1 year ago
Read 2 more answers
Other questions:
  • What number should be placed in the box to help complete the division calculation? (1 point) Long division setup showing an inco
    15·1 answer
  • Factorise 6x^2 - 21x
    5·1 answer
  • Please tell me the answer
    11·2 answers
  • 1. Different students drew random samples of size 50 from the mystery bag. The number of red chips each drew is given below. In
    11·1 answer
  • Need help wit number 60 plz. Math.
    10·1 answer
  • Compressed by a factor
    12·1 answer
  • 6 The diagonal of a quadrilateral is 30m in length and the length of the
    10·1 answer
  • 4 × (3 + 7) = (4 ×[]) + (4 ×[])
    8·1 answer
  • Round 4746.13662611 to the nearest whole number.<br> Answer:<br> Submit Answer
    13·2 answers
  • Sally has 24 cookies. She has to share the cookies with 3 friends. How can they split them evenly?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!