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
Kazeer [188]
3 years ago
5

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

he angle of depression to the boat is 16°23'. When the boat stops, the angle of depression is 49°29' . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
Mathematics
1 answer:
matrenka [14]3 years ago
3 0

Answer:

509.35 feet

Step-by-step explanation:

16°23' means 16 degrees and 23 minutes.  A minute is 1/60 of a degree.

16°23' = 16 + (23/60) = 16.383°

Similarly:

49°29' = 49 + (29/60) = 49.483°

When the boat is first noticed:

tan(16.383°) = 200 / a

a = 200 / tan(16.383°)

a = 680.27

When the boat stops:

tan(49.483°) = 200 / b

b = 200 / tan(49.483°)

b = 170.92

So the difference is:

a − b = 680.27 − 170.92 = 509.35

The boat traveled 509.35 feet from the time it was first noticed to the time it stopped.

You might be interested in
To rent a bounce house: At Mike's Bounce Shop costs $30 plus $2 per hour. At Jose's Bounce Rentals, it costs $12 plus $8 per hou
ANEK [815]

Answer: After 3 hours both will have the same cost.

Step-by-step explanation:

Let x = Number of hours and y be the total cost.

Total cost = Initial cost + (cost per hour)(Number of hours)

At Mike's Bounce Shop,

Total cost (y)= 30+2x

At Jose's Bounce Rentals,

Total cost(y) =  12+8x

When both shops have the same cost, then

12+8x=30+2x\\\\\Rightarrow\ 8x-2x=30-12\\\\\Rightarrow\ 6x=18\\\\\Rightarrow\ x=3

Total cost = 12+8(3)=12+24=$36

Hence, After 3 hours both will have the same cost.

3 0
3 years ago
Graph the following inequality. Then click to show the correct graph.<br><br><br>3x - 2y ≤ 6
max2010maxim [7]

Answer:

We want to graph the inequality:

3x - 2y ≤ 6

The first step is to write this as a linear equation, to do it, we can isolate y in one side of the inequality.

3x  ≤ 6 + 2y

3x - 6  ≤ 2y

(3/2)x  - 6/2  ≤ y

(3/2)x  - 3  ≤ y

or:

y ≥ (3/2)x  - 3

Because we have the symbol ≥

The points on the line are solutions, then the first part is to graph the line:

y = (3/2)*x - 3

Next, we have:

y equal to or larger than  (3/2)*x - 3

Then we need to shade all the region above that line.

The graph can be seen below.

3 0
3 years ago
So far Monica has read 56 of a book she has read the same number of pages each day for five days what fraction of the book does
alexandr1967 [171]

Answer:

14/125

Step-by-step explanation:

56 % ÷ 5 days ie 11.2% per day ie 112/1000 or 14/125

4 0
2 years ago
8624 to the nearest thousand
Alika [10]
<span>✡ Answer: 9000 </span><span>✡

- - Solve:

If your 3 numbers to the right (in this problem its 3) are 499 or less, you round down, if its 500 or up, you round up.

In this case, round up.

- - Solve furthermore:
          9000


</span>
✡Hope this helps<span>✡</span>
4 0
3 years ago
Read 2 more answers
Which situation CANNOT be represented by this equation? 4x+7=31
mash [69]
The correct answer to your question is going to be option C. if we look at the equation 4x + 7 = 31, we can see that 4x stands for a number that changed depending on how much of something x can be. the 7 in the equation stands for something doesnt change depending upon variables how much or how little x will be. knowing this, if we look at option C we read that each phone case cost $7 while $4 is how much it costs to ship. since this problem is about how many $4 phone cases Taliba can get, C would incorrect because they say that $7 is the post of each phone case. 
let me know if you have any further questions
:)
3 0
3 years ago
Read 2 more answers
Other questions:
  • Marisol is preparing a care package to send her brother the package will include a board game that weighs 4 lb in several 1/4 lb
    12·2 answers
  • In the equation, 1/4n+5=51/2 what is n equal to?
    10·2 answers
  • How to find and solve this ? <br><br>Shape A = ______ units<br><br>Shape B = _______ units​
    5·1 answer
  • F(x) = 2x + 3<br> What function is this
    13·2 answers
  • The angle shown is in standard position. Select the possible measures of the angle. –450° –360° –270° –90° 90° 270° 360° 450° On
    6·2 answers
  • What is 3x² + 3x - 36 and x² - 3x - 28 in factored form?
    12·2 answers
  • Scientists are preparing two satellites to be launched. The equation y = 8000.C represents the number of miles, y, that the sate
    7·2 answers
  • PLEASE HELP!!!!!!!! Identify the angle of elevation.
    6·1 answer
  • PLEASE HELP! DUE SOON!!!!
    8·1 answer
  • 2020 to the square root of 6
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!