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
Salsk061 [2.6K]
2 years ago
6

A tourist at scenic Point Loma, California uses a telescope to track a boat approaching the shore. If the boat moves at a rate o

f 10 meters per second, and the lens of the telescope is 35 meters above water level, how fast is the angle of depression of the telescope (θ) changing when the boat is 210 meters from shore? Round any intermediate calculations to no less than six decimal places, and round your final answer to four decimal places.
Mathematics
1 answer:
Taya2010 [7]2 years ago
8 0

9514 1404 393

Answer:

  0.4424°/s

Step-by-step explanation:

We can get an answer to the desired accuracy by approximating the rate of change over a small time interval.

0.05 seconds before the time of interest, the boat will be ...

  210 +10(0.05) = 210.5

meters from shore. The angle of depression from the observer is ...

  tan(θ) = (35 m)/(210.5 m)   ⇒   θ = arctan(35/210.5) ≈ 9.440251°

Then 0.05 seconds after the time of interest, the angle of depression will be ...

  θ = arctan(35/(210-0.05(10))) = arctan(35/209.5) ≈ 9.484495°

The rate of change of angle of depression over that 0.1-second period is ...

  (9.484495° -9.440251°)/(0.1 s) ≈ 0.4424°/s

_____

<em>Additional comment</em>

If you write the function relating angle θ and time t, you would have ...

  θ = arctan(35/(210-10t))

The derivative of this with respect to time is ...

  θ' = 1/(1 +(35/(210-10t))²)×(350/(210 -10t)²) = 350/((210 -10t)² +35²)

At t=0, this is 350/(210² +35²) = 2/259 . . . . . radians per second

Then in degrees per second, the rate of change of angle is ...

  (2/259)(180/π) = 360/(259π) °/s ≈ 0.4424°/s

You might be interested in
What is 8x + -13x I just want to see if the answers are as quick as it says it is
Dafna1 [17]
- 5x. 
In case you actually want to know how I got it:
the question is just saying "8x - 13x".
8 - 13 = -5 
4 0
3 years ago
Read 2 more answers
24x10=?? (Please explain in zero the hero or in 4 square..)
Tamiku [17]
240, you just add a zero to 24, I don't know what you mean by zero the hero of 4 square, hope this helps!
6 0
3 years ago
Read 2 more answers
the original price of a collectible model airplane is $115. The discounted price is $99. What is the percent of discount to the
storchak [24]

Answer:

$99/$115 x 100% = 86.086% of the original price  

So 100% - 86.086  

= 13.9 = 14%  

Or you could just do (115 - 99) x 100 which gets the same answer.

8 0
3 years ago
A chain 5 links long is joined to a chain 7 links long. How many links long is the resulting chain
Anna [14]

12 links long because 5 + 7 = 12

3 0
2 years ago
Read 2 more answers
Ms. Anderson deposits $7,000 into a savings account that pays a simple interest of 2% per year. Which of the following would be
ANEK [815]

Answer:

$7,428.46

Step-by-step explanation:

A = 7000(1 + .02)³

A = 7000(1.02)³

A = 7000(1.0612)

A = $7,428.46

7 0
3 years ago
Other questions:
  • BRAINLIESTTT ASAP!!! PLEASE HELP ME :)
    13·2 answers
  • What is seven more than six times a number y
    14·1 answer
  • Change each fraction or mixed number to a percent. a. 2⁄5 b. 7⁄20 c. 111⁄16 d. 141⁄4
    13·1 answer
  • Simplify to create an equivalent expression -4(z+3)-4(5-4z)
    14·1 answer
  • If the temperature were to drop 38 degrees, which number would display this best?
    12·1 answer
  • Convert 4.824 meters per second to kilometers per hour
    6·1 answer
  • X - 4x - 12 = (x __ 2)(x ____ 6)<br> where do the plus and equal sign go
    7·1 answer
  • you deposit $1050 into an account that pays 7.25% interest per year. find the amount after six year given the following: a) comp
    9·1 answer
  • How much wood could a wood chuck if 100 wood was timed by 24?
    7·1 answer
  • Answer fast please, thank you.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!