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 3d − 7d + 2.8 &lt; 5.8 − 27
weqwewe [10]
3d -7d+ 2.8 < 5.8 -27
⇒ -4d+ 2.8 < 5.8 -27
⇒ -4d < 5.8 -27 -2.8
⇒ -4d < -24
⇒ d > (-24)/(-4)
⇒ d > 6

Final answer: d > 6~
3 0
3 years ago
Given the demand equation 6x+p-50=0 and the supply equation 6x-p+14=0 where p is the unit price in dollars and x represents the
Katarina [22]

Answer:

The equilibrium quanity and equilibrium price is 3 Thousand units and 32 dollars respectively.

Step-by-step explanation:

Market equilibrium occurs in those markets in which the quantity demanded by consumers equals the quantity supplied by firms. In this state, the equilibrium point has its corresponding equilibrium quantity and price. That is, the equilibrium point is that point where, for a given price, the quantity supplied is equal to the quantity demanded.

The supply and demand curves represent the quantities that consumers are willing to buy and producers are willing to sell at that price respectively.

Being:

  • demand equation: 6x+p-50=0 ⇒ 6x= 50 - p ⇒ x=\frac{50 - p}{6}
  • the supply equation 6x-p+14=0 ⇒ 6x= p - 14 ⇒ x=\frac{p-14}{6}

Since when the market reaches equilibrium, the quantity demanded equals the quantity supplied and x representing the quantity demanded in units of thousand, then:

\frac{50 - p}{6}=\frac{p-14}{6}

Solving, you get:

6*\frac{50 - p}{6}=p-14

50 - p= p -14

50 - p +14 = p

50 +14= p + p

64= 2*p

p=\frac{64}{2}

P=32 dollars

This value is the equilibrium price. Replacing this value in the demand and supply equation, the equilibrium quantity is obtained, which should be the same for both cases:

  • demand equation:  x=\frac{50 - 32}{6} ⇒ x= 3 Thousand units
  • the supply equation  x=\frac{32-14}{6} ⇒ x=3 Thousand units

So, <u><em>the equilibrium quanity and equilibrium price is 3 Thousand units and 32 dollars respectively.</em></u>

In its graphical representation, the equilibrium point can be seen as that point where the supply and demand curves intersect. You can see this in the attached image, where the blue line represents the supply and the red line the demand.

7 0
3 years ago
The expression x4 + 6x3 – 11x2 – 60x + 100 is equivalent to (x – 2)(x – 2)(x + 5)(x + 5). At what points does the graph of the f
nikdorinn [45]
Since y equals the product of the factors, any value for x which makes any factor equal to zero is a point where the graph touches the x-axis.

x=-5 and 2  (technically the points (-5,0) and (2,0))
6 0
3 years ago
Read 2 more answers
What is the area in square units of the figure shown below??help asap!don't share links or anything pleasee
wel

Answer:

area equals 36 and 3 fourths because if you cut the triangle off of one of the sides and add it to the other side it makes a rectangle then you do length times width to find regular area of a rectangle.

7 0
2 years ago
Round 98,471 to the nearest ten thousands
d1i1m1o1n [39]
The answer to this question is 98000
4 0
3 years ago
Other questions:
  • Rolex worked 40 hours last week she had $74 deducted from his earning for taxes . if he had $286 left after the deduction how mu
    9·1 answer
  • Find the slope of the line using (4,-4) (8,-1) (0,-7) (-4,-10)
    5·2 answers
  • X =<br><br> 10<br> 8<br> 9<br> ---------------------
    12·2 answers
  • Graph the line using a point and a slope. Write the equation of each line.
    8·2 answers
  • What are the leading coefficient and degree of the polynomial <br><br> 6x^2-10+18x^3+x
    5·1 answer
  • Can someone please answer this question. Identify the vocabulary word that matches the picture. ​
    7·1 answer
  • Represent √10 , √17 and √13 in a number line.​
    13·1 answer
  • Select the correct answer.
    6·1 answer
  • Given that 3p+2=5(p-2),hitung nilai p
    15·1 answer
  • A furniture maker used 5/6 of a can of paint to paint some chairs. He used 1/6 of a of paint for each chair. How many chairs did
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!