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
guapka [62]
3 years ago
11

A boat is sighted from a 50-meter observation tower on the shoreline at an angle of depression of 4 degrees moving directly towa

rds the shore at a constant speed. Five minutes later the angle of depression of the boat is 12 degrees. What is the speed of the boat in kilometers per hour?
Mathematics
1 answer:
MAXImum [283]3 years ago
4 0

Answer:

  5.76 km/h

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides of a right triangle. Here, we are given the side opposite the angle (angle of depression), and we want to find the adjacent side (distance from shore).

  Tan = Opposite/Adjacent

  tan(4°) = (height of tower)/(distance from shore)

  tan(4°) = (50 m)/(distance from shore)

Then the distance from shore is ...

  distance from shore = (50 m)/tan(4°) ≈ 715.03 m

__

At the second sighting, the distance from shore is ...

  distance from shore = (50 m)/tan(12°) ≈ 235.23 m

So, the distance traveled in 1/12 hour is ...

  715.03 m - 235.23 m = 479.80 m

and the speed in km per hour is ...

  speed = 0.4798 km/(1/12 h) = 5.7576 km/h

The speed of the boat is about 5.76 km per hour.

You might be interested in
Describe the sampling distribution of p(hat). Assume the size of the population is 30,000.
Naya [18.7K]

Answer:

a) \mathbf{\mu_ \hat p = 0.6}

b) \mathbf{\sigma_p =0.01732}

Step-by-step explanation:

Given that:

population mean \mu = 30,000

sample size n = 800

population proportion p = 0.6

a)

The mean of the the sampling distribution is equal to the population proportion.

\mu_ \hat p =  p

\mathbf{\mu_ \hat p = 0.6}

b)

The standard deviation of the sampling distribution can be estimated by using the formula:

\sigma_p = \sqrt{\dfrac{p(1-p)}{n}}

\sigma_p = \sqrt{\dfrac{0.6(1-0.6)}{800}}

\sigma_p = \sqrt{\dfrac{0.6(0.4)}{800}}

\sigma_p = \sqrt{\dfrac{0.24}{800}}

\sigma_p = \sqrt{3 \times 10^{-4}}

\mathbf{\sigma_p =0.01732}

7 0
2 years ago
Tom sells baseball cards at 10 for 35 cents. Is that a better deal than 12 for 40 cents?
AVprozaik [17]
For either one of the deals, just find what one card equals and times it by how many cards the other equation has.

e.g. 0.35 cents divide by 10 = 0.035. And now, you times it by 12 since the other deal is 12 cards for 40 cents.

0.035 x 12 = 0.48

So, 10 cards for 35 cents is not the better deal.
7 0
3 years ago
Read 2 more answers
(PLSSS HELP!! 35 points!!) Ted has to gift wrap a box of chocolates that is shaped like a triangular prism. What is the minimum
vichka [17]

Answer:

C

Step-by-step explanation:

just multiply them together should work

6 0
3 years ago
Suppose you have 5 riders and 5 horses, and you want to pair them off so that every rider is assigned one horse (and no horse is
maw [93]

There are 120 ways in which 5  riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways ^nN_r = \frac{n!}{(n-r)!},

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways ^nN_r = \frac{n!}{(n-r)!},

Now,

Substituting values,

We get,

^5N_5 = \frac{5!}{(5-5)!}

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5  riders and 5 horses can be arranged.

Learn more about arrangements here

brainly.com/question/15032503

#SPJ4

7 0
2 years ago
Drag and drop math problem thing pls help WILL MARK BRAINLIEST
BaLLatris [955]
Tbh ion even kno what you talm bout
5 0
3 years ago
Other questions:
  • what is the difference in there elevation an airplane flies at an altitude of 25,000 feet a submarine dives to a depth of 600 fe
    9·1 answer
  • What is the exact value
    8·1 answer
  • Carmen measured a house and made a scale drawing. The scale of the drawing was 9 millimeters = 1 meter. What is the drawing's sc
    15·1 answer
  • The perimeter of a rectangle is 53 meters. The length is 2.3 meters longer than the width, w. Write and solve an equation to fin
    10·2 answers
  • I need help on this. ive been struggling. TwT<br><br>lateral area<br>surface area<br>volume<br>​
    9·2 answers
  • LMN is a straight angle. What is the<br> measure of ZOMP?<br><br> Pls answer ASAP!
    10·1 answer
  • What is a possible factorization of a polynomial with 3, –2, and i as zeros?
    11·1 answer
  • What are the square roots of 25
    11·1 answer
  • Please help will give brainliest if correct​
    7·2 answers
  • Which expression is equivalent to -2( x-7 )?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!