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
Naddika [18.5K]
3 years ago
8

After leaving camp for a three-day journey into the frozen tundra, Daniela has just returned to camp. The

Mathematics
2 answers:
expeople1 [14]3 years ago
5 0

Answer:

  a) 8.7 km

  b) 187.6°

Step-by-step explanation:

<u>Given</u>

Travel vectors (distance)∠(direction) ...

  • d₁ = 8∠3°
  • d₂ = unknown
  • d₃ = 1∠47°
  • total travel was a round trip

<u>Find</u>

(Rounded to the nearest tenth ...)

  a) |d₂|

  b) ∠d₂

<u>Solution</u>

In order for the sum of the three travel vectors to represent a round trip, their sum must be zero. That is, the value of d₂ must be the opposite of the sum of the other two vectors. A vector calculator can find the desired value easily. Here, we will show the calculation using the law of cosines and the law of sines.

__

a) A diagram can be helpful. Since we want to find the opposite of the sum of the given vectors, we can start by drawing their sum. In our diagram, d₁ is segment AB, and d₃ is segment BC. Their sum is the segment AC.

The internal angle ABC is the supplement of the difference of the angles for d₁ and d₃, so is 180° -(47° -3°) = 136°. Then the law of cosines gives length AC as ...

  AC² = AB² +BC² -2AB·BC·cos(B)

  AC² = 8² +1² -2·8·1·cos(136°) = 65 -16cos(136°) ≈ 76.5094

  AC ≈ √76.5094 ≈ 8.747

The distance traveled on day 2 is about 8.7 km.

__

b) Given the side lengths of a triangle and one angle, the law of sines can be used to find the other angles. Here, it is convenient to find the internal angle at A. The law of sines tells us ...

  sin(A)/BC = sin(B)/AC

  sin(A) = BC/AC·sin(B)

  A = arcsin(BC/AC·sin(B)) = arcsin(1/8.747·sin(136°)) ≈ 4.555°

The direction angle from C to A will be the sum of the 3° direction angle of AB and the internal triangle angle A we just found, added to 180°. That sum is ...

  ∠CA = 180° +3° +4.6° = 187.6°

  ∠d₂ = 187.6°

Amanda [17]3 years ago
3 0

Answer:

Distance traveled 8.6 kilometers on day two

Daniela traveled in a direcrion of 234degrees on day two

Step-by-step explanation:

I had the same exact question and found the answers after having it incorrect

You might be interested in
Please help me I will give brainliest
Pani-rosa [81]

Answer:Yes, I checked.. it is option 2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What two numbers are added together and equal -8.
Anastasy [175]

Answer: You might need to be more descriptive, there's a lot of numbers that could be added together to equal -8.

-4 + -4 = -8.

-6 + -2 = -8.

etc.

4 0
3 years ago
Read 2 more answers
How r u so good at this
iren [92.7K]

Answer:

Step-by-step explanation:

Good at what?

4 0
3 years ago
Read 2 more answers
Riley has a farm on a rectangular piece of land that is 200200200 meters wide. This area is divided into two parts: A square are
777dan777 [17]

Answer:

The inequality that models the situation for her to have money to save is

7L² > 3(200L - L²)

On simplifying and solving,

L > 60 meters

Step-by-step explanation:

The length of her farm = L meters

The farm where she grows avocados is of square dimension

Area of the farm = L × L = L²

The piece of land is 200 m wide.

Total area of the piece of land = 200 × L = (200L) m²

If the area of her farm = L²

Area of the side where she lives will be

(Total area of the land) - (Area of the farm)

= (200L - L²)

= L(200 - L)

Every week, Riley spends $3 per square meter on the area where she lives, and earns $7 per square meter from the area where she grows avocados.

Total amount she earns from the side she grows the avocados = 7 × L² = 7L²

Total amount she spends on the side where she lives = 3 × (200L - L²) = 3(200L - L²)

For her to save money, the amount she earns must be greater than the amount she spends, hence the inequality had to be

(Amount she earns) > (Amount she spends)

7L² > 3(200L - L²)

To simplify,

7L² > 3L(200 - L)

Since L is always positive, we can divide both sides by L

7L > 3(200 - L)

7L > 600 - 3L

10L > 600

L > 60 meters

Hope this Helps!!!

7 0
3 years ago
Which of the following represents 1.65 rounded to the nearest whole number?
Ksju [112]
1.65 rounded to the nearest whole number is 2
8 0
3 years ago
Other questions:
  • Electromagnetic radiation is more common than you think. Radio andTV stations emit radio waves when they broadcast their program
    13·1 answer
  • Wrote theses in scientific notation
    7·1 answer
  • A square ____ has a symmetry with respect to a line containing a median of the square
    10·2 answers
  • What is the common ratio of the Fibonacci sequence called
    14·1 answer
  • The first term of a geometric sequence is equal to a and the common ratio of the sequence is r.
    8·1 answer
  • Can you help me find the slope intercept on the second one?
    14·1 answer
  • Hiii, What is a common factor of both terms in 22m - 33?
    15·1 answer
  • DUE IN 30 MINUTES HELP NEEDED ASAP!!!!
    7·2 answers
  • Find the missing number in the proportion.
    7·1 answer
  • OPRobert made a design on his wall with the similar pentagon tiles shownR9 cm9 cmKMQs15 cm10 cm10 cm15 cmUT10 cmP15 cmNnot drawn
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!