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
Anettt [7]
2 years ago
11

Two airplanes leave an airport at the same time, the first headed due north and the second at a bearing of N42^ E . At 2:00PM, t

he first airplane is 312 miles from the airport while the second airplane is 487 miles from the airport. Assuming both followed linear paths from the airport, how far apart are the two airplanes at 2:00PM?
Mathematics
1 answer:
Leno4ka [110]2 years ago
3 0

Answer:

The two airplanes are about 330miles apart.

Step-by-step explanation:

The diagram interpreting the question has been attached to this response.

As shown in the diagram,

i. the airplanes leave at point C.

ii. at 2.00pm the first and second airplanes are at points A and B respectively, where they are 312miles and 487miles away from the starting point C in directions due north and N42E from the point C.

iii. the points A, B and C form a triangle with sides a, b and c.

To solve for the value of c which is the distance between the two planes at 2.00pm, the cosine rule is used.

c² = a² + b² - 2abcosC            --------------(i)

where;

b  = 312miles

a = 487miles

C = 42°

Substitute these values into equation (i) and solve as follows;

c² = (487)² + (312)² - 2(312)(487)cos(42)

c² = (237169) + (97344) - 303888cos(42)

c² = (237169) + (97344) - 303888(0.7431)

c² = 334513 - 225819.1728

c² = 108693.8272

<em>Take the square root of both sides</em>

√c² = √108693.8272

c = 329.69

c ≅ 330miles

Therefore, the two airplanes are far apart by 330miles

You might be interested in
Multiply the polynomials.
Oxana [17]
I’m pretty sure that the answer is D
3 0
2 years ago
If 2x + 5 = 8x, then 12x = ?A.5B.10C.15D.20
butalik [34]
<h2>Answer:</h2>10.\text{ Option B is correct}

<h2>Explanation:</h2>

Given the equation expressed as:

2x+5=8x

First, we need to calculate the value of "x" from the given expression.

Step 1: Given the equation 2x + 5 = 8x

Step 2: Subtract 5 from both sides:

\begin{gathered} 2x+5-5=8x-5 \\ 2x+\cancel{5}-\cancel{5}=8x-5 \\ 2x=8x-5 \end{gathered}

Step 3: Subtract 8x from both sides

\begin{gathered} 2x-8x=8x-8x-5 \\ -6x=\cancel{8x}-\cancel{8x}-5 \\ -6x=-5 \end{gathered}

Step 4: Divide both sides by -6

\begin{gathered} \frac{-6x}{-6}=\frac{-5}{-6} \\ x=\frac{5}{6} \end{gathered}

Step 5: Get the value of 12x. Substitute x = 5/6 into the expression to have:

\begin{gathered} 12x=12(\frac{5}{6}) \\ 12x=\cancel{12}^2(\frac{5}{\cancel{6}^1}) \\ 12x=2\times5 \\ 12x=10 \end{gathered}

Therefore the value of 12x is 10

3 0
10 months ago
Rewrite the equation in ax+by=c form. <br> Y+3=2(x-5)
Deffense [45]
Y+3=2(x-5)

y+3=2x-10

y+3+10=2x

y+13=2x

2x-y=13
6 0
2 years ago
There are 49 floors. There are 26 offices on each of the bottom31 floors. The top of 18 floors have 38 offices. About how many o
zysi [14]
31 × 26 = 806

18 × 38 = 684

806 + 684 = 1490
7 0
3 years ago
Va doctor prescribes 10 mg of cough syrup. available is 5 mg/5 ml. how many teaspoons would you give?
scoundrel [369]
10 ÷ 5 = 2 

ans: 2 teaspoons
4 0
2 years ago
Other questions:
  • Ms Chavez bought 20 eggs at a market.she will use %30 of these eggs to make cookies. How many eggs will Ms Chavez use to make co
    10·1 answer
  • The students at Linda's school voted for a new school cooler. 144 students voted for green. If there are 160 students in Linda's
    5·1 answer
  • A department store is haveing 30% off sale on all pair of jeans. If you have an coupon for an additional 15% off any items price
    10·2 answers
  • X-y&lt;3<br> How I can solve this inequality?
    15·1 answer
  • As a contestant on a televised game show, Kiara gets to spin the big prize wheel, which has a radius of 2 meters. What is the pr
    7·1 answer
  • Algebra 1 Homework Thanks to whoever helps, have a nice day;)
    10·2 answers
  • Samuel bought a cement mixer for $54,205. The value of the cement mixer depreciated at a constant rate per year. The table shows
    9·1 answer
  • Please please please help meeeeeeeee and I WILL mark you brainliest ​
    10·1 answer
  • 8. The table represents some points on the graph of a linear function.
    12·2 answers
  • The area of a window measures 336 Square inches. If the window is 16 inches wide. How long is the window?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!