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]
3 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]3 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
What is the solution to ln (x2 - 16) = 0?
bogdanovich [222]
ANSWER

x = \pm \sqrt{17}
EXPLANATION

The given equation is

ln( {x}^{2} - 16) = 0

Take antilogarithm of both sides to base e.

{e}^{ ln( {x}^{2} - 16) } = {e}^{0}

This will simplify to

{x}^{2} - 16 = 1

Group like terms to obtain,

{x}^{2} = 1 + 16

{x}^{2} = 17

Take square root of both sides to get,

x = \pm \sqrt{17}
6 0
3 years ago
Read 2 more answers
Mai is visiting Paris to see the Eiffel Tower. She is 80 feet away
Jlenok [28]

Answer: height of the tower is 1064 feet

Step-by-step explanation:

We want to determine the height of the tower.

Assuming her line of sight of the top of the tower is a straight line, then a right angle triangle is formed. The height, h of the tower represents the opposite side of the triangle. Her distance from the foot of the tower represents the adjacent side of the triangle.

To determine h, we would apply the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side

Therefore,

Tan 85.7 = h/80

h = 80tan 85.7

h = 1064 feet

7 0
3 years ago
Read 2 more answers
A collection of dimes and nickels is worth $8.40 there are 106 coins how many of each are there
kotegsom [21]
There are 62 dimes and 44 nickels.

N + D = 106 (There are 106 coins in all.)
1 nickel = 5 cents.
1 dime = 10 cents.
5*N + 10*D = 840 ($8.40 = 840 cents)
N + D = 106 -------(1)
N = (106 - D)
5*N + 10*D = 840 ---------(2)
5*(106-D) + 10*D = 840
530 - 5*D + 10*D = 840
5*D = 840 - 530
5*D = 310
D = 310/5 = 62
Eq(1) N + D = 106
N + 62 = 106
N = 106 - 62
N = 44
7 0
3 years ago
(x-25) (x-5) square root
Fittoniya [83]

x^2-30x+125 square root


6 0
3 years ago
Which graph represents the solution set of the system of inequalities?
Nimfa-mama [501]
Well first we need to change the format of the equations to slope-intercept, or y=mx+b.
So the first one (x + y < 1) will be changed to   y < -x + 1.
The second one (2y ≥ x - 4) will be changed to   y <span>≥ x/2 - 2.
Now we can analyze each graph.
In every single graph the first equation (y < -x + 1) is graphed correctly.
Now for the second equation, we can see that only the first and last graph correctly format to the equation.
Now for the shading:
The first equation shows us that y is less than -x +1, making the shading go under the dotted line. (to the left)
The second equation shows us that y is greater than or equal to x/2 - 2, making the shading go above the line. (also to the left)
Therefore, when we shade, the overlapping shading is correctly formatted in the first graph.
Hope this helped, comment any questions you have for me.</span>
5 0
3 years ago
Other questions:
  • How many feet does it take to make a 6 foot circle?
    11·1 answer
  • is it possible for a system with linear equation and one expontential equation to have two solutions? If so sketch a graph
    12·1 answer
  • The scatterplot shows the depth of water in swimming pools, y, based on the days after filling, x. graph What can you conclude f
    6·2 answers
  • The length of a rectangle is 3x - 5 in and the width is 2x inches what is the area of the rectangle
    13·1 answer
  • PLZZ ANSWER THE QUESTION ​
    9·1 answer
  • what are the coordinates of the vertices of the the triangle under the traslation (x,y)-&gt; (x+3, y +2)
    7·1 answer
  • 13 divided by 321 plz anser
    15·2 answers
  • What are the coordinates of V′ for the transformation (T(–3, 1)° D4 )(ΔTUV) of T(–7, –6), U(–8, 3), and V(2, 1)?
    13·1 answer
  • Plzzz help hurry !!!
    11·2 answers
  • 2(-1)+y=3<br><br><br> What is the answer
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!