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Dima020 [189]
1 year ago
9

two ships leave a port at the same time. the first ship sails on a bearing of 55° at 12 knots (natural miles per hour) and the s

econd on a bearing of 145° at 22 knots. how far apart are they after 1.5 hours
Mathematics
1 answer:
Korvikt [17]1 year ago
8 0

Answer:

37.59 nautical miles

Explanation:

Distance = Speed x Time

The speed of the first ship = 12 knots

Thus, the distance covered after 1.5 hours

\begin{gathered} =12\times1.5 \\ =18\text{ miles} \end{gathered}

The speed of the second ship = 22 knots

Thus, the distance covered after 1.5 hours

\begin{gathered} =22\times1.5 \\ =33\text{ miles} \end{gathered}

The diagram representing the ship's path is drawn and attached below:

The angle at port = 90 degrees.

The triangle is a right triangle.

Using Pythagorean Theorem:

\begin{gathered} c^2=a^2+b^2 \\ c^2=18^2+33^2 \\ c^2=324+1089 \\ c^2=1413 \\ c=\sqrt[]{1413} \\ c=37.59\text{ miles} \end{gathered}

The two ships are 37.59 nautical miles apart after 1.5 hours.

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PLZ HELP, AND PLZ EXPLAIN
shutvik [7]

Answer:

C

Step-by-step explanation:

To make it easy let's start by organizing our information :

  • AC=12 AND BD=8
  • ABCD is a rhombus
  • K and L are the midpoints of sides AD and CD
  • we notice that the rhombus ABCD is divided into four right triangles

What do you think of when you hear a right triangle ?

  • The pythagorian theorem !

AC and BD  are khown so let's focus on them .

If we concentrated we can notice that AB and BD are cossing each other in the midpoints . why ?

Simply because they are the diagonals of a rhombus .

ow let's apply the pythagorian theorem :

  • (AC/2)² + (BD/2)² = BC²
  • 6²+4²=52
  • BC²= 52⇒\sqrt{52}=BC

Now we khow that : AB=BC=CD=AD=\sqrt{52}

This isn't enough . Let's try to figure out a way to calculate the length of KL  wich is the base of the triangle

  • KL is parallel to AC
  • k is the midpoint of AD and L of DC

I smell something . yes! Thales theorem

  • KL/AC=DL/DC=DK/AD WE4LL TAKE OLY ONE
  • KL/12=\sqrt{52}/2*\sqrt{52}  
  • KL/12=1/2⇒ KL=6

Now we have the length of the base kl

Now the big boss the height :

  • notice that you khow the length of KL
  • BD crosses kl from its midpoint and DL = \sqrt{52} /2

What I want to do is to apply the pythgorian thaorem to khow the lenght of that small part that is not a part of the height of the triangle . I will call it D

  • DL²=(KL/2)²+D²
  • 52/4= 9+ D²
  • D² = 52/4-9 +4 SO D=2

now the height of the trigle is H= BD-D= 8-2=6

NOw the area of the triangle is :

  • A=(KL*H)/2 ⇒ A= (6*6)/2=18

THE ANSWER IS 18 SQ.UN

5 0
3 years ago
Which is the equation of OB?
GrogVix [38]
The answer is b I hope this helps
6 0
3 years ago
Identify the 4 basic transformation
Pavlova-9 [17]

Answer:

Rotation, Reflection, dilation, and translation

Step-by-step explanation:

Rotation: Just rotating the shape; spinning the shape around a point

Reflection: Your shape is either reflecting on the x axis or y axis meaning it is either side by side (y) or up and down (x)

Dilation: Your shape is either going to shrink or get bigger

Translation: Shifting all the points of the figure

8 0
3 years ago
Can the sum of two mixed numbers be equal to 2? Explain why or why not.
Serga [27]
No, because 1 is not a mixed and there is not another pair of nubers that equal 2 in mixed numbers.
6 0
3 years ago
In ΔKLM, k = 700 cm, l = 460 cm and ∠M=78°. Find the length of m, to the nearest centimeter.
pashok25 [27]

Answer:

753

Step-by-step explanation:

m^2 =700^2 +460^-2 −2(700)(460)cos78

m^2 = 490000+211600-2(700)(460)(0.207912)

m^2 = 490000+211600-133895.12889

m^2 = 567704.87111

m=753.462=753

6 0
3 years ago
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