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Rus_ich [418]
3 years ago
6

1. SPOTLIGHTS Ship A has coordinates (–1, –2) and Ship B has coordinates (–4, 1). Both ships have their spotlights fixated on th

e same lifeboat. The light beam from Ship A travels along the line y = 2x. The light beam from Ship B travels along the line y = x + 5. What are the coordinates of the lifeboat?
Mathematics
1 answer:
Alexeev081 [22]3 years ago
7 0

Answer:

( 5 , 10 )

Step-by-step explanation:

Solution:-

- There are two ships, A and B, currently located by their respective coordinates in the cartesian coordinate system:

          <u>Position of ship A: ( - 1 , -2 )</u>

          <u>Position of ship B: ( -4 , 1 )</u>

- Both ships try to locate a lifeboat. The spotlights used by each ship are modelled as straight line functions of cartesian coordinate originating from their respective ships.

- Spot lights for each ship were able to locate the same lifeboat. The respective spotlights are modelled by the following functions:

         <u>Spotlight Ship A: y = 2x</u>

         <u>Spotlight Ship B: y = x + 5 </u>

- To locate the position of the lifeboat with respect to the origin ( 0 , 0 ) we will use the spotlight model functions and equate them. This is because the spotlights must converge or meet at the position of lifeboat provided the lifeboat is found by both ships.

- Therefore,

       

         Spotlight A = Spotlight B

         y = 2x = x + 5

         2x = x + 5

         x = 5 , y = 10

<u>Answer:</u> <em>The two spotlight meet at the coordinates ( 5 , 10 ). This is also the position of the lifeboat located by both the ships</em><em>. </em>

       

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The sum of the squares of the lengths is 58

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From the question, we have

AB² = (-2-3)² +(7-5)²= 25+4 =29

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Here we can see that,

AB²+BC² = AC²

The sum of the squares of the lengths of two sides (the legs) equals the square length of the third side (hypotenuse).

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Pythagoras Theorem:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

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1 year ago
408 rounded to the nearest tenth
andreev551 [17]
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Matt bought a home in 2001 and paid $150,000 for it. He sold the home for $450,000. How much of the profit on his home will be t
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Answer:

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Step-by-step explanation:

Matt home cost = $150,000

Matt sold his home for = $450,000

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