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tresset_1 [31]
3 years ago
6

A stereo system is being installed in a room with a rectangular floor measuring 13 feet by 11 feet and a 7​-foot ceiling. The st

ereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. You must run a wire from the amplifier to the​ speaker, and the wire must run along the floor or walls​ (not through the​ air). What is the shortest length of wire you can use for the​ connection? (Hint: Turn the problem into an equivalent simpler problem by imagining cutting the room along its vertical corners and unfolding it so that it is flat. You will be able to apply the Pythagorean​ theorem.)

Mathematics
1 answer:
zhuklara [117]3 years ago
6 0

Answer:

  about 22.2 feet

Step-by-step explanation:

The wire can run diagonally across the floor and, from the intersection with the wall, diagonally up the wall. The total length is computed per the hint to be ...

  d = √(18^2 +13^2) = √493 ≈ 22.20 . . . .  feet

___

If the wire were to go up the short wall, its length would be ...

  d = √(11^2 +20^2) = √521 ≈ 22.83 . . . . feet

_____

<em>Comment on the attachment</em>

The red represents the floor; the green represents the long wall.

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kondaur [170]

Answer:

c ≈ 9.1 m

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

c² = 4.1² + 8.1² = 16.81 + 65.61 = 82.42 ( take square root of both sides )

c = \sqrt{82.42 } ≈ 9.1 m ( to the nearest tenth )

5 0
2 years ago
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icang [17]

Answer:

CD ≠ EF

Step-by-step explanation:

Using the distance formula

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with (x₁, y₁ ) = C(- 2, 5) and (x₂, y₂ ) = D(- 1, 1)

CD = \sqrt{(-1+2)^2+(1-5)^2}

      = \sqrt{1^2+(-4)^2}

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Repeat using (x₁, y₁ ) = E(- 4, - 3) and (x₂, y₂ ) = F(- 1, - 1)

EF = \sqrt{(- 1+4)^2+(-1+3)^2}

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6 0
3 years ago
What is the value of x in the diagram?
DerKrebs [107]
The answer is 27 (hope this helps you)
7 0
2 years ago
Read 2 more answers
Factor the expression completely.
Ksju [112]

Answer:

A

Step-by-step explanation:

-9.75 + 3.25x

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8 0
3 years ago
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earnstyle [38]

Answer:

One time

Step-by-step explanation:

In both the numbers 72 and 78, the place value of 7 is 70.

Hence, 7 in 72 represents one time the value of the 7 in 78.

7 0
3 years ago
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