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schepotkina [342]
2 years ago
11

In circle o,find the value of x, rounded to the nearest tenth.

Mathematics
1 answer:
Gemiola [76]2 years ago
4 0

Answer:

\huge\boxed{x \approx 5.4}

Step-by-step explanation:

We can break down this problem by first realizing different parts of the circle.

  • The line which is 8 units long is a chord of the circle.
  • The line that is 3.6 is <em>almost</em> the radius of the circle
  • The line that x sits on is the radius.

With this, we can find out if we find the radius of the circle, we have our answer.

We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.

<em>What we need is a way to find the radius of the circle</em><em>. This will get us x</em>. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.

If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).

We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:

  • \displaystyle a^2 + b^2 = c^2

Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!

  • 3.6^2 + 4^2 = c^2
  • 12.96+16=c^2
  • 28.96=c^2
  • \sqrt{28.96} = c
  • 5.4 \approx c

Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.

The line X does just that. Therefore, the value of x is also 5.4.

Hope this helped!

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Step-by-step explanation:

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<h2>According to the question </h2>

15\% \:ofx + 55\% \: of \: x + 12750 = x

=  >  \frac{15}{100} x +  \frac{55}{100} x + 12750 = x

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a 12-ft ladder leans against a building so that the angle between the ground and the ladder is 74°. how high does the ladder rea
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Answer:

12 feet

Step-by-step explanation:

Sometimes, a simple drawing is a great way to start! In the attached drawing, the red line represents the ladder, the brown represents the ground, and the black represents the building!

We want to find the side of the triangle from where the ladder meets the building to where the building meets the ground. This can be found using trigonometric identities, namely sine:

sin\theta=\frac{opposite}{hypotenuse}

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Rearrange to isolate the variable:

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<em />

Given details

To make a complete tour, at least 1 economy seats

and 6 deluxe seats

Maximum passengers per tour = 30

<em />

<em>"Boat Tours makes $40 profit for each </em><em>economy</em><em> seat sold and $35 profit for each deluxe seat sold"</em>

<em> </em>Therefore, to maximise profit, he needs to take more of economy seats

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6 x+ 24y = 30

The maximum profit from one tour is  = 6*35+ 24*40 = 210+960= $1170

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