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igor_vitrenko [27]
2 years ago
11

An observer (O) spots a bird flying at a 35° angle from a line drawn horizontal to its nest. If the distance from the observer (

O) to the bird (B) is 21,000 feet, how far is the bird (B) from its nest (N)? Round to the nearest whole number.
options 12,045 14,704 16,980 17,202
Mathematics
1 answer:
lara [203]2 years ago
5 0

It’s NOT 16,980

I just took the test

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Elena-2011 [213]

Answer(s):

  • 154 in²
  • 3168/7 km²
  • 38.5 m²

Revising the area of a circle formula

We already know that the area of a circle is expressed as \pi r^{2}.

  • The "r" variable is known as the radius.
<h2><u>Solving each problem given:</u></h2><h3>Solving Problem 4:</h3>

We are given the radius of circle, which is 7 in. Let us substitute the radius in the formula. Once substituted, we can simplify the expression obtained to determine the area of the circle shown in the picture.

\implies \pi (7)^{2}

<u>Take π as 22/7</u>

\implies \huge\text{(}\dfrac{22}{7} \huge\text{)}(7)^{2}<em> </em>

\implies \huge\text{(}\dfrac{22}{7} \huge\text{)}(7)(7)

\implies (22)(7)

\implies 154 \ \text{in}^{2}

<h3>Solving Problem 5:</h3>

In this problem, we are given the diameter to be 24 kilometers. Since the radius of the circle is half the diameter, we can tell that the radius of the circle is 24/2 kilometers, which is 12 kilometers.

\implies \pi (12)^{2}

<u>Take π as 22/7</u>

\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (12)^{2}

\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (12)(12)

\implies \dfrac{3168}{7} \ \text{km}^{2}

<h3>Solving Problem 6:</h3>

We are given the radius of circle, which is 3.5 in. Let us substitute the radius in the formula. Once substituted, we can simplify the expression obtained to determine the area of the circle shown in the picture.

\implies \pi (3.5)^{2}

<u>Take π as 22/7</u>

\implies \huge\text{(}\dfrac{22}{7}\huge\text{)}  (3.5)^{2}

\implies \huge\text{(}\dfrac{22}{7}\huge\text{)}  (3.5)(3.5)

\implies \huge\text{(}\dfrac{22}{2}\huge\text{)} (3.5) = (11) (3.5)

\implies 38.5 \ \text{m}^{2}

Note: <em>The radius given in this problem was not clearly stated. If the radius I stated here, is incorrect, please notify me in the comments. Thanks!</em>

Learn more about area of circles: brainly.com/question/12414551

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<u>Answer</u><u>:</u><u> </u><u>y</u><u> </u><u>=</u><u> </u><u>(</u><u>2</u><u>k</u><u> </u><u>-</u><u>pw</u><u>)</u><u>/</u><u>p</u>

Step-by-step explanation:

k =  \frac{p}{2} (y + w)

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k \times 2 = 2 \times  \frac{p}{2} (y + w) \\  \\ 2k = p(y + w)

open the bracket:

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divide p on both sides:

\frac{2k - pw}{p}  =  \frac{py}{p}  \\  \\ y =  \frac{2k - pw}{p}

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