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2 years ago

A regular hexagon is inscribed in a circle with a diameter of 8 inches.

Mathematics

1 answer:

love history [14]2 years ago

3 0

Answer:

b) 41.6 square inches

Step-by-step explanation:

A regular hexagon is inscribed in a circle with a diameter of 8 inches.

Step 1

We find the radius

Radius = Diameter/2

= 8 inches/2 = 4 inches

a. What is the perimeter of the hexagon?

b. What is the area of the hexagon?

An hexagon has 6 sides

The number of angles in an hexagon is calculated as:

[(Number of sides - 2) x 180]

= (6 - 2) x 180 = 720 ÷ 6 = 120°

The hexagon into 6 equilateral triangles with 4 for each of its sides.

The area of one of the triangles:

Height = 2√3

- one triangle's area = (1/2)bh = (1/2)(4)(2√3) = 4√3

The area of the hexagon by multiplying the one triangle's area by 6:

6 x 4√3 = 24√3 square inches

= 41.569219382 square inches

Approximately = 41.6 square inches

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2 years ago

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12. Use a trigonometric ratio to find the measure of O in the triangle below. Give your answer to the nearest degree.

larisa [96]

Given :-

A right angled triangle with two sides 10cm and 9cm .

To Find :-

The value of theta .

Solution :-

At angle theta , 9cm side will be considered as the perpendicular and 10cm side will be hypotenuse . So , as we know that ;

$\longrightarrow sin\theta =\dfrac{perpendicular}{hypotenuse}$

Substituting the respective values,

$\longrightarrow sin\theta =\dfrac{9cm}{10cm}$

Simplify,

$\longrightarrow sin\theta= 0.9$

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$\longrightarrow \theta =sin^{-1}(0.9)$

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Hence the required answer is 64.15° . 

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2 years ago

Which is the interval notation represent the domain?

Kazeer [188]

Answer:

The first choice, $(-\infty, 7) \cup (7, \infty)$ .

Step-by-step explanation:

The dashed vertical line is a vertical asymptote. The x-coordinate of all points on this vertical asymptote are equal to 7. In other words, when the x-value of a point on the graph approaches $7$ , its y-value approaches infinity (or negative infinity.)

Either way, the graph is not defined for $x = 7$ . The point $7$ should thus be excluded from the domain of the graph.

The graph is apparently defined for all other x-values. The domain of the function should thus be all real numbers with the exception of $x = 7$ . Here's how to write that in interval notation:

The set of all real numbers can be expressed as the interval $(-\infty, \infty)$ . Note that infinity $\infty$ (or $(- \infty)$ itself isn't a real number. The round brackets indicate that both endpoints are excluded from the from the interval.
The set of all real numbers less than (not equal to) $7$ is $(-\infty,7 )$ (both ends are excluded.) The set of all real numbers greater than (not equal to) $7$ is $(7, \infty)$ .
The set of all real numbers that is not equal to $7$ is the union of all real numbers less than $7$ and all real numbers greater than $7$ . The union operator $\cup$ connects two intervals.

In other words, the domain is $(-\infty, 7) \cup (7, \infty)$ .

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3 years ago

Suppose that a cyclist began a 476

mojhsa [17]

Well, we know the cyclist left the western part going eastwards, at the same time the car left the eastern part going westwards

the distance between them is 476 miles, and they met 8.5hrs later

let's say after 8.5hrs, the cyclist has travelled "d" miles, whilst the car has travelled the slack, or 476-d, in the same 8.5hrs

we know the rate of the car is faster... so if the cyclist rate is say "r", then the car's rate is r+33.2

thus $\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
\textit{eastbound cyclist}&d&r&8.5\\
\textit{westbound car}&476-d&r+33.2&8.5
\end{array}\\\\
-----------------------------\\\\
\begin{cases}
\boxed{d}=8.5r\\\\
476-d=(r+33.2)8.5\\
----------\\
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\end{cases}$

solve for "r", to see how fast the cyclist was going

what about the car? well, the car's rate is r + 33.2

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