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3 years ago

A circle with radius 6 has a sector with a central angle of 48 what is the area of the sector

Mathematics

2 answers:

inn [45]3 years ago

5 0

Answer:

≈ 15.08 units²

Step-by-step explanation:

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

= πr² × $\frac{48}{360}$ ( r is the radius )

= π × 6² × $\frac{48}{360}$

= 36π × $\frac{48}{360}$ = π × $\frac{48}{10}$ = $\frac{48\pi }{10}$ ≈ 15.08

Reil [10]3 years ago

3 0

Answer:

24/5 pi

Step-by-step explanation:

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What is the area of this parallelogram?

Lelechka [254]

A = base * height
A = 4.9 * 3.5
A = 17.15 if my mental math is correct. You might want to double check that though

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What ate the coordinates of the fourth point that could be connected with (-8, 0), (1,0), and (1-5)

Gnesinka [82]

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3 years ago

Claudia's father is 7 times as old as Claudia. 20 years from now, Claudia will be 1/2 as old as her father. How old is Claudia's

Rudik [331]

I hope this helps you

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3 years ago

What is the measurement of the longest line segment in a right rectangular prism that is 26 inches long, 2 inches wide, and 2 in

EastWind [94]

Answer:

$6\sqrt{19} \approx 26.153$ inches.

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment $\mathsf{AG}$ .

In this diagram (not to scale,) $\mathsf{AB} = 26$ (length of prism,) $\mathsf{AC} = 2$ (width of prism,) $\mathsf{AE} = 2$ (height of prism.)

Pythagorean Theorem can help find the length of $\mathsf{AG}$ , one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.

Start by finding the length of line segment $\mathsf{AD}$ . That's the black dotted line in the diagram. In right triangle $\triangle\mathsf{ABD}$ (second diagram,)

Segment $\mathsf{AD}$ is the hypotenuse.
One of the legs of $\triangle\mathsf{ABD}$ is $\mathsf{AB}$ . The length of $\mathsf{AB}$ is $26$ , same as the length of this prism.
Segment $\mathsf{BD}$ is the other leg of this triangle. The length of $\mathsf{BD}$ is $2$ , same as the width of this prism.

Apply the Pythagorean Theorem to right triangle $\triangle\mathsf{ABD}$ to find the length of $\mathsf{AB}$ , the hypotenuse of this triangle:

$\mathsf{AD} = \sqrt{\mathsf{AB}^2 + \mathsf{BD}^2} = \sqrt{26^2 + 2^2}$ .

Consider right triangle $\triangle \mathsf{ADG}$ (third diagram.) In this triangle,

Segment $\mathsf{AG}$ is the hypotenuse, while
$\mathsf{AD}$ and $\mathsf{DG}$ are the two legs.

$\mathsf{AD} = \sqrt{26^2 + 2^2}$ . The length of segment $\mathsf{DG}$ is the same as the height of the rectangular prism, $2$ (inches.) Apply the Pythagorean Theorem to right triangle $\triangle \mathsf{ADG}$ to find the length of the hypotenuse $\mathsf{AG}$ :

$\begin{aligned}\mathsf{AG} &= \sqrt{\mathsf{AD}^2 + \mathsf{GD}^2} \\ &= \sqrt{\left(\sqrt{26^2 + 2^2}\right)^2 + 2^2}\\ &= \sqrt{\left(26^2 + 2^2\right) + 2^2} \\&= 6\sqrt{19} \\&\approx 26.153\end{aligned}$ .

Hence, the length of the longest line segment in this prism is $6\sqrt{19} \approx 26.153$ inches.

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3 years ago

Multiply 8 times the square root of 3 by 9 times the square root of 27.

Viktor [21]

8√3 · 9√27
8 · 9 ·√3 · √27
72 · √81
72 · 9
648

The answer is 648. :)

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3 years ago