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givi [52]
3 years ago
6

Regular pentagon abcde is inscribed in a circle. find arch measure ab. if the radius is 6, find ab.​

Mathematics
2 answers:
SSSSS [86.1K]3 years ago
4 0

a. Your answer and reasoning are correct.

b. If O is the center of the circle, then angle ABO has measure 72º, so that by the law of cosines

AB^2=6^2+6^2-2\cdot6\cdot6\cos72^\circ\implies AB=3\sqrt{10-2\sqrt5}

OleMash [197]3 years ago
4 0

just to add to the superb reply above by @LammettHash

\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=6\\ \theta =72 \end{cases}\implies s=\cfrac{\pi (72)(6)}{180}\implies s=\cfrac{12\pi }{5}\implies s\approx 7.54

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Find the rectangular coordinates of the point (sqrt3,pi/6)
madreJ [45]

Answer:

(x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)

Step-by-step explanation:

The rectangular coordinates of the point are:

(x,y) = \left(\sqrt{3}\cdot \cos\frac{\pi}{6}, \sqrt{3}\cdot \sin\frac{\pi}{6}\right)

(x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)

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Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| > 4
nadezda [96]

Answer:

***********o                                                         o**************

<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->

x>4 or x<-4

Step-by-step explanation:

You are looking for numbers that give you a distance, x, greater than 4 from 0. That wouldn't be anything between -4 and 4 because these would all give you a distance less than 4 from 0. So the answer would be to shade everything greater than 4 while also shading everything less than -4.

Here is a number line <-----|-----|-----|-----|-----|-----|-----|-----|-->

                                          -6    -4   -2    0     2     4    6    8

                                                 

Let's think about this more which of these numbers on this number line would satisfy |x|>4?

Numbers inside the numbers -4 and 4.

Or the numbers on the outside.

Let's try the inside numbers:

-2,02

|-2|>4

 2>4 is false which means -2 doesn't satisfy |x|>4

|0|>4

 0>4 is false which means 0 doesn't satisfy  |x|>4

|2|>4

 2>4 is false which means 2 doesn't satisfy  |x|>4

We could also try -4 and 4... but these will both give you a distance equal to 4 from 0.  And we are looking for greater than.

|-4|>4

 4>4 is false which mean -4 doesn't satisfy |x|>4

|4|>4

 4>4  is false which means 4 doesn't satisfy |x|>4

Now let's try the numbers on the outside:

-6,6,8

|-6|>4

 6>4 is true so -6 does satisfy |x|>4

|6|>4

 6>4 is true so 6 does satisfy |x|>4

|8|>4

 8>4 is true so 8 does satisfy |x|>4

So what I'm trying to do is convince you more that the only numbers that would satisfy |x|>4 are numbers outside the interval from -4 to 4.

So x>4 or x<-4.

On a number line the solution would look like this:

***********o                                                         o**************

<----------(-4)--------(-2)--------(0)--------(-2)----------(4)-------------->

We have holes at -4 and 4 to mean we do not include those numbers.  We would have if the inequality read |x| \ge 4.  The line underneath this inequality means to include or equals.  We do not want to include; we did not have the equal sign.   The only difference between the two solutions would be to fill the holes if you |x| \ge 4.

4 0
3 years ago
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BigorU [14]

Answer:

(1/2, 1&1/2)

Step-by-step explanation:

the x-axis, which is the horizontal axis, is always written first. the y-axis, vertical, is written second. because the points give are spaced out every other line, it shows that there fractional numbers must be used

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How many surgeon are either office-based or ophthalmologist.?
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Answer:

Is there a graph related to this question?

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