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3 years ago

Find the measure of one interior angle in the regular polygon hexagon

1 answer:

7 0

All sides are the same length (congruent) and all interior angles are the same size (congruent).
To find the measure of the interior angles, we know that the sum of all the angles is 720 degrees (from above)... And there are six angles...

So, the measure of the interior angle of a regular hexagon is 120 degrees.

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can anyone help me with this ??

Mars2501 [29]

Answer:

A. 336

B. Arranging 3 people in 8 chairs.

C. 42

B. Arranging 2 people in 7 chairs.

Step-by-step explanation:

$P(n, r) = P(8, 3)$

Formula for Permutation is given as:

$P(n, r) = \dfrac{n!}{(n-r)!}$

Putting the value of $n$ = 8 and $r =3$ , we get:

$P(8, 3) = \dfrac{8!}{(8-3)!} \\\Rightarrow \dfrac{8\times 7 \times 6 \times 5\times 4 \times 3 \times 2\times 1}{5\times 4 \times 3\times 2\times 1}\\\Rightarrow 8\times 7 \times 6 \\\Rightarrow 336$

B. Real world situation for part A:

Arranging 3 people on 8 chairs.

First person has 8 options.

Second person has 7 options.

Third person has 6 options.

$P(n, r) = P(7, 2)$

Formula for Permutation is given as:

$P(n, r) = \dfrac{n!}{(n-r)!}$

Putting the value of $n$ = 7 and $r$ = 2 , we get:

$P(7, 2) = \dfrac{7!}{(7-2)!} \\\Rightarrow \dfrac{7 \times 6 \times 5\times 4 \times 3 \times 2\times 1}{5\times 4 \times 3\times 2\times 1}\\\Rightarrow 7 \times 6 \\\Rightarrow 42$

D. Real world situation for part AC:

Arranging 2 people on 7 chairs.

First person has 7 options.

Second person has 6 options.

4 0

3 years ago

Which function is best represented by this graph?

Reil [10]

Answer:

y= $\frac{2}{7}$ x-2

Step-by-step explanation:

Slope intercept form is a way to describe a function using its slope and y-intercept and is written as y=mx+b.

m=slope

b=y-intercept

Looking at the graph we can see it goes through x=0 at y=-2 making -2 the y-intercept.

Then we must solve for slope, slope is rise/run. From the point (0,-2) the function travels to (7,0).

This gives us a rise (change in x) of 2 and a run (change in y) of 7 and 2/7 as our slope.

4 0

3 years ago

− 0.25(−8+12) PLS HELP I HAVE A TESTTTT

Semmy [17]

Answer: -1

Step-by-step explanation:

− 0.25(−8+12) = -0.25 x 4 =-1

3 0

3 years ago

The assumptions made are: The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. The atmosphere

Dovator [93]

Answer:

$2.6\times 10^{19}m^{3}$

Step-by-step explanation:

we have given thickness of atmosphere =50 km

radius of earth =6400 km

average temperature of atmosphere=15°C

Average pressure of atmosphere= 0.20 atm

we have to calculate the volume of atmosphere

so the we have to calculate the volume of atmosphere = ( volume of earth +atmosphere) - volume of earth

volume of atmosphere = $\frac{4}{3}\times\pi \times \left ( 6400+50 \right )^{3}-\frac{4}{3}\times \pi\times 6400^3$

= $2.6\times 10^{19}m^{3}$

6 0

4 years ago

Find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 5

masha68 [24]

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Given:

f(x) = ln(x)

n = 4

c = 3

nth Taylor polynomial for the function, centered at c

The Taylor series for f(x) = ln x centered at 5 is:

$P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}$

Since, c = 5 so,

$P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}$

Now

f(5) = ln 5

f'(x) = 1/x ⇒ f'(5) = 1/5

f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25

f'''(x) = 2/x³ ⇒ f'''(5) = 2/5³ = 2/125

f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625

So Taylor polynomial for n = 4 is:

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Hence,

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Find out more information about nth taylor polynomial here

brainly.com/question/28196765

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3 0

2 years ago