All categories

4 years ago

A regular hexagon is inscribed in a circle of radius 77 m. Find the length of a side of the hexagon.

Mathematics

1 answer:

marysya [2.9K]4 years ago

3 0

Hi there!

We'll use the image below as a reference diagram. As you can see, the hexagon is divided into 6 triangles. And, one red line (center to point on the hexagon) would be the radius. Since we know that all of the triangles are equilateral triangles, and the hexagon is a regular hexagon, we know that one side of the hexagon is equal to 77m.
(If the circle actually has a diameter (all the way across the circle), the answer would be 38.5m)

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

You might be interested in

There are some Chicken and rabbits in a cage. There are 20 heads and 62 feet in total, the question is: how many chicken and rab

horsena [70]

Answer:There are 72 heads (chicken and rabbit) and 200 legs. How many chickens and rabbits are present totally?

Step-by-step explanation

There are 72 heads (chicken and rabbit) and 200 legs. How many chickens and rabbits are present totally?

Legs of a chicken = 2

Legs of a rabbit = 4

Total heads = 72

Total legs= 200

Let's assume that each of them has minimum 2 legs.

So 72*2 = 144 legs

Remaining legs: 200-144= 56

These remaining legs belong to rabbit because rabbit has 4 legs each.

2*Rabbits= 56

Rabbits= 56/2 = 28

Out of 72, 28 are rabbits. So there are 72-28= 44 chicken.

5 0

3 years ago

What is the slope of the line that passes through the points (3, 4) and (0, -2)

Vaselesa [24]

Answer:

The slope is :

4-(-2)/0-3

4+2/-3

6/-3

-2

-2 is the slope

8 0

3 years ago

Read 2 more answers

What does x equal?. 3/4 x + 5/8=4x

Aleonysh [2.5K]

6x +5 = 8x after make the common denominator on both sides

5 = 2x

x = 5/2

hope this will help you

5 0

3 years ago

Read 2 more answers

Tom drove to visit a museum in Chicago. He traveled at a constant rate of 50 miles per hour for 2 hours. Then he traveled at a c

Dmitry [639]

Answer:

165

Step-by-step explanation:

First, we multiply 50 and 2 to find out how much they traveled first, which is 100. And then, multiply 65 and 1 to get 65 for the second part. Add then, to get 165. Hope this helps!

5 0

2 years ago

Read 2 more answers

As Sales Manager for ISeeYou Productions, you are planning to review the prices you charge clients for television advertisement

aksik [14]

The development fee p can be modeled by the equation p=-400q+9600 where p is the price the company charges and q is the number of contracts they get. The total revenue R ISeeYou obtains by signing q contracts is found by using the function: $R(q)=-400q^{2}+9600q$ . The cost ISeeYou Productions can be found by using the following function: C(q)=800q+16000. The monthlhy profit of Express ISeeYou Productions if found with the next function: $P(q)=-400p^{2}+8800q-16000$ . ISeeYou should sign 2 or 20 contracts to break even.

a) In order to solve part a of the problem, we will suppose the price will have a linear relation with the amount of contracts they signed, so we need to find two points to build this function.

We know that when signing 6 contracts, the company charges $7,200, so our first point will be:

(6, 7200)

we also know that the company signs 14 contracts when they charge $4,000. So our second point is:

(14, 4000)

so we can use these points to find the slope of the line by using the

slope formula:

$m=\frac{p_{2}-p_{1}}{q_{2}-q_{1}}$

$m=\frac{4000-7200}{14-6}$

so the slope is:

m=-400

We can now use one of those points and the slope to find the function for the price, so we get:

$y-y_{1}=m(x-x_{1})$

$p-p_{1}=m(q-q_{1})$

if we used the point: (6, 7200) we get:

$p-7200=-400(q-6)$

which can now be simplified:

p=-400q+2400+7200

so the price function is:

p=-400q+9600

b) In order to find the revenue equation we need to multiply the price equation by the amount of contracts they signed in a month, so we get:

R(q)=pq

$R(q)=(-400q+9600)q$

$R(q)=-400q^{2}+9600q$

c) The cost can be found by adding the fixed cost and the variable cost, so we get:

C(q)=800q+16000

d) The profit is found by subtracting the montly cost from the monthly revenue, so we get:

P(q)=R(q)-C(q)

$P(q)=-400q^{2}+9600q-(800q+16000)$

so we can now simplify our function to get:

$P(q)=-400q^{2}+9600q-800q-16000$

$P(q)=-400q^{2}+8800q-16000$

e) In order to find the number of contracts for the company to break even, we need to find the q contracts that will give a profit of $0 so we set the function of the previous part of the problem equal to zero so we get:

$P(q)=-400q^{2}+8800q-16000$

$-400q^{2}+8800q-16000=0$