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3 years ago

What is the area of a regular hexagon if a side is 30

Mathematics

1 answer:

sergij07 [2.7K]3 years ago

4 0

<h3>Answer:</h3>

$1350\sqrt{3}$ square units (approximately 2338.26859)

<h3>Step-by-step explanation:</h3>

The formula for finding the area of a regular hexagon when you know its side length is $A=\frac{3\sqrt{3}*s^2}{2}$ , where $A$ is the area and $s$ is the side length.

Substitute in the side length. $A=\frac{3\sqrt{3}*30^2}{2}$
Simplify the exponent. $A=\frac{3\sqrt{3}*900}{2}$
Multiply. $A=\frac{2700\sqrt{3}}{2}$
Divide. $A=1350\sqrt{3}$

$1350\sqrt{3}$ is as simple as the solution can get without estimating, but you can estimate with a calculator to find that it is approximately 2338.26859.

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3 years ago

PLEASE HELP<br> how can you simplify 208/1000??

dsp73

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3 years ago

Which number is additive inverse of -4 1/4

Nadusha1986 [10]

Answer:

4 1/4

Step-by-step explanation:

the additive inverse is a number that when you add it with the number you already had, makes 0

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so 4 1/4 is the inverse of -4 1/4

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3 years ago

A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer. Find the rate of change of the an

lubasha [3.4K]

The rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground is 1/20 degree/sec.

<h3>What is angle of elevation?</h3>

It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.

Calculation for the rate of change of angle of elevation-

According to the question,

A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer.

The balloon is 100 feet above the ground.

Let the height of the balloon be 'h' ft.

Then tanØ = h/100

h = 100tanØ

Differentiate the above equation with respect to time.

dh/dt = 100 sec² Ø (dØ/dt)

We know dh/dt = 10 ft/sec.

when h = 100

tanØ = 100/100 = 1/1

tanØ = Perpendicular/Base

On comparing above two equations,

Perpendicular = 1; Base = 1.

By Pythagoras the hypotenuse is,

H² = P² + B²

= 1² + 1²

= 2

H = √2

Now, calculate the value of cosØ.

cosØ = B/H = 1/√2

Squaring both side

cos² Ø = 1/2

sec² Ø = 1/cos² Ø

sec² Ø = 2

The main equation was,

dh/dt = 100 sec² Ø (dØ/dt)

Substitute the values,

dØ/dt = (dh/dt )/100 sec² Ø

= (10)/(100×2)

dØ/dt = 1/20 degree/sec.

Therefore, the rate of change of the angle of elevation of the balloon from the observer is 1/20 degree/sec.

To know more about the angle of elevation, here

brainly.com/question/9817377

#SPJ4

8 0

2 years ago

José is blocking off several rooms in a hotel for guest coming to his wedding. The hotel can reserve small rooms that can hold 3

miv72 [106K]

Answer:

$x=2y\,,\,3x+4y=70$ where x denotes number of small rooms and y denotes number of large rooms

Step-by-step explanation:

Given: Small rooms can hold 3 people, and large rooms can hold 4 people.

Number of small rooms is twice the number of large rooms.

Small rooms and large rooms altogether can accommodate 70 guests.

To find: system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved

Solution:

Let x denotes number of small rooms and y denotes number of large rooms.

As number of small rooms is twice the number of large rooms,

$x=2y$

As small rooms and large rooms altogether can accommodate 70 guests such that small rooms can hold 3 people, and large rooms can hold 4 people,

$3x+4y=70$

4 0

3 years ago