If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the Circle that is not covered by the hexagon? ( with explanation )
Answers
Answer:
[tex]\left(100\pi - 150\sqrt{3}\right)[/tex] square inches.
Step-by-step explanation:
Area of the Inscribed HexagonRefer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be [tex]10[/tex] inches (same as the length of each side of the regular hexagon.)
Refer to the second attachment for one of these equilateral triangles.
Let segment [tex]\sf CH[/tex] be a height on side [tex]\sf AB[/tex]. Since this triangle is equilateral, the size of each internal angle will be [tex]\sf 60^\circ[/tex]. The length of segment
[tex]\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}[/tex].
The area (in square inches) of this equilateral triangle will be:
[tex]\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}[/tex].
Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:
[tex]\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}[/tex].
Area of of the circle that is not coveredRefer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is [tex]10[/tex] inches, the radius of this circle will also be [tex]10[/tex] inches.
The area (in square inches) of a circle of radius [tex]10[/tex] inches is:
[tex]\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi[/tex].
The area (in square inches) of the circle that the hexagon did not cover would be:
[tex]\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}[/tex].
Related Questions
Wanda decided to purchase a $33,000 MSRP vehicle at a 6.5% interest rate
for 3 years. The dealership offered her a $5500 cash-back incentive, which
she accepted. Taking all these factors into consideration, what monthly
payment amount can she expect?
Answers
Answer: $842.85
Step-by-step explanation:
Sarah claims that when you divide, the number you are dividing always gets smaller. John says this is not true. Who is correct? If John is correct, give a counterexample.
A) Sarah is correct.
B) John is correct. A counterexample is 4 ÷ 5.
C) John is correct. A counterexample is 4 ÷ 1.25.
D) John is correct. A counterexample is 4 ÷ 1/2
Answers
Answer:
D
Step-by-step explanation:
John is correct as Dividing does not always gets the quantity smaller for example if we divide 4 by 0.5
We get
4/0.5= 8
What is the median for 1,2,4,6,4
Answers
4 is the median. Please mark as brainlist.
Answer:
4
Step-by-step explanation:
The probability of not choosing a black shirt is...? please explain!
Answers
Answer:
80% or 8/10.
Step-by-step explanation:
Assuming the shirts in the bottom right are the "black" shirts, there is ten total shirts (1 red, 4 blue, 2 green, 1 white, 2 black.) Out of the ten shirts, 8 are not black. This means that there is an 80% chance that you will select a shirt that is NOT black.
Can someone pls tell me
Answers
Answer:
Part A would be B, and Part B would be C
Step-by-step explanation:
With the graph that B shows, the distance to time ratio is cut very sharply, indicating that there wasn't a constant speed throughout the entire time, up until where the graph went from shooting upwards to slightly inclining.
With the graph that C shows, out of all of the graphs, it is the only graph that shows the fact that the person went back to their starting point, indicating that they did return home because they forgot something.
I hope this helps :)
Which number is divisible by 10?
113
60
114
137
Answers
Answer:
60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
Only number 60 is divisible by 10 because 60/10= 6
Help me with this Please
Three ballet dancers are positioned on stage. Mia is straight behind Jane and
directly left of Christine. If Jane and Mia are 3 meters apart, and Christine and Jane
are 5 meters apart, what is the distance between Mia and Christine?
Answers
Answer:3 m
Step-by-step explanation:
Given
Mia is 3 m behind Jane
Mia is left to the Christine
Distance between Mia and Christine is 5 m
Thus they form a right angles triangle shown in fig
So we can write
[tex]5^2=x^2+3^2[/tex]
Where x =distance between Mia and christine
[tex]x^2=25-16[/tex]
[tex]x^2=9[/tex]
[tex]x=3\ m[/tex]
simplify
4/12 + 9/12
Answers
Answer:
4/12 + 9/12 is 13/12 ( the mix number is 1 1/12)
Step-by-step explanation:
Answer:
1 1/12
Step-by-step explanation:
4/12 + 9/12 = 13/12
13/12 = 1 1/12
Ms. Wilmith bought 4 bags of candies. Each bag contained 8 candies. She put an
equal number of these cand es into each of 9 gift boxes
How many candies were left over?
3
4
0
5
Answers
Answer:
Number of candy left = 5
Step-by-step explanation:
Given:
Number of bags = 4
Number of candies in each bag = 8
Number of Gift boxes = 9
Find:
Number of candy left = ?
Computation:
Total number of candies = Number of bags × Number of candies in each bag
Total number of candies = 4 × 8
Total number of candies = 32
According to Euclid division lemma:
a = bq +r
32 = (3)(9) + Remainder
32 = 27 + Remainder
Remainder = 5
Number of candy left = 5
20 points! I need the answer ASAP! Thanks!
Answers
Answer: y=5/7x+2
Step-by-step explanation:
The y- intercept would be 2 since that is where the line goes through the y axis. Also if you use slope form you will see that the slope is 5/7.
An account pays 6% coumpound interest in a year 1, the amount in tha account is $70 . How much is in the account in year 5?
Answers
Answer:
The amount in account in year 5th should be:
A = 70 x (1 + 6/100)^5 = 93.68$
Hope this helps!
:)
The surface area of which composite figure is the sum of the areas of eight triangular faces?
VX
O two rectangular pyramids joined at their congruent bases
two rectangular pyramids joined at two congruent lateral faces
O two triangular prisms joined at their congruent bases
two triangular prisms joined at two congruent lateral faces
Answers
Answer:
B
Step-by-step explanation:
Answer:
Its B
Step-by-step explanation:
What is the maximum of f(x) = sin(x)?
- 2π
-1
01
2π
Answers
Answer:
1
Step-by-step explanation:
The maximum value of sin(x) is 1.
When x = 90 degrees sinx = 1.
Find def, help geometry
Answers
Answer:
d
Step-by-step explanation:
Please help what is the solution to the equation AX = B?
Answers
Answer:
The first one
Step-by-step explanation:
In this question, we are trying to find X, so can solve this by back-solving. multiply the choices by the A until they equal B. If you do it for the first one then you should gett B.
Answer:
Option D.
Step-by-step explanation:
edge test
what is the distance between the pair of points.
(3, 3) and (3, −5)
Answers
Answer: 8
Step-by-step explanation:
So the right answer is 8units
Look at the attached picture
hope it will help you...
Good luck on your assignment
PLEASE HELP ME
10 points
Answers
Answer:
Between -2 and 0
Step-by-step explanation:
I need help with the puzzle plsssss it’s due Wednesday!
Answers
Answer:
f=f g=g e=e
Step-by-step explanation:
The volume of the giant beach ball is approximately 267.95 feet^3 . Find the diameter of the ball. Use 3.14 for pie.
Answers
Answer:
8 feet
Step-by-step explanation:
Hello, I can help you with this.
the volume of a sphere is given by.
[tex]Volume= \frac{4}{3} \ \pi\ radius^{3}\\\\[/tex]
Step one
isolate radius
[tex]\frac{3}{4}* volume= \pi\ radius^{3}\\\\\\\ \frac{3}{4 \pi }* volume=radius^{3}\\radius=\sqrt[3]{\frac{3}{4 \pi }* volume}[/tex]
According to the question the volume is 267.95 cubic feet , and pi= 3.14
put this values into the equation
let
volume =267.95
pi=3.14
[tex]volume=radius^{3}\\radius=\sqrt[3]{\frac{3}{4 \pi }* volume}\\radius=\sqrt[3]{\frac{3}{(4 *3.14) }*267.95}\\radius=\sqrt[3]{64}\\\\radius=4[/tex]
so the radius of the beach ball is 4 feet, but we need its diameter
Diameter=2* radius
radius=4 feet
Diameter= 4 feet*2
Diameter=8 feet
what a big ball¡¡
I hope it helps, have a great day.
help please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
4 feet by 3 feet
Step-by-step explanation:
I hope this helped you out
Use the quadratic formula to find the solutions to the quadratic equation
below.
2x2 - 5x+ 5 = 0
Answers
Answer:
x=9/5
Step-by-step explanation:
2*2-5x+5=0
4-5x+5=0
9=5x
x=9/5
Please mark it as brainliest
Tomas selects one of these garments at random. Let AAA be the event that he selects a blue garment and let BBB be the event that he chooses a shirt.
Please help!!!
Answers
Answer:
can u explain it more lol
Step-by-step explanation:
1)The probability of choosing a blue garment is 1/2
2)The probability of choosing a shirt is 1/3.
Thomas has 1 blue shirt
Thomas has 1 green shirt
Thomas has 1 blue hat
Thomas has 1 green scarf
Thomas has 1 blue pair of pants
Thomas has 1 green pair of pants
So, number of blue garments = 3
Number of shirts = 2
Total garments =6
What is probability?Probability is the measure of the likelihood of an occurrence.
P(event) = Favorable outcomes / Total outcomes
P(blue garment) = 3/6 =1/2
P(shirt) = 2/6 =1/3
Hence, 1)The probability of choosing a blue garment is 1/2
2)The probability of choosing a shirt is 1/3.
To get more about probability visit:
https://brainly.com/question/24756209
What will be the new coordinates of point B if the red triangle is reflected over the y.Axis
Answers
Answer:
(-4, 5)
Step-by-step explanation:
(-4, 5) are the correct coordinates of point B after reflecting the figure over the y-axis.
Gtftgohcigcigcigvvohvlkk gm
Answers
Answer:
its 34 the first person is correct
What is the solution to the equation = 3?
x = 1
x = 3
x = 9
x = 27
Answers
Multiply both sides by 9.
x/9 = 3
(x/9) * (9) = (3) * (9)
x=27
The solution of the expression x/9 = 3 is,
⇒ x = 27
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The expression is,
⇒ x/9 = 3
Now, Simplify the expression as;
⇒ x/9 = 3
Multiply by 9, we get;
⇒ 9 × x/9 = 9 × 3
⇒ x = 27
Thus, The solution is,
⇒ x = 27
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ2
Find the measure of x.
15(x+2)
X=-1
x = 7
X = 9
x=13
Answers
Answer:
x=7
Step-by-step explanation:
7+2 = 9. 9*15 = 135 degrees
The five-number summary for the number of teams in each of Brad's fantasy football leagues is shown in the following table.
The five-number summary suggests that about 50% of Brad's fantasy football leagues have fewer than how many teams?
Choose 1 answer:
(Choice A)
4
(Choice B)
7
(Choice C)
10
(Choice D)
14
(Choice E)
18
Answers
Answer:
The correct option is (C) 10.
Step-by-step explanation:
The five-number summary for the number of teams in each of Brad's fantasy football leagues is as follows:
Minimum: 4
Q₁: 7
Median: 10
Q₃: 14
Maximum: 18
The minimum value is the smallest value in the data set.
The first quartile (Q₁) is the value that is less than 75% of the observations.
The median is the middle most value of the data set. It is the value that is less than 50% of the observations.
The third quartile (Q₃) is the value that is less than 25% of the observations.
And the maximum value is the largest value in the data set.
So, the five-number summary suggests that about 50% of Brad's fantasy football leagues have fewer than 10 teams.
Thus, the correct option is (C).
A plane intersects one cone of a double-napped cone such that the plane is parallel to the generating line.
A. hyperbola
B. circle
C. parabola
D. ellipse
Answers
What does the equation, 2 + 2 = fish, really mean?
Answers
Answer:
This is subjective to the viewer of such an equation.
Step-by-step explanation:
Please give brainliest lol
If f(x) = 5x^3 and g(x) = x+1, find (f•g)(x).
Answers
Answer:
(fg)(x) = 5x^4 + 5x^3
Step-by-step explanation:
(fg)(x) = (5x^3)(x+1)
(fg)(x) = 5x^4 + 5x^3
