Peter has built a gazebo, whose shape is a regular heptagon, with a side length of $1$ unit. He has also built a pathway around the gazebo, of constant width $1$ unit, as shown below. (Every point on the ground that is within $1$ unit of the gazebo and outside the gazebo is covered by the pathway.) Find the area of the pathway.
Answers
Answer:
Area of pathway = 10.375 unit²
Step-by-step explanation:
Given - Peter has built a gazebo, whose shape is a regular heptagon, with
a side length of 1 unit. He has also built a pathway around the
gazebo, of constant width 1 unit, as shown below.
To find - Find the area of the pathway.
Proof -
Central angle = [tex]\frac{360}{7}[/tex] = 51.43°
Now,
Central angle / 2 = [tex]\frac{360}{14}[/tex] = 25.71°
And
height = [tex]\frac{1}{2}.\frac{1}{tan25.41}[/tex] = 1.038
Now,
Inner area of gazebo = 7·[tex]\frac{1}{2}[/tex]·1·(1.038) = 3.634 unit²
Outer area of gazebo = ([tex]\frac{2.038}{1.038}[/tex])²·(3.364) = 14.009 unit²
∴ we get
Area of pathway = Outer area - Inner area
= 14.009 - 3.634
= 10.375 unit²
⇒Area of pathway = 10.375 unit²
Related Questions
2/x + 5/3 = 7/2, trynna solve for x
Answers
Answer:
x= 12/11
Step-by-step explanation:
2. What are the zeroes of P(x) = x3 – 6x2 – x +62
-6, -1, 1
A.
C. 6, -1, 1
B. -6, -1, -1
D. 6, 1, 1
Answers
Step-by-step explanation:
if u mean (x^3 -6x^2 -x- 6) then the answer is C
(6,-1,1)
..................,..........
but if u mean P(x) = x3 – 6x2 – x +62
then the answer is None of the above
-2.724
4.361+1.9328i
4.361+1.9328i
17 POINTS! I will also give Brainliest!
Find the perimeter of the coordinates below:
Figure PQRST is shown. P is at negative 2, 11. Q is at negative 4, 5. R is at 2, 0. S is at 1, 7. T is at 8, 7.
37 units
38 units
39 units
40 units
Answers
Answer:
c 39
Step-by-step explanation:
Parameter is the sum of the lengths of all sides of a polygon. The sides of the polygon are PT, TS, SR, RQ, and QP. To get the length of a side, we use the distance formula: Each vertex in the polygon has its corresponding points:\
So to get the length of side PT, we use the distance formula and the vertices of side PT:
The length of PT is
The same procedure is done for the other 4 sides and the following are the answers:
And by adding all the sides, you get the perimeter:
By rounding off, the answer is 39 units.
have a nice day
guys patulong naman.
Answers
Answer:
Step-by-step explanation:
i dont know what patulang naman but you have to make your own
What is the perimeter of a square if the length of one of the diagonals is 12 cm?
6v2 cm
2412 cm
48 cm
24 cm
Answers
Answer:
Step-by-step explanation:
Use Pythagorean theorem to find the length of the square.
Length of the square = a
a² +a² = diagonal²
2a² = 12²
2a² = 144
a² = 144 ÷ 2
a² = 72
[tex]a =\sqrt{72}\\\\ = \sqrt{2*2*2*3*3}\\\\ = 2*3\sqrt{2}\\\\a = 6\sqrt{2}\\\\\\\\Perimeter= 4a\\\\ = 4*6\sqrt{2}\\\\= 24\sqrt{2} cm[/tex]
1/3 plus blank equals 5/6
Answers
Answer: 3/6 + 2/6 = 5/6
Step-by-step explanation: 1/3 is equal to 2/6 then 3/6+ 2/6 equals 5/6
. To convert the ratio of 3:5 to 5:6, which number should be added on both?
Answers
Answer:
7
Step-by-step explanation:
3:5 + 7 = 10:12
10:12 when shortened is 5:6
Fill in the blank to make an equivalent ratio.
4:7 = ______ : 56
Answers
Answer:
4:7 = 32:56
Step-by-step explanation:
4 x 8 = 32
7 x 8 = 36
Hope this helped!
PLZZZZZ give me brainliest
Answer: 32:56
Step-by-step explanation:
because first I divided 56/7=8 and then did 4*8=32. You're welcome!!! c:
What is the verb in the following sentence? “It is too cold for ice cream.”
too
is
cold
It
Answers
Answer:
Is is the verb.
Hope u understand.... :P
Hope it helps...
Step-by-step explanation:
is because it is actually happening
cold is an ADVERB to describe something
Last week Maria ran 19 miles less than Arjun. MAria ran 8.7 miles. How many miles did Arjun run?
Answers
Answer:
22.7 miles
Step-by-step explanation:
19+8.7=22.7
Give one pair of supplementary angles and one pair of vertical angles shown in the figure below.
Answers
Answer:
Supplementary- 5 and 6
Vertical- 1 and 6
Step-by-step explanation:
5 and 6 are supplementary, because they make a straight line together. 1 and 6 are vertical angles, bu the vertical angles congruence theorem.
Identify the slope and the y-intercept
y = 4x-7
Answers
Step-by-step explanation:
y = 4x - 7
Comparing the given equation with y = mx + c Then
slope (m) = 4
y -intercept (c) = - 7
Hope it will help :)
Answer: the slope is negative 4
Step-by-step explanation:
because its ez
help me I need this now!!!!!!!!!
Answers
Answer:
45
Step-by-step explanation:
All angles of a triangle should add up to 180
35 + 80 + 45 = 180
-37=5w-7
w=
Please I need an answer ASP
Answers
Answer:
-6
Step-by-step explanation:
-37+7=5w
-30=5w
w=-30÷5
w=-6
Answer:
w=-6
Step-by-step explanation:
-37=5w-7
-37+7=5w-7+7 (add 7 both sides)
-30/5=5w/5 (divide both sides by 5 to remove 5 and make it equal to w)
-6=w or w=-6
To verify the answer:
5(-6)-7
-30-7
-37
Shane bought an 18 pound bag of dog food. He feeds his dog pound of dog food 5/3 for each meal. If Shane feeds his dog twice a day every day, how many days will the 18 pound bag of dog food last?
Answers
Answer:
18 pounds of dog food will last 3 days.
Step-by-step explanation:
We know that he has 18 pound of dog food and he is giving 3 pound of food twice every day, so 3 * 2 would be 6. So we need 6 pounds of dog food is being fed every day. Since we want to find out how much dog food 18 pound bag could last, you would divide 18 by 6 so 18/6 would get you 3. So we know 18 bag of dog food will last 3 days.
6x + 8
10x
60°
A) 64°
C) 70°
B) 45°
D) 50°
Answers
10x + 60 + 6x + 8 = 180
16x + 68 = 180
16x = 112
x = 7
6x + 8
6(7) + 8
42 + 8
50
10x
10(7)
70
to fact check, 180 = 70 + 60 + 50, which evens out, making this the correct answer
please mark as brainliest, hope this helped :)
if there is a remainder, express
Answers
Answer:
Once you have the answer in division the same way - divide, multiply, subtract, bring down and then you're going to let a remainder. Instead of writing R and then the number, you are going to take your remainder and make it the numerator of a fraction.
Step-by-step explanation:
I majored in Mathematics
(b-3)squared expanded
Answers
Answer:
Step-by-step explanation:
(x - y)² = x² - 2xy + y²
x = b ; y = 3
(b - 3)² = b² - 2 *b * 3 + 3²
= b² - 6b + 9
Emily is entering a bicycle race for charity. Her mother pledges $0.60 for every 0.5 mile she bikes. If Emily bikes 10 miles, how much will her mother donate?
Answers
Hope this answer helps :)
Which measurement is closest to the volume of the sphere in cubic inches ?
Answers
A sphere is a three-dimensional figure where the volume is given as:
The volume of a sphere = 4/3 πr³
The volume of the sphere is 3754.7 m³.
The measurement closest to the volume of the sphere is 3431.4 m³
Option B is the correct answer.
What is a sphere?It is a three-dimensional figure where the volume is given as:
The volume of a sphere = 4/3 πr³
Example:
The volume of a sphere with a radius of 2 cm is 32π/3.
We have,
The radius of the sphere = 8 m
Now,
The volume of the sphere.
= 4/3 x π x r³
= 4/3 x 22/7 x 8 x 8 x 8
= 3754.7 m³
This is closest to the 3431.4 m³
Thus,
The volume of the sphere is 3754.7 m³.
The measurement closest to the volume of the sphere is 3431.4 m³
Option B is the correct answer.
Learn more about spheres here:
https://brainly.com/question/12390313
#SPJ6
hiiii everyone my previous account has been deleted who knows me plz follow
Answers
Answer:
I don't know you but I can follow you if you want
a
II. Express the given fraction to decimal.
3
11.
=
12.
NLD
1
3
13.
=
14.
+ I co
4
10
3
1
15.
16.
100 ml
4
17.
=
18.
10
5
15
3
19.
20.
60
16
Answers
Answer:
the question is invalid. please rewrite the question.
Which of these figures has rotational symmetry?
Answers
Answer:
i dont know bro
Step-by-step explanation:
What is the area of this parallelogram?
4.9 cm²
12.25 cm²
17.15 cm²
24.01 cm²
Parallelogram A B C D is composed of a square and two triangles. The square has a length and height of 3.5 centimeters each. There are two identical triangles. Each triangle has a base of 1.4 centimeters and a height of 3.5 centimeters.
Answers
Answer:
17.15
Step-by-step explanation:
Answer:
17.15cm
Step-by-step explanation:
I did the quiz and got it right (K12)
Someone help me please what is 4.3 x 20
Answers
Answer:
86
Step-by-step explanation:
Answer:
86
Step-by-step explanation:
Multiply the two numbers together as if there was no decimal, then move the decimal in the number of places that it is given in one of the factors.
(This is a question from arithmetic sequence) Jay’s dog weighs 35 kilograms and is overweight. The dog is put on a diet, losing 0.4kg
every week. How long does it take to reach the target weight of 28 kilograms?
Answers
Answer:
17.6 weeks
Step-by-step explanation:
The computation of the time taken to reach the target weight is shown below:
35, 34.6, 34.2...............28
As we know that
a_n = a + (n - 1)d
28 = 35 + (n - 1)(-0.4)
28 = 35 -0.4n + 0.4
28 = 35.04 - 0.4n
0.4n = 35.04 - 28
0.4n = 7.04
n = 17.6
Which of the I-values are solutions to both of the following inequalities?
19 < c and r < 25
Choose all answers that apply:
А
= 18
B
= 20
c
= 27
Answers
x = 27
Explanation:
For x = 18 19 < 18 and 18 < 25 one is false
***For x = 20 19 < 20 and 20 < 25 True
For x = 27 19 < 27 and 27 < 25 One is false
Good luck to you!
Which set of ordered pairs represents y as a function of x?
a
{(0, 1), (2, 4), (5, -1), (2, 5)}
b
{(1, 1), (2, 2), (3, 3), (1, 0)}
c
{(4, 1), (4, 2), (4, 3), (4, 4)}
d
{(1, 4),(2, 4), (3, 4), (4, 4)}
Answers
Figure 1 is dilated to get Figure 2.
What is the scale factor?
Enter your answer in simplest form in the box.
Two trapezoids with the same shape but different sizes. One trapezoid has a side measured at 8 units and is labeled figure 1. The other trapezoid has the corresponding side measured at 18 units and is labeled figure 2.
Answers
Answer: what is a scale factor
Step-by-step explanation:
The diameter of a spherical basketball is 10 inches. What is the volume of the basketball? Give the exact solution.
Answers
Step-by-step explanation:
Volume of sphere =4/3pir3
=4/3 X pie X rXrXr
R=diameter /2=10/2=5 inches
V=4/3 X 22/7 X 5 X 5 X 5
= 11000/21=523.8in3
