Answers
========================================================
Explanation:
Check out the diagram below.
We have the following points
A = center of both the circle and the squareB = point on the circle directly to the left of point AP,Q,R,S = corner points of the squareE = intersection of segments AB and PSF = point on the square directly to the right of point AC and D = intersection of segment PS and the circleLet x be the length of segments DE and EC. Note how segment AB bisects segment DC. Whenever the radius is perpendicular to the chord like this, the radius will bisect the chord.
We're told that the chord length CD is the same as the radius AD, since CD = CE+ED = x+x = 2x, this means AD = 2x as well.
At this point, you probably can recognize we have a 30-60-90 triangle. One useful property of such triangles is that the hypotenuse is double the length of the short leg. The long leg is [tex]x\sqrt{3}[/tex] which is the length of segment EA. You can use the pythagorean theorem to confirm this.
----------------------------------
To summarize that last section, we formed triangle DAE and this triangle is a 30-60-90 triangle as shown in the diagram below.
Notice how the segments EA and FA span the entire width of the square. That width being [tex]EA+FA = x\sqrt{3}+x\sqrt{3} = 2x\sqrt{3} = EF[/tex]
The square has side lengths of [tex]2x\sqrt{3}[/tex] while the circle has radius 2x.
Use these two facts to find the area of each in terms of x.
[tex]A_1 = \text{area of square} = (\text{side})^2 = (2x\sqrt{3})^2 = 12x^2[/tex]
[tex]A_2 = \text{area of circle} = \pi*r^2 = \pi*(2x)^2 = 4\pi x^2[/tex]
-----------------------------------
The last step is to divide the two results. The x^2 terms cancel out.
We'll be left with...
[tex]\frac{A_1}{A_2} = \frac{12x^2}{4\pi x^2} = \frac{12}{4\pi} = \frac{3}{\pi} \approx 0.9549[/tex]
There are many ways to express this ratio. One way we could write it is to say 3:pi to indicate that if the area of the square is 3, then the circle has area of pi (approximately 3.14). No matter what the square's area is, the circle is always slightly larger in area.
Related Questions
How do I draw perpendicular line
Answers
Answer:
Follow these steps and you will find how to make a perpendicular line.
Step-by-step explanation:
Open the compass to a radius less than half the segment.
Draw two arcs intersecting the line on both sides of the point.
Draw two arcs using the intersection points as the centers. ...
Construct a line between this point and the original point.
Hope this helped :) -ish
200m - 125m + 48,750 = 50,000 - 175m
Answers
Answer:
m = 5
Step-by-step explanation:
200m - 125m + 48,750 = 50,000 - 175m
=> 75m + 48,750 = 50,000 - 175m
=> 75m + 175m = 50,000 - 48,750
=> 250m = 1250
=> m = 5
Hoped this helped.
The first three terms of an arithmetic sequence are as follows.
28, 23, 18
Find the next two terms of this sequence.
Answers
Answer:
13, 8, 3
Step-by-step explanation:
Subtract 5 from the following terms.
Mark me as the brainliest please, Thank you!
please help i'm stuck and it's a unit test if correct i will give brainiest
Which inequality represents this statement?
A number is no more than 5.
a. n≥5
b. n<5
c. n>5
d. n≤5
Answers
Answer:
d. n≤5
Step-by-step explanation:
This is the answer
Answer:
D) n≤5
Step-by-step explanation:
No more than 5 means that the number cannot exceed 5, but it's ok to have any number less than 5 or equal to 5. So, this means that D is correct.
Solve for x
3x+7=28
Answers
Answer:
X=7
Step-by-step explanation:
Answer:
x = 7Step-by-step explanation:
3x + 7 = 28=> 3x = 28 - 7=> 3x = 21=> x = 7Conclusion:
Therefore
x = 7.Hoped this helped.
[tex]GeniusUser[/tex]
Josh makes a fruit salad with bananas, blueberries, and strawberries. He uses 234 pounds of bananas, 112 pounds of blueberries, and some strawberries. The fruit salad weighs 618 pounds. How many pounds of strawberries does Josh use?
Answers
Answer:
234+112=346
618-346=272
Josh used 272 pounds of strawberries in his fruit salad.
Step-by-step explanation:
Answer:
272
Step-by-step explanation:
Help!! Ill give 100 points if your correct
Answers
[tex]\\ \sf\Rrightarrow 12\dfrac{5}{6}-5\dfrac{1}{6}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{77}{6}-\dfrac{31}{6}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{77-31}{6}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{46}{6}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{23}{3}[/tex]
[tex]\\ \sf\Rrightarrow 7\dfrac{2}{3}[/tex]
Given info:- Subtract and simplify. 12(5/6) - 5(1/6) The given options are (a) 6(1/3) (b) 5(2/3) (c) 7(1/3) (d) 7(2/3)
Solution: 12(5/6) - 5(1/6)
= (72+5)/6 - (30+1)/6
= 77/6 - 31/6
Take the LCM of 6 and 6 is 6.
so,
= (77*1 - 31*1)/6
= (77-31)/6
= 46/6
= (46÷2)/(6÷2)
= 23/3
= 7(2/3) Ans.
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Jerome solved the equation 1 3 x + 5 6 = 1 as shown. 1. Subtraction property of equality: 1 3 x + 5 6 − 5 6 = 1 1 − 5 6 2. LCD: 1 3 x = 1 6 − 5 6 3. Multiply by...
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It would be too much to write so here is a photo instead :D
Answers
Answer:
C) Justine left her grandmother's house and walked 3 blocks directly south. Then she walked 3 blocks directly north. At this point, how many blocks was Justine from her grandmother's house?
Explanation:
C is the only answer choice where you are starting at 0. Justine goes down 3 blocks and comes back up 3 blocks getting her back to 0.
Answer choice A goes from -10 to 10.
Answer choice B goes from -16 to 16.
Answer choice D goes from 10 to -10.
Victor has put 1000 hours into playing an online video game he has paid 671.34 over the course of the entire game how much did much did he pay per hour played?
Answers
Answer:
Give the person above me brainliest plz
Step-by-step explanation:
Which best describes how to add 9.73 and 21.6?
Answers
Answer:
31.33
Work:
1 1
9.73
+ 21.60
--------------------
31.33
Final Answer:
Therefore, 31.33 is our answer.
Hoped this helped.
It takes 2 yards of material to
make 6 scarves, how many yards of material are needed to make 24
scarves?
Answers
Hope this helped
A circle has a circumference of 45 cm. What is the BEST estimate of the circle’s diameter?
A) 3cm
B)7.5
C) 15cm
D) 18.5cm
Answers
Answer:
C) 15 cm is the best estimate.
Step-by-step explanation:
The exact answer is not there, so 15 is the best estimate.
You can use this equation to help you:
d=C/π
Where d is the diameter.
C is the circumference.
And the last one is Pi.
You know that C = 45, so divide that by Pi (3.14).
45/3.14159 = 14.32
The closest answer is 15.
Hope this helps! Have a great day!
Answer:
The best estimate of the circle's diameter is 15cm.Step-by-step explanation:
Circumference = 2πr = 45cm=> 2 x π x r = 45 cm=> 2 x 22/7 x r = 45 cm=> 44/7 x r = 45=> 44r/7 = 45=> 44r = 315=> r = 7.16 (Rounded)=> Dia. = 7.16 x 2=> Dia. = 14.32=> Dia. ≈ 15 cmConclusion:
Therefore, the best estimate of the circle's diameter is 15cm.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
A?
B?
C?
D?
Who ever is right gets brainlest<3
Answers
Answer:
i think that the answer is b
hope it helps
Let f(x) = x − 2 and g(x) = x2 − 7x − 9. Find f(g(−1))
Answers
(-1)2-7(-1)-9=-4
(-4)-2=-6
it’s -6
Allison buys some cloud storage for her files. On average, she adds files that take up 2 megabytes each day. After 64 days, she has 96 megabytes of memory remaining in the cloud.
Determine the equation, in slope-intercept form, of the line that represents the amount of memory remaining after xecks days.
Answers
Answer:
the answer would be a because i had this exact question on ed2020, i think i remember it being A.
Step-by-step explanation:
how does 9 + 9 = 6 ?
Answers
Answer:
it does not, it equals 18
Step-by-step explanation:
9+9=18 - true
9+9=6 - false
Solve for x.
2x + 20=2x - 4
+
x = [?]
Enter
Answers
Answer:
x=24
Step-by-step explanation:
2x+20=2x-4+x
Subtract 2x from both sides
2x+20-2x=2x-4+x-2x
Simplify
20=-4+x
Add 4 to both sides
24=x
Switch sides
x=24
PLS HELP ME ASAP
NO LINKS
Answers
Answer:a
Step-by-step explanation:
-2(x - 3.5) = -2
First step:
Work for first step:
Urgent!!
Second Step:
Work for second step
Value of x:
Answers
London is deciding between two different movie streaming sites to subscribe to. Plan A costs $9 per month plus $1.50 per movie watched. Plan B costs $38 per month plus $0.50 per movie watched. Let AA represent the monthly cost of Plan A if London watches xx per month, and let BB represent the monthly cost of Plan B if London watches xx movies per month. Write an equation for each situation, in terms of x,x, and determine which plan would be cheaper if London plans on watching 26 movies each month
Answers
Answer:
Plan A is $3 cheaper can Plan B.
Step-by-step explanation:
first equation: 1.5t+9
second equation: .50t+38
Then substiute the 26 for x. So you get 48 for Plan A and 51 for Plan B. Then subtract so you can get 3, for Plan A is three dollars cheaper than Plan B.
Would you rather have your boss pay you 10,000 a day for 3 full weeks
Answers
Answer:
yes I would............
Ryan works at a donut shop where he makes $10.25 per hour. He works on at the school bookstore where he makes $8.75 per hour to worked 20 hours last week and made $196, how many hours did he work at each place?
Answers
Step-by-step explanation:
x = hours donuts
y = hours books
x + y = 20
10.25x + 8.75y = 196
from the first equation we get
x = 20 - y
that we use now in the second
10.25×(20 - y) + 8.75y = 196
205 - 10.25y + 8.75y = 196
-1.5y = -9
1.5y = 9
y = 9/1.5 = 6
x = 20 - y = 20 - 6 = 14
he worked 14 hours in the donut shop and 6 hours in the bookstore.
2
Question 7(Multiple Choice Worth 1 points)
(04.04LC)
Point P on the coordinate grid below shows the location of a stage light. A second stage light is 6 units above P. The length of each square on the grid is
2 units. What are the coordinates of the location of the second stage light?
2
16-14-12-1046
012101
O (8.-10)
O (8,2)
(14,2)
(14.-10)
Answers
Answer:
Add 8 to the y value of point p, (4, -2 +8)So the location of the second light is on point (4,6)
which is the next two equivalent fractions of 2/3 , 5/7
Answers
Answer:
[tex]\frac{2}{3}[/tex] X [tex]\frac{2}{2}[/tex] = [tex]\frac{4}{6}[/tex]
[tex]\frac{2}{3}[/tex] X [tex]\frac{3}{3}[/tex] = [tex]\frac{6}{9}[/tex]
Ans: [tex]\frac{2}{3}[/tex] => [tex]\frac{4}{6}[/tex] and [tex]\frac{6}{9}[/tex]
[tex]\frac{5}{7}[/tex] X [tex]\frac{2}{2}[/tex] = [tex]\frac{10}{14}[/tex]
[tex]\frac{5}{7}[/tex] X [tex]\frac{3}{3}[/tex] = [tex]\frac{15}{21}[/tex]
Ans: [tex]\frac{5}{7}[/tex] => [tex]\frac{10}{14}[/tex] and [tex]\frac{15}{21}[/tex]
If you are SMART? What is 100 x 100 without using a calculator?
Answers
Answer:
i got you it 10,000
Step-by-step explanation:
all you have to do is add the zeros
The number of purchases made on a new online store is modeled by
p(d) 15d + 45, where d is the number of days since the store opened.
The average amount spent in dollars per purchase is modeled by
s(d) = 0.15d? – 4d + 80. Write a function R(d) to model the total daily
revenue. Then predict the total amount of revenue on the 23rd day.
-
Answers
The total amount of revenue on the 23rd day is 322.65
Given the following parameters:
purchases made p(d) = 15d + 45sales made s(d) = 0.15d² – 4d + 80The revenue will be exprssed as:
r(d) = s(d) - p(d)
r(d) = 0.15d² – 4d + 80 - (15d + 45)
r(d) = 0.15d² – 19d + 35
Hence a function R(d) to model the total daily revenue is r(d) = 0.15d² – 19d + 35
To get the total amount of revenue on the 23rd day, you will substitute t = 23 into the function
r(d) = 0.15d² – 19d + 35
r(23) = 0.15(23)² – 19(23) + 35
r(23) = 79.35 - 437 + 35
r(23) = -322.65
Hence the total amount of revenue on the 23rd day is 322.65
Learn more on function here: https://brainly.com/question/14307385
what is the perimeter of 4in. 4in.
Answers
Perimeter = 4 × side
[tex] = 4 \times 4 \\ = 16in[/tex]
The perimeter of a 4-inch square is 16 inches.
What is the slope of a line if x equals (-2 and y equals 4?
Answers
Answer:
can't be determined unless you give two points which is two sets of x and y points
The cafe sells Beetle Juice and Potion Punch. A cup of Beetle Juice costs $2.50 and a cup of Potion Punch costs $3. Owen ordered 5 drinks for his group and spent $14. Write a system of equations to find the number of cups of beetle juice, j, and potion punch, p, that Owen purchased.
Answers
Answer:
2 Beetle juices and 3 Potion Punch
Step-by-step explanation:
j = Beetle Juice cost $2.50
p = Potion Punch Cost $3
j + p = 5 Multiply by -3 -3j - 3p = -15
$2.50j + $3p = $14 Do not change + 2.50j -3p = 14
- .50j = -1
j = 2 Beetle Juice
Substitute into the fist equation and solve for y j + p = 5
2 + p = 5
p = 3 Potion Punch
solve for x (x-6)^2-5=0
Answers
Answer:
x=6+√5 or x=6−√5