Answer:
The number π (/paɪ/; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159. It is defined in Euclidean geometry[a] as the ratio of a circle's circumference to its diameter, and also has various equivalent definitions. The number appears in many formulas in all areas of mathematics and physics. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in 1706.[1] It is also referred to as Archimedes's constant.[2][3]
Being an irrational number, π cannot be expressed as a common fraction, although fractions such as
22
/
7
are commonly used to approximate it. Equivalently, its decimal representation never ends and never settles into a permanently repeating pattern. Its decimal (or other base) digits appear to be randomly distributed, and are conjectured to satisfy a specific kind of statistical randomness.
It is known that π is a transcendental number:[2] it is not the root of any polynomial with rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematics approximated π to seven digits, while Indian mathematics made a five-digit approximation, both using geometrical techniques. The first computational formula for π, based on infinite series, was discovered a millennium later, when the Madhava–Leibniz series was discovered by the Kerala school of astronomy and mathematics, documented in the Yuktibhāṣā, written around 1530.[4][5]
The invention of calculus soon led to the calculation of hundreds of digits of π, enough for all practical scientific computations. Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have pursued new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits.[6][7] The primary motivation for these computations is as a test case to develop efficient algorithms to calculate numeric series, as well as the quest to break records.[8][9] The extensive calculations involved have also been used to test supercomputers and high-precision multiplication algorithms.
Because its most elementary definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses, and spheres. In more modern mathematical analysis, the number is instead defined using the spectral properties of the real number system, as an eigenvalue or a period, without any reference to geometry. It appears therefore in areas of mathematics and sciences having little to do with the geometry of circles, such as number theory and statistics, as well as in almost all areas of physics. The ubiquity of π makes it one of the most widely known mathematical constants—both inside and outside the scientific community. Several books devoted to π have been published, and record-setting calculations of the digits of π often result in news headlines.
Step-by-step explanation:
Use the image to the right to determine how tall the tree is . The hypotenuse is 7.5m and the leg is 6.2m
Answer:
4.22m.
Step-by-step explanation:
Using Pythagoras theorem:
7.5^2 = h^2 + 6.2^2
h^2 = 7.5^2 - 6.2^2
h^2 = 17.81
Height h= 4.22.
can someone answer not just use my points
Answer:
35
Step-by-step explanation:
Well if m<YVW = (12x-1) and x=3 then just plug in x
So,
m<YVW = (12(3)-1)
m<YVW = 36-1
m<YVW = 35
6/7 x 5/6 Multiple. into the simpelst form
Answer:
5/7
Step-by-step explanation:6x5 =30 7x6=42 =30/42divided by 6 =5/7
4n+12=92. What does n equal?
Answer:
n=20
Step-by-step explanation:
4n = 80
n=80/4
n=20
Complete the proof that m∠QSR+m∠UVX=180°.
Answer:
Co - interior angles of a parallelogram add up to 180 degrees
Step-by-step explanation:
Since UW and RT are parallel lines we can infer that if the QSR was flipped and joined to UVX it would create a parallelogram. Angle theorem states that co -interior angles of a parallelogram add up to 180 degrees.
Using properties of parallel line we can prove that
m ∠QSR + m ∠UVX =180°.
What parallel lines?Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are complementary, others are congruent (equal).
Properties of Parallel Lines
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines that are always the same distance away from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
We have to prove that m ∠QSR+ m ∠UVX=180°.
Now, using parallel line property
<QSR = <SUV ( corresponding angle).........(1)
and, <SVU + <UVX = 180 (linear pair)
<QSR + <UVX = 180 ( from (1))
Learn more about parallel lines here:
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#SPJ2
read base and height to find area of triangle in algorithm and flowchart
answer please!!!!!!!!!!!!1
Answer:
Given points= (0,2) (1,0)
0-2/1-0= -2/1
Slope= -2
PLEASE HELP I REALLY NEED IT ITS MATH ,
Answer:
a) y=200x+450
b) y=200(8)+450 = $2050
c) 21 months
Step-by-step explanation:
a) y=200x+450
200 per month plus her initial deposit of 450
b) y=200(8)+450 = 2050
To see how much she'll have after 8 months, plug in 8 for x
c) 4500<200x+450
4050<200x
20.25<x
x>20.25, so after 21 months since 20.25 is more than 20 months you have to round up to 21
What percent of the students prefer superhero movies? Round your answer to the nearest whole number percent.
Answer:
36%
Step-by-step explanation:
47/132=36%
The = is means the equal sign with the ~ position
The percent of the students prefer superhero movies rounded to the nearest percent is; 36%
How to work with percentages?The table of this random survey of students when seen online tells us that;
Total number of students that prefer super hero movies = 47
Total Number of Students that prefer Comedy = 50
Total Number of Students that prefer drama = 35
Thus;
Total number of students surveyed = 47 + 50 + 35
Total number surveyed = 132
Thus;
Percent of the students that prefer superhero movies = 47/132 * 100%
Percent of the students that prefer superhero movies = 36%
Read more about percentages at; https://brainly.com/question/843074
a=8 b=24 what is ab?
Answer:
Step-by-step explanation:
ab = 8 * 24
= 192
Which best describes the character type of Curt Lemon in “The Dentist”?
stock character
foil character
dynamic character
flat character
Answer:
dynamic character
Step-by-step explanation:
You just won the lotto. You have two options, you can take the full $1,000,000 now or they will pay you 1000 dollars
this year and then double the amount they pay you every year for 10 years. Which way will get you more money?
Plz help
3k-3=15 k equals what??
5
Answer:
k = 6
Step-by-step explanation:
What you do is use inverse operations
15 + 3 =18
18 divided by 3 = 6
k = 6
3(6) - 3 = 15
Answer:
-3=15k-3k
-3=12k
-3÷12=12k÷12
k=-3 over 12
The cost for 4 hamburgers and 3 drinks is $14.75. The cost for 5 hamburgers and 4 drinks is $18.75. How much does 1 hamburger cost.
Answer:
each hamburger is $2.75
Step-by-step explanation:
We can solve for this system of equations where x are the burgers, and y are the drinks:
4x+3y=$14.75
5x+4y=$18.75
We need to multiply the first row by 4, and multiply the second row by -3 to be able to solve for x
Multiplying, we get:
16x+12y=$59
-15x-12y=$56.25
Now subtracting the top by the bottom, we are left with:
x=$2.75
Thus, each hamburger cost $2.75
side note, you can plug in x=$2.75 into either equation and solve for y to figure out what each drink costs :)
this question is about quadrlaterals pls help
Answer:
The answer is A trapezoid
Can someone solve this for me plis
Answer:
x = 1
Step-by-step explanation:
Here is what you need to know:
f(x) represents the y-value.
The x in the parenthesis represents the x-value.
Another way to write f(x) = 1 is y = 1.
So now you are just finding the x-value for when y = 1. Looking at the graph, when y is 1 ( 1 on the y-axis), x has to be 1! This is because when you go up one, the only value that matches that point is 1!
Hope this helps :)
(sorry if my explanation was a bit confusing)
Can anyone help me with this problem?
Answer:
yes I can solve it
Step-by-step explanation:
according to mid point theorem
2×13.8=n+6.7
n= 27.6-6.7
n=20.9
A 6-month-old Sheltie puppy gets 2.5 cups of food twice per day.
Select the equation that describes how many cups of food she eats in terms of days.
A) y = x + 2.5
B) y = 2.5x
C) y = x + 5
D) y = 5x
Answer: D (y = 5x)
Explanation:
Read the question.
2.5 cups of food twice per day
Hence, y = 5x
9
8
7
PER
6+
57
4-
3
As:
24
MY
4
-9 -8 -7 -6 -5 -4 -3 -2
→ 2
8 9
1
2
3 4
5
67
Co
-2
-3
-4
-5
-6-
MY
Pro
-7
-8
Pro
-9
Tea
Answer:
That's quantum mathematics
Simplify.
∣∣−13∣∣
3
13
−13
−3
Answer:
The answer is = 13
Step-by-step explanation:
Hope it helped youuuuu
PLEASE ANSWER! GIVE AN STEP-BY-STEP EXPLANATION, PLEASE for Brainliest! :)
*links are prohibited. *
Answer:
-4 4/5 = - 24/5
1 1/3 = 4/3
-(24/5) / (4/3) = -72 / 20 = -3 12/20 = -3 3/5
Using a calculator -(4 4/5) / (1 1/3) = -3 3/5
Does (6,2) make the equation y = x true?
Answer:
No it doesnt because 6 does not equal 2
Solve the equation-
[tex] \frac{5}{x - 3} - \frac{4}{x + 4} = \frac{1}{x} [/tex]
Help me SalmonWorldTopper please please
Given info:- 5/(x-3) - 4/(x+4) = 1/x. And here the problem has asked to find out the value of x ?
Let's solve!!
Given equation is 5/(x-3) - 4/(x+4) = 1/x
⇛ [5(x+4) - 4(x-3)]/(x-3)(x+4) = 1/x
⇛ (5x+20-4x+12)/(x-3)(x+4) = 1/x
⇛ (x+32)/(x-3)(x+4) = 1/x
On applying cross multiplication then
⇛ x(x+32) = (x-3)(x+4)
⇛ x²+32x = x(x+4)-3(x+4)
⇛ x²+32x = x²+4x-3x-12
⇛ x²+32x = x²+x-12
⇛ x²+32x-x²-x = -12
⇛ (x²-x²)+(32x-x) = -12
⇛ 0+31x = -12
⇛ 31x = -12
⇛ x = -12/31
∴ x = -12/31
The value of x for the given problem -12/31
VERIFICATION:
Check
If x = -12/31 then LHS of the equation is
5/(x-3) - 4/(x+4)
⇛ 5/[(-12/31)-3] -4/[(-12/31)+4]
⇛ 5/[(-12-93)/31] -4/[(-12+124)/31]
⇛ 5/(-105/31) - 4/(112)/31
⇛ (5×-31)/105 - (4×31)/112
⇛ (-115/105)-(124/112)
⇛ (-31/21) - (31/28)
⇛ (-31)[(1/21)+(1/28)]
⇛ (-31)(21+28)/(21×28)
⇛ (-31×49)/(21×28)
⇛ (-31×7)/(21×4)
⇛-31/12
And RHS = 1/x
⇛ 1/(-12/31)
⇛ -31/12
⇛ LHS = RHS is true for x = -31/12
A rental car company charges $75.77 per day to rent a car and $0.07 for every mile
driven. Scarlett wants to rent a car, knowing that:
• She plans to drive 325 miles.
She has at most $340 to spend.
Which inequality can be used to determine d, the maximum number of days Scarlett
can afford to rent for while staying within her budget?
340 < 75.77d + 22.75
340 < 75.77(d + 22.75)
Submit Answer
340 > 75.77(d + 22.75)
340 > 75.770 + 22.75
The daily rent is an illustration of a linear inequality.
The inequality is (d) [tex]\mathbf{340 > 75.77d + 22.75 }[/tex]
The daily charge is given as:
[tex]\mathbf{Daily = 75.77}[/tex]
The rate is:
[tex]\mathbf{Rate = 0.07}[/tex]
Let the number of days be d.
So, the total charges is:
[tex]\mathbf{Total = Daily \times d + Rate \times Miles}[/tex]
This gives
[tex]\mathbf{Total = 75.77 \times d + 0.07\times 325}[/tex]
[tex]\mathbf{Total = 75.77 \times d + 22.75}[/tex]
From the question, we understand that he has at most $340 to spend.
At most means <=
So, we have:
[tex]\mathbf{75.77 \times d + 22.75 \le 340}[/tex]
[tex]\mathbf{75.77d + 22.75 \le 340}[/tex]
Rewrite as:
[tex]\mathbf{340 > 75.77d + 22.75 }[/tex]
Hence, the inequality is (d) [tex]\mathbf{340 > 75.77d + 22.75 }[/tex]
Read more about linear inequalities at:
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HELP ASAP I ONLY HAVE 2 MINS
Each month, Ellie spends 4 hours in tap class at her dance studio. If each month she spends 20% of her class time in tap class, what is the total number of hours she spends in dance classes each month? Show your work or explain how you found your answer in complete sentences.
Answer:
20 hours
Step-by-step explanation:
20 hours, since you have to find the remaining 80% of her dance time.
I thought of this as follows:
1/5 = 4
2/5 = 8
3/5 = 12
4/5 = 16
5/5 (100% of her dance time!) = 20 hours!
I hope this helped a bunch! Tell me if you need any further assistance...
( :
Express as a trinomial.
(x-1)(2x-8)
(x−1)(2x−8)
Answer:
this is a binomial, but its 2x^2-10x+8
Step-by-step explanation:
you use the distributive property
can someone please help me answer one of these? thank u sm if u help!! :)
Answer:
w = 28
x = 18
Step-by-step explanation:
To make the triangles congruent, the hypotenuse and leg need to be the same length.
5w +x -59 = -w +2x +91
4w+4x -92 = 2x +2w
These two equations can be written in general form by subtracting the right-side expression from both sides.
6w -x -150 = 0
2w +2x -92 = 0
The second of these equations can be divided by 2 to give ...
w +x -46 = 0
When that is added to the first equation, we have ...
7w -196 = 0
w -28 = 0
w = 28
Using this in our simplified second equation, we have ...
x = 46 -w = 46 -28
x = 18
_____
Additional comment
These values of w and x make the side lengths ...
UV = 2x -w +91 = 2(18) -28 +91 = 8 +91 = 99
UT = 2x +2w = 92 . . . . from 2nd equation
Using the Pythagorean theorem, this makes ...
TV = √(99^2 -92^2) = √1337 ≈ 36.57
-25=-5/3u help please
Step-by-step explanation:
-25 = -5/3u
-25.3u = -5
-75u = -5
u = -5/-75
u = 1/15
why do people keep adding links instead of answering my? question
I know! It's kind if annoying tbh...
luka invests $8000 at 6% interest for three years
what is the overall percentage increase if it is 6% compound interest?
