take a square of arbitary measure assuming its area is one square unit.divide it in to four equal parts and shade one of them.again take one shaded part of that square and shade one fourth of it.repeat the same process continuously and find the sum area of shaded region​

Answers

Answer 1

Answer:

In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.[1][2] The order of the magic square is the number of integers along one side (n), and the constant sum is called the magic constant. If the array includes just the positive integers {\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}, the magic square is said to be normal. Some authors take magic square to mean normal magic square.[3]

The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3

Magic squares that include repeated entries do not fall under this definition and are referred to as trivial. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant we have semimagic squares (sometimes called orthomagic squares).

The mathematical study of magic squares typically deals with its construction, classification, and enumeration. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares. There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. Magic squares are generally classified according to their order n as: odd if n is odd, evenly even (also referred to as "doubly even") if n is a multiple of 4, oddly even (also known as "singly even") if n is any other even number. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect magic squares, and so on. More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares. Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge. The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century.

Magic squares have a long history, dating back to at least 190 BCE in China. At various times they have acquired occult or mythical significance, and have appeared as symbols in works of art. In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations.

Answer 2

The sum area of shaded region​ is [tex]\frac{1}{3}[/tex].

Summation formula for geometric progression

The formula to find the sum of infinite geometric progression is

[tex]S_{n}=\frac{a_{1}(1-q^{n}) }{1-q} \ \ q \ne 1[/tex]

Given

S = [tex]\frac{1}{4} +\frac{1}{16} +\frac{1}{64} +.........[/tex]

Using geometric progression

S = [tex]\lim_{h \to \infty} [\frac{1}{4} +(\frac{1}{4} )^{2} +(\frac{1}{4} )^{3} +.........+(\frac{1}{4} )^{n}][/tex]

Using summation formula for geometric progression

[tex]S_{n}=\frac{a_{1}(1-q^{n}) }{1-q} \ \ q \ne 1[/tex]

= [tex]\lim_{h \to \infty} \frac{\frac{1}{4} (1-(\frac{1}{4} )^{n} }{1-\frac{1}{4} }[/tex]

= [tex]\lim_{h \to \infty} \frac{\frac{1}{4} (1-\frac{1}{4^{n} }) }{\frac{3}{4} }[/tex]

= [tex]\lim_{h\to \infty} \frac{1}{3}(1-\frac{1}{4^{n} } )[/tex]

[tex]\lim_{h\to \infty} \frac{1}{4^{n} }[/tex] = 0

S  = [tex]\frac{1}{3}(1-0) = \frac{1}{3}[/tex]

The sum area of shaded region​ is [tex]\frac{1}{3}[/tex].

Find out more information about summation formula for geometric progression here

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Related Questions

What is the value of 1/4 {38-14} + 3^3 divided by 9

Answers

Answer:

9

Step-by-step explanation:

See the picture for steps :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{1}{4} (38 -14) + \dfrac{3^3}{9}}[/tex]

[tex]\mathsf{38-14=\bf 24}[/tex]

[tex]\mathsf{= \ \dfrac{1}{4} (24)+\dfrac{3^3}{9}}[/tex]

[tex]\mathsf{\dfrac{1}{4}(24)= \bf 6}[/tex]

[tex]\mathsf{= \ 6+\dfrac{3^3}{9}}[/tex]

[tex]\mathsf{3^3}\\\mathsf{= 3\times3\times3}\\\mathsf{= 9\times3}\\\mathsf{= \bf 27}[/tex]

[tex]\mathsf{= \ 6+\dfrac{27}{9}}[/tex]

[tex]\mathsf{\dfrac{27}{9}}\\\mathsf{= 27\div9}\\\mathsf{= \bf 3}[/tex]

[tex]\mathsf{= \ 6 + 3}[/tex]

[tex]\mathsf{= \bf 9}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf 9}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

A fruit seller bought 160 kg of apples at Rs. 32 per kg. He sold one fourth of them at Rs. 40 per kg and sold the rest at Rs. 31 per kg. Find his profit or loss.​

Answers

Answer:

A fruit seller bought 160 kg of apples at Rs. 32 per kg. He sold one fourth of them at Rs. 40 per kg and sold the rest at Rs. 31 per kg. Find his profit or loss.

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A class of 245 students went on a field trip. They took 9 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 5 students and each bus hold 45 students.

Answers

5 busses, 4 cars. 5x45= 225. 4x5=20. 225+20=245

Answer:

4 cars and 5 buses

Step-by-step explanation:

245÷ 45=5.4

45×5=225

245-225=20

20÷5=4

Which data set could be represented by the box plot below?

Answers

Answer:

Step-by-step explanation:

B

Answer is B


Explanation:

Match the word to know with its definition


Expanded form

Product

Place value

Digit


A number that is written as a sum of single digit multiples of powers of 10

Any of the symbols ( 0 to 9 ) that are used to write a number

The result of multiplying two or more numbers together

The value of where a digit is located in a number

Answers

Expanded form
- A number that is written as a sum of single digit multiples of powers of 10.
Consider the number 3,559,761
The expanded form of it is:
3,000,000 + 500,000 + 50,000 + 9,000 + 700 + 60 + 1

Product
- The result of multiplying two or more numbers together.
EXAMPLE:
Multiply 4 x 3 = 12
12 is the product
Product is the answer you get from multiplying two or more numbers together.


Place value
- The value of where a digit is located in a number.
Consider the number “350”
The place value of 3 in 350 is 300
Place value of 5 = 50
Place value of 0 = 0

Digit
- Any of the symbols (0 to 9) that are used to write a number.

I HOPE THIS HELPS!


Match the part of the circle to its correct name.

Answers

Answer:

a. major arc

b. minor arc

c. semi circle

d. central angle

Beatrice graphed the relationship between the time (in seconds) since she sent a print job to the printer and the number of pages printed.

10
10
20
20
30
30
40
40
5
5
10
10
15
15Seconds since sending print jobPages printed
What does the
x
xx-intercept represent in this context?
Choose 1 answer:

Answers

Given:

Consider the below figure attached with this question.

To find:

The interpretation for x-intercept in this context.

Solution:

In the given graph x-axis represents the second since sending print job and y-axis represents the Pages printed.

At x-axis the y-coordinate is 0. It means the x-axis represents the number of seconds that passed before the printer started printing pages.

Therefore, the correct option is C.

Answer:

B. The number of seconds that passed before the printer started printing pages

Step-by-step explanation:

Ken needs a surgery on his foot. The estimated cost of the surgery is $5,000. The insurance policy provided by Ken's company has $500 deductible and 20% co-pay. How much will Ken have to pay for foot surgery?

Answers

9514 1404 393

Answer:

  $1400

Step-by-step explanation:

Ken will be required to pay the deductible and 20% of the remaining amount.

  Ken pays $500 + 0.20(5000 -500) = $500 +900

  Ken pays $1400

List the coordinates for the plotted points A, B, C, and D.

Answers

Answer:

A= (3,1) ; B=(-2,-1) ; C=(-4,1) ; D=(-4,0)

Step-by-step explanation:

Plotted points are expressed by (x,y) , where the x is equal to the value that you read on the x plot and y is equal to the value that you read on the y plot.

can i get some help on this question please? ASAP!!

Answers

Answer:

left is a very good approximately .9 POSITIVE correlation

right is a very good approximately -.9 NEGATIVE correlation

Step-by-step explanation:

What is the sum of the greatest number and least number formed by the digits 4,7,0and 9​

Answers

Answer:

13819

Step-by-step explanation:

The biggest number is :9740

The smallest number is :4079

Sum means addition so...

9470 + 4079 = 13819

m/HCB = 60°, m/DCB = 9x-1, and m/DCH = 2x+ 16. Find x​

Answers

Answer:

[tex]x=11[/tex]

Step-by-step explanation:

Note that ∠DCB is the sum of ∠HCB and ∠DCH. Hence:

[tex]m\angle DCB = m\angle HCB + m\angle DCH[/tex]

Substitute in the appropriate values/expressions:

[tex](9x-1) = (60) + (2x+16)[/tex]

Solve for x. Combine like terms:

[tex]9x - 1 = 2x + 76[/tex]

Subtract 2x from both sides:

[tex]7x - 1 = 76[/tex]

Add one to both sides:

[tex]7x = 77[/tex]

And divide. Hence:

[tex]x=11[/tex]

Answer:

x=11

Step-by-step explanation:

<DCB = <DCH + < HCB

9x-1 = 2x+16 + 60

Combine like terms

9x-1 = 2x+76

Subtract 2x from each side

9x-1-2x= 2x+76-2x

7x-1 = 76

Add 1 to each side

7x-1 +1 = 76+1

7x = 77

Divide by 7

7x/7 = 77/7

x=11

Round 2.12747677748 to the nearest ten-thousandth.

Answers

Answer:

2.1275 is 2.12747677748 rounded to the nearest ten-thousandth.

Step-by-step explanation:

Since the hundred-thousandth place is 5 or above, we would round the ten-thousandths place up. THis makes the number 2.1275.

given: y=8-3x find the slope and y intercept

Answers

Answer:

Step-by-step explanation:

y = mx + b

"m" is slope ; "b" is y-intercept.

~~~~~~~

y = - 3x + 8

m = - 3

b = 8

PLEASE HELP IT IS DUE IN TWO HOURS AND I CANT UNDERSTAND IT PLSSSSSS

Answers

Answer:

The distance from Tre’s house to Owen’s house is 10 miles.

The distance from Owen’s house to Alejandro’s house is 14 miles.

The distance from Alejandro’s house to the beach is about 10.77 miles.

The total distance of the trip to the beach is about 33.53 miles

Step-by-step explanation:



5 x 1/4
how can you use addition to show that your answer is correct?​

Answers

Answer:

Step-by-step explanation:

[tex]5*\dfrac{1}{4}=\dfrac{5}{4}\\[/tex]

Using addition,

Add (1/4) , five times

[tex]\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1+1+1+1+1}{4}\\\\=\dfrac{5}{4}[/tex]

Answer:

5/4

Step-by-step explanation:

Add 1/4 together 5 times:

1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/4

Laura brought some fish; salt water ($2 each) and fresh water ($1 each). If she has 15 fish and the total was $23 - how many of each fish did she buy?

Answers

Answer:

8 salt water

7 fresh water

Step-by-step explanation:

Let's represent salt water fish with the variable "s" and fresh water fish with the variable "f".

We can make a system of equations - one equation for the number of fish and the other for the price of the fish.

We know that the total number of fish Laura has is 15, and the total price of the fish was $23.

s + f = 15 2s + f = 23

Solve the system of equations by subtracting the bottom equation from the top equation.

-s =-8s = 8

Laura bought 8 salt water fish. Since the total number of fish is 15, the number of fresh water fish must be 7.

Answer:

8  

7

Step-by-step explanation:

Let the number of fresh water be: - x

Number of salt fishes be 15 - x

x + 2 (15 - x) = 23

x + 30 - 2x = 23

x = 7

Number of fresh water fish bought: -7

Number of salt water fish bought by: -15 -7 = 8

Correct answer gets brainliest and 5 stars

Answers

Answer:

10 units

Does the answer help you?

Answer:

there is 10 units between LAnd M

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side a. Find the area of the signal board, using Heron’s formula.If its perimeter is 180 cm, what will be the area of the signal board?​

Answers

Answer:

[tex]900\sqrt{3}\:\mathrm{cm^2}\text{ or }\approx 1,558.85\:\mathrm{cm^2}[/tex]

Step-by-step explanation:

Heron's formula can be used to find the area of any triangle and is given by:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are three sides of the triangle and [tex]s[/tex] is the semi-perimeter ([tex]s=\frac{a+b+c}{2}[/tex]).

By definition, all three sides and angles of an equilateral triangle are equal. Therefore, if the total perimeter is 180 cm, each side must have a length of [tex]180\div 3=60\text{ cm}[/tex].

The semi-perimeter is therefore:

[tex]s=\frac{60+60+60}{2}=90\text{ cm}[/tex]

Substitute values into Heron's formula to get:

[tex]A=\sqrt{90(90-60)(90-60)(90-60)},\\A=\sqrt{90\cdot 30\cdot30\cdot 30},\\A=\sqrt{2,430,000},\\A=\boxed{900\sqrt{3} \:\mathrm{cm^2}}\approx \boxed{1,558.85\:\mathrm{cm^2}}[/tex]

What is the distance from the plane

Answers

Answer:

here's the answer to your question about

(18x²+11x+1) divided by (x+2)​

Answers

Answer:

It's not divisible

Step-by-step explanation:

18x²+11x+1

= 18x²+9x+2x+1

= (9x+1)(2x+1)

So, you see there's no terms (x+2) so it's not divisible

Although if you simplify it, it'll look like,

18x+51/(x+2)-25

So you can't remove the (x+2)

2x-3=5
(x+2)(3x-15)=0

Answers

Answer:

the first one gat to be x=4

Answer: 17

Step-by-step explanation: :)

factorise 1000a^2+27b^2​

Answers

1000a+27b with 2 on top of the number

There are 3 red marbles and 2 black marbles in a bag. What is the probability of drawing a black marble from the bag two times in a row if the marbles are replaced after each draw?

Answers

Answer:

4/25

Step-by-step explanation:

3 red marbles and 2 black marbles in a bag = 5 marbles

P(black) = black/total = 2/5

Replace marble

3 red marbles and 2 black marbles in a bag = 5 marbles

P(black) = black/total = 2/5

P(black, replace, black) = 2/5 * 2/5 = 4/25

At the mall you spent a total of $170.86. You bought 2 pairs pf jeans for $39.95 each, a jacket for
$45.99, and shirts for $14.99 each. How many shirts did you buy?


Answers

Answer:

3

Step-by-step explanation:

Total Money Spent = $170.86

Cost of each jeans = $39.95x2 = 79.9

Cost of each Jacket  = $45.99

Cost of each shirt = $14.99

=79.9 + 45.99

=125.89

=170.86 - 125.89

=44.97

=44.97 / 14.99

=3

Answer From Gauth Math

3 1/2 + (-5 2/3 ) ÷ ( 1 3/4)²

Answers

1 191/294 ≅ 1.6496599
1 55/192 or 247/192 or 1.286

Follow order of BEDMAS. Converting fractions into decimals may help, just make sure you add the remainder.

Simplify 4x (2x−y) − 3x (x-2y) −2x + 1 and find its value for = -1 and y = 2.

Answers

Answer:

Step-by-step explanation:

4x*(2x - y) - 3x(x - 2y) - 2x + 1  

Use distributive property

= 4x*2x - 4x*y -3x *x - (-3x) * 2y - 2x +1

= 8x² - 4xy - 3x² + 6xy - 2x + 1

= 8x² - 3x² - 4xy + 6xy - 2x + 1

Combine like terms

= 5x² + 2xy - 2x + 1

Substitute  x = -1  & y = 2

= 5(-1)² + 2*(-1)*2 - 2(-1) + 1

= 5*1 - 4 + 2 + 1

= 5 - 4 + 2 + 1

= 4

1. Match the letter of the centre to the lines that define it.
A Orthocentre
B. Incentre
C. Centroid
D. Circumcentre
median
altitude
perpendicular bisector
angle bisector

Answers

Answer:

A. (Orthocenter) → Altitude

B. (Incenter) → Angle bisector

C. (Centroid) → Median

D. (Circumcenter) → Perpendicular bisector

Step-by-step explanation:

A. The orthocenter is the point of concurrency of the three altitudes of a triangle, therefore, the matching line with the letter A is altitude

B. The incenter is the point of concurrency of the bisectors of three interior angles of a triangle, therefore, the matching line with the letter B is angle bisector

C. The centroid is the point of concurrency of the three medians of the triangle, therefore, the matching line to the letter C is median

D. The circumcenter is the point of concurrency of the three perpendicular bisectors of the three sides of a triangle, therefore, the matching line to the letter D (which corresponds with the circumcenter) is perpendicular bisector.

kx - c = 9 solve for x

Answers

Answer:

x = [tex]\frac{9+c}{k}[/tex]

Step-by-step explanation:

Given

kx - c = 9 ( add c to both sides )

kx = 9 + c ( isolate x by dividing both sides by k )

x = [tex]\frac{9+c}{k}[/tex]

you start by isolating the variable by dividing each side by factors that don’t contain the variables
therefore your answer would be x = 9/k + c/k

How many degrees are in 25n/18?

Answers

Answer:

250°

There are 250°

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