1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
swat32
3 years ago
7

A 1x1 square and an n-tiling is a group of n tiles placed so that every tile is contiguous along at least one side to another ti

le. (The tiles cannot be offset. That is, they must be placed into a grid like Scrabble tiles.) The edge length of a tiling is the total length of edges that are not touching other tiles. For instance, a 20-tiling, the edge length is 36.
Required:
Prove that for all n-tilings where n >= 1, the edge length is even.
Mathematics
1 answer:
bixtya [17]3 years ago
6 0

Answer:

Step-by-step explanation:

The first picture below shows the missing image in the question.

There are 4 edges of each tile;

This clearly explains to us that the total number of edges present in the n tiles is 4n.

Now, if a tile "X" touches and comes in contact with another tile "Y", then edges touching each other are one edge of a tile X and one edge of a tile Y.

From the second diagram below, the edge, X_2, and Y_4 are touching each other.

Now, the total number of edges that touch some edges is always even.

We can now say that:

The edge length of filling = No. of edges that do not touch another file

= Total no. of edges  -  No. of edges that touch another edge.

However, the total number of edges is even.

The number of edges that touch another edge is also even.

Thus, the difference is also even and the number of edges that do not touch another is even.

So, the edge length of filling is always even.

You might be interested in
What two nonnegative real numbers with a sum of 64 have the largest possible product?
Otrada [13]

The two non negative real numbers with a sum of 64 that have the largest possible​ product are; 32 and 32.

<h3>How do we solve the nonnegative real numbers?</h3>

Let the two numbers be x and y.

Thus, if their sum is 64, then we have;

x + y = 64

y = 64 - x

Their product will be;

P = xy

Putting (64 - x) for y in the product equation we have;

P = (64 - x)x

P = 64x - x²

Since the product is maximum, let us find the derivative;

P'(x) = 64 - 2x

At P'(x) = 0, we have;

64 - 2x = 0

2x = 64

x = 64/2

x = 32

Thus; y = 64 - 32

y = 32

Read more about nonnegative real numbers

brainly.com/question/9580755

#SPJ4

6 0
1 year ago
The sum of the measures of angle 4,7, and _____ is equal to 180
8_murik_8 [283]
7 I think because if you would put a zero behind the 4 and 7 and add them together it will be 110 and all that's left if u subtract them from 180 is 70 (7)
6 0
3 years ago
Three multiplied by the sum of 4 and a number is the same as 18 more than the number. Find the number.
arsen [322]
3(4+n)=18+n
distribute
12+3n=18+n
minus n both sides
12+2n=18
minus 12 both sides
2n=6
divide by 2
n=3

the number is 3
equation is
3(4+n)=18+n
6 0
3 years ago
Car A is currently traveling 8 miles per hour slower than Car B. If Car A is currently traveling at a speed of 58 mile per hour,
garri49 [273]
58 + 8 = 66 miles per hour
3 0
3 years ago
Daisy Hill has saved $5,000 for her first semester of college. She plans to
Katarina [22]

Amount Daisy plans to spend on food is $625

Step-by-step explanation:

  • Step 1: Given total savings of Daisy = $5000. Find the amount spent by Daisy on her room

Amount spent on room = 3/4 of 5000 = 3/4 × 5000 = $3750

  • Step 2: Calculate the remaining amount.

Remaining amount = $5000 - $3750 = $1250

  • Step 3: Calculate the amount Daisy plans to spend on food

Amount to be spend on food = 1/2 of 1250 = 1/2 × 1250 = $625

5 0
3 years ago
Read 2 more answers
Other questions:
  • 5(y5x4+1) simplify please answer now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    10·1 answer
  • I don't understand this Help please!!
    13·1 answer
  • Complete the ratio table to convert the units of measure from ounces to grams or grams to ounces.
    6·1 answer
  • Given two objects represented by the tuples (7, 21, 8, 28) and (19, 64, 3, 12): (a)Compute the Euclidean distance between the tw
    14·1 answer
  • if the body makes 100 billion new blood cells each day,approximately how many blood cells can it make each hour
    15·2 answers
  • How do I solve this word problem?
    9·1 answer
  • 50 × 8000 = 4 × 10^ what is the unknown exponent
    15·2 answers
  • Identify the vertex of the function, f(x) = 3(x - 1)² + 5.​
    5·1 answer
  • 1
    6·1 answer
  • A cube has a surface area of 96 square inches. If 16 cubes are combined to make a rectangular prism, what is the volume of the r
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!