How many squares are there in n x3 array with n >=5
Question 15: There are seven squares in the picture. How many triangles than squares are there in the picture?
không có hình à bạn?
in the figure, eight doves each are perching in one of the sixteen squares of the arry.At least how many doves need to move from where they are to new squares (not necessarily adjacent to the original squares) so that there are just two doves on each row, each column
thiếu đề bài
dịch thì dịch thế này
Trong hình này, có 8 con chim bồ câu nằm trên một trong mười sáu ô vuông. Ít nhất có bao nhiêu con chim bồ câu cần phải di chuyển từ nơi chúng đến những ô vuông mới (không nhất thiết phải cạnh những ô vuông ban đầu) sao cho chỉ có hai chim bồ câu Trên mỗi hàng, mỗi cột
Fill in the gap with “How much or How many”
1. ___________ beer is there in the fridge?
2. ___________ eggs do you want?
3. ___________ languages do you speak?
4. ___________ people are there in the class?
5. ___________ days are there in a week?
6. ___________ milk do you drink everyday?
7. ___________ kilos of rice do you want?
8. ___________ soda does she want?
9. We don’t have ___________ bananas, and we don’t have ___________ fruit juice.
10. How _____________ is this? It’s ten dollars.
11. How _________________ do you want? Six, please.
12. I wrote _________________ poems.
13. I visited _____________________ European cities.
14. She hasn’t got _________________ patience.
15. How ________ does the shirt cost ?
1. How much
2. How many
3. How many
4. How many
5. How many
6. How much
7. How many
8. How much
9. many/ much
10. much
11. many
12. many
13. many
14. much
15. much
1. How much beer is there in the fridge?
2. How many eggs do you want?
3. How many languages do you speak?
4. How many people are there in the class?5. How many days are there in a week?
6. How much milk do you drink everyday?
7. How many kilos of rice do you want?
8. How much soda does she want?'
9. We don't have much bananas, and we don't have much fruit juice.( câu này hơi lạ =))
10. How much is this? It's ten dollars.
11. How many do you want? Six, please.
12. I wrote much poems.
13. I visited many European cities.
14. She hasn't got much patience.
15. How much does the shirt cost?
How many boxes are crossed by a diagonal in a rectangular table formed by 199 x 991 small squares?
Another alternative explanation.
Mark the leftmost square crossed of each row as ‘r’, and the topmost crossed square of each column with ‘c’. Thus, each square can be marked either ‘r’ or ‘c’ or ‘both r and c’ or ‘neither r nor c’. We’ll examine each case.
For a square to be marked both ‘r’ and ‘c’, the diagonal must pass through the upper left corner of the square.
For square to be marked ‘r’, diagonal should pass through its upper edge.
For square to be marked ‘c’, diagonal must pass through its left edge.
For square to be marked neither ‘r’ nor ‘c’, diagonal must pass through it’s upper as well as left edge, which is not possible. Therefore, no triangles are unmarked.
Now, no. of squares crossed = no. of squares marked ‘r’ + no. of squares marked ‘c’ - no. of squares marked both ‘r’ and ‘c’
Now, no. of r’s = no. of rows (only 1 leftmost crossed square in each row)
no. of c’s = no. of columns (only 1 topmost crossed square in each column)
all rows and columns are crossed by the diagonal.
Therefore, squares crossed = rows + columns - (no. of squares marked both ‘r’ and ‘c’)
Now, only 1 square is marked both ‘r’ and ‘c’ as 199 and 991 are coprime.
Therefore squares crossed = 199 + 991 - 1 = 1189
Look at this video if you want a clearer visual explanation:
How many boxes are crossed by a diagonal in a rectangular table formed by 199 x 991 small squares?
Tham khảo:
Another alternative explanation.
Mark the leftmost square crossed of each row as ‘r’, and the topmost crossed square of each column with ‘c’. Thus, each square can be marked either ‘r’ or ‘c’ or ‘both r and c’ or ‘neither r nor c’. We’ll examine each case.
For a square to be marked both ‘r’ and ‘c’, the diagonal must pass through the upper left corner of the square.
For square to be marked ‘r’, diagonal should pass through its upper edge.
For square to be marked ‘c’, diagonal must pass through its left edge.
For square to be marked neither ‘r’ nor ‘c’, diagonal must pass through it’s upper as well as left edge, which is not possible. Therefore, no triangles are unmarked.
Now, no. of squares crossed = no. of squares marked ‘r’ + no. of squares marked ‘c’ - no. of squares marked both ‘r’ and ‘c’
Now, no. of r’s = no. of rows (only 1 leftmost crossed square in each row)
no. of c’s = no. of columns (only 1 topmost crossed square in each column)
all rows and columns are crossed by the diagonal.
Therefore, squares crossed = rows + columns - (no. of squares marked both ‘r’ and ‘c’)
Now, only 1 square is marked both ‘r’ and ‘c’ as 199 and 991 are coprime.
Therefore squares crossed = 199 + 991 - 1 = 1189
For a rectangle of size m×nm×n with sizes being coprime:
when a diagonal leaves the starting corner, it goes through the first square;and before it reaches the opposite corner it crosses n−1n−1, say, horizontal lines of the grid, and m−1m−1 vertical lines, each time entering a new square.So the diagonal visits m+n−1m+n−1 unit squares.
For sizes not coprime let d=gcd(m,n)d=gcd(m,n). Then we can reduce the problem to dd rectangles of size md×ndmd×nd which makes a result of
d⋅(md+nd−1)=m+n−dd⋅(md+nd−1)=m+n−d=m+n−gcd(m,n)=m+n−gcd(m,n)
And we can see, that the former result is a special case of the latter: the 'minus one' term is a 'minus GCD of sizes', since a GCD of coprime numbers is 11.
Chúc bạn học tốt nhớ cho mình 1 like nhé !
Fill in the blanks with "How much" or "How many"
1. _____cheese do you buy ?
2. _____books are there in your bag ?
3. _____people are there in this classroom ?
4._____time is there to the end for the lesson ?
5._____milk does your son drink every day ?
1 How much
2 How many
3 How many
4 How much
5 How much
-Much đi với N không đếm được
-Many đi với N đếm được
fill each blank with how many or how much
1...................apples are there in the fridge?
2....................pepper do you want?
3......................bananas are there on the table?
4......................sandwiches are there in your bag?
5...................water is there in the bottle?
1..How many.................apples are there in the fridge?
2...How much................pepper do you want?
3....How many..................bananas are there on the table?
4...How many...................sandwiches are there in your bag?
5.....How much..............water is there in the bottle?
1. How many apples are there in the fridge?
2. How much pepper do you want?
3. How many bananas are there on the table?
4. How many sandwiches are there in your bag?
5. How much water is there in the bottle?
fill each blank with how many or how much
1......How many .............apples are there in the fridge?
2.......How much .............pepper do you want?
3.....How many .................bananas are there on the table?
4..........How many ............sandwiches are there in your bag?
5...........How much ........water is there in the bottle?
USE IT! Work in groups. Look at Wassily Kandinsky’s painting Squares with Concentric Circles. Choose two squares in the painting and say how the colours in each square are related. Which square do you like best and why?
Tham khảo:
A: (Square 3) Red and yellow are harmonious colors. Red and blue are complementary colors. I like square 5 because it looks impressive. It reminds me of my eyes.
B: (Square 9) Blue and green are harmonious colors. Green and red are complementary colors. I like square 9 because it looks like harmony and peace. It reminds me of images of the earth or a forest around the lake.
Trả lời các câu hỏi
1 What's your name's ?
2 How do you spell your name ?
3 Where are you from ?
4 Where are you live ?
5 How many chairs are there in your house ?
6 Do you want to be friend with me
7 How many people are there in your house ?
8 What do you do after playing with your friends
1 My name is Alice Zuberg
2 A - L - I - C - E
3 I come from SAO alicization
4 I live in Rulid village
5 there are five chair in my house
6 No , I to be alone
7 there are four
8 I come back home and do my homework
Okay, i will answer:
1 My name is Nguyen Le Huy ( but my friends only call me Huy )
2 H - U - Y
3 I'm from VietNam
4 I'm live in HaNoi
5 i have a lot of chairs in my house
6 No, cause i don't know who are you,......bruh
7 there are 8 people.
8 i come to my room do my homework
thanks for asking me, stranger. XD
1. My name is Khanh Linh.
2.L-I-N-H.
3.I'm from VietNam.
4. I'm live in Phu Tho town.
5. There are twenty- six chairs in my house.
6. Uhhh no , because I don't known who are you ?
7. There are 9 people in my house.
8. I and my friend are doing to homework, listening to the music and playing badminton.
Thank for watching, thanks for asking me.