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Stella [2.4K]
2 years ago
8

What are the possible values of remainder r, when a positive integer 'a' is divided by 3​

Mathematics
1 answer:
fredd [130]2 years ago
6 0

Answer:

0, 1, 2

Step-by-step explanation:

Euclid's division Lemma states that for any two positive integers ‘a’ and ‘b’ there exist two unique whole numbers ‘q’ and ‘r’ such that , a = bq + r, where 0≤ r < b.

Here, a= Dividend, b= Divisor, q= quotient and r = Remainder.

According to Euclid's division lemma a 3q+r, where 0≤r≤3 and r is an integer.

Therefore, the values of r can be 0, 1 or 2.

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Estimate √53 between two numbers to the tenths place.
ZanzabumX [31]

Answer:

  53 lies between 7.2² and 7.3²

Step-by-step explanation:

Estimating a root to the nearest tenth can be done a number of ways. The method shown here is to identify the tenths whose squares bracket the value of interest.

You have answered the questions of parts 1 to 3.

__

<h3>4.</h3>

You are given that ...

  7.2² = 51.84

  7.3² = 53.29

This means 53 lies between 7.2² and 7.3², so √53 lies between 7.2 and 7.3.

53 is closer to 7.3², so √53 will be closer to 7.3 than to 7.2.

7.3 is a good estimate of √53 to the tenths place.

_____

<em>Additional comment</em>

For an integer n that is the sum of a perfect square (s²) and a remainder (r), the square root is between ...

  s +r/(2s+1) < √n < s +r/(2s)

For n = 53 = 7² +4, this means ...

  7 +4/15 < √53 < 7 +4/14

  7.267 < √53 < 7.286

Either way, √53 ≈ 7.3.

__

The root is actually equal to the continued fraction ...

  \sqrt{n}=\sqrt{s^2+r}=s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}

7 0
2 years ago
QUESTION: Josephine put a frame round his picture which measured 36 cm by 34 cm. A margin 4cm wide was left all the way round. W
Mandarinka [93]
36x34= 1224cm²
(36-4)x(34-4)= 32x30= 960cm²

Area of frame= 1224
Area of picture inside frame= 960
So border = 1224-960= 264

ANSWER = 264cm²
5 0
3 years ago
Help❗️❗️❗️❗️❗️The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132 units.
yarga [219]

Answer:

The answer is D.

Step-by-step explanation:

She forgot to find the square root of 7225.

4 0
3 years ago
Read 2 more answers
Pint 16oz $3.98
LiRa [457]
Okay, so when dealing with unit rates you want to see how much you have of your main measurement. In this case your main measurement is ounces. Since you have 16 and 32 you are going to divide your dollar amount by those and round to the nearest tenth. 
Here are the equations that need to be used. Figure out the answers to them and round. This will give you your answer
3.98/16=
5.98/32=
4 0
3 years ago
F (n)=3+4 (n-1). find f(5) and f(6)
Rasek [7]
3+16=19,

3+20=23

So the correct answer would be 19 and 23
5 0
3 years ago
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