If x is a positive integer, for how many different values of x is sqrt48/x a whole number?

Mathematics

1 answer:

slava [35]3 years ago

6 0

Answer:

<u>The only possible values of x that fulfill with both conditions are 3, 12 and 48.</u>

Step-by-step explanation:

1. What are the positive integers? Also know as the whole numbers or the counting numbers. They start from 1, and continue to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, etc.

2. What are the whole numbers? The definition of whole numbers is that they are the number with no fractions or decimals.

3. According to those definitions, x must be a positive integer and the result of √48/x, must be a whole number.

4. For fulfilling the first condition, x must be only a value from 1 to 48.

5. For fulfilling the second condition, the result of √48/x must be a whole number. It means it must be 1, 2, 3, 4, 5 or 6. From 7 is not possible to continue because those numbers are bigger than 48, for example √49, √64, √81, √100 and so on, and it would be impossible to fulfill with the first condition.

6. So, we have just 6 possible options (√48/x = 1, √48/x = 2, √48/x = 3, √48/x = 4, √48/x = 5 and √48/x =6). Let's review in detail one by one.

√48/x = 1, Is there any value of x for fulfilling both conditions? <u>Yes, it's. It's 48. </u>

√48/x = 1 and let's replace x by 48.

√48/48 = √1 = 1

√48/x = 2, Is there any value of x for fulfilling both conditions? <u>Yes, it's. It's 12. </u>

√48/x = 2 and let's replace x by 12.

√48/12 = √4 = 2

√48/x = 3, Is there any value of x for fulfilling both conditions? No, it isn't.

There isn't any whole number that allow us to fulfill with this: √48/x = √9 = 3

√48/x = 4, Is there any value of x for fulfilling both conditions? <u>Yes, it's. It's 3. </u>

√48/x = 4 and let's replace x by 3.

√48/3 = √16 = 4

√48/x = 5 Is there any value of x for fulfilling both conditions? No, it isn't.

There isn't any whole number that allow us to fulfill with this: √48/x = √25 = 5

√48/x =6 Is there any value of x for fulfilling both conditions? No, it isn't.

There isn't any whole number that allow us to fulfill with this: √48/x = √36 = 6.

<u>The only possible values of x that fulfill with both conditions are 3, 12 and 48.</u>

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B. What are the second and third terms of this arithmetic sequence? 80, 페, 페, 125,...........

nataly862011 [7]

The 2nd and 3rd term of an AP is found to be (a₂ = 95) and (a₃ = 110).

<h3>What is the sequence of AP arithmetic progression?</h3>

In Arithmetic Progression, the difference between the two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come across a few key concepts in AP that had been labeled as:

The first term (a)
Common difference (d)
Term nth (an)
The total of first n terms (Sn)

As shown below, the AP can also be referred to in terms of common differences.

The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × d
The arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].
Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.

Now, the given sequence is; 80, _, _, 125.

The series comprises of four given terms.

Let the first term be 'a₁' = 180.

The second term be 'a₂'.

The third term be 'a₃'.

And, the fourth term is 'a₄' = 125.

Use the nth term formula to find the common difference 'd'.

n-th term: an = a + (n − 1) × d

a₄ = a + (n - 1)d

125 = 80 + (4 - 1)d

45 = 3d

d = 15