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2 years ago

QUESTION 2

Mathematics

2 answers:

iragen [17]2 years ago

4 0

Answer:

✓2=1.41421

✓5=2.23607

✓8=2.82842

✓11=3.31662

✓14=3.74166

Step-by-step explanation:

Therefore the numbers are increasing by three so they cant be perfect square

Misha Larkins [42]2 years ago

3 0

9514 1404 393

Answer:

squares are of the form 3n or 3n+1; the sequence is of the form 3n-1, so none of the sequence will be a square

Step-by-step explanation:

The given arithmetic sequence has first term 2 and common difference 3, so its explicit formula is ...

an = 2 +3(n -1) = 3n -1 . . . . for counting numbers n

All integers are of one of these forms: 3n-1, 3n, 3n+1, for some integer n. The squares of these are ...

(3n -1)² = 9n² -6n +1 = 3(3n² -2) +1 = 3k+1 for some k

(3n)² = 3(3n²) = 3k for some k

(3n +1)² = 9n² +6n +1 = 3(3n² +2) +1 = 3k+1 for some k

Note that none of these squares is of the form 3n -1.

Hence, the square of an integer cannot be in the given sequence.

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How many times larger is 2 x 1012 than 5 x 106?

vfiekz [6]

Answer: It is 3.81886792453 times larger

Step-by-step explanation: 2 x 1012 is 2024

5 x 106 is 530

so take 2024 and divide it by 530 and you get 3.81886792453

in case you were wondering this rounds to 3.82

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muminat

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Step-by-step explanation:

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2 years ago

Find the value of x such that 365 based seven + 43 based x = 217 based 10.

Pepsi [2]

We need to find the base x in the following equation:

$365_7+43_x=217_{10}$

First, lets convert 365 from base 7 to base 10. This is given by

$365_7=3\times7^2+6\times7^1+5\times7^0$

where the upperindex denotes the position of eah number. This gives

$\begin{gathered} 365_7=3\times49+6\times7+5\times1 \\ 365_7=147+42+5 \\ 365_7=194_{10} \end{gathered}$

that is, 365 based 7 is equal to 194 bases 10.

Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:

$43_x=4\times x^1+3\times x^0$

where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives

$43_x=(4x+3)_{10}$

Now, we have all number in base 10. Then, our first equation can be written in base 10 as

$194_{10}+(4x+3)_{10}=217_{10}$

For simplicity, we can omit the 10 and get

$194+4x+3=217$

so, we can solve this equation for x. By combining similar terms. we have

$197+4x=217$

and by moving 197 to the right hand side, we obtain

$\begin{gathered} 4x=217-197 \\ 4x=20 \end{gathered}$

Finally, we get

$\begin{gathered} x=\frac{20}{4} \\ x=5 \end{gathered}$

Therefore, the solution is x=5

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