Given :
A sequence of numbers consists of natural numbers that are
not perfect squares.
To Find :
The 1000th member of this sequence .
Solution :
Now , and .
So , there are 31 numbers before 1000 which are perfect square .
Therefore , the is 1000+31 = 1031 .
Also , the first perfect square after 1000 is 32 .
So , we have to continue to 1031 + 1 = 1032 to compensate for the 32nd square.
Therefore , the 1000th member of this sequence is 1032 .
Hence , this is the required solution .
Answer: 7.8
Step-by-step explanation:
Answer:
open
left
Step-by-step explanation:
Answer:
Step-by-step explanation:
We have the equation:
Let's simplify this a bit. Let . Then . We can substitute the exponents:
Use the properties of exponents, we can write . We can do the same thing on the right. So:
We can now factor out a from the left and a on the right. This yields:
Evaluate the expressions within the parentheses:
Evaluate:
Now, let's multiply both sides by . So:
Also, let's divide both sides by . Multiply on the right:
Therefore:
We can now substitute back u. Notice that 27 is the same as 3 cubed and 1000 is the same as 10 cubed. So:
Since they have the same base, their exponents must be equal. Therefore:
Add 2 to both sides:
So, the value of x is 5.
And we're done!