Log798 What is equivalent to it
2 answers:
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Answer:
The correct answer is:
d)
Step-by-step explanation:
The given question is regarding polynomial division.
Please find the attached file for the explanation.
Polynomial division gives:
Quotient:
Remainder: 3
Answer:
C
Step-by-step explanation:
The right triangle on the right side of the figure has a height of 6 (two same sides lengths) and a base of 3.
x is the hypotenuse (side opposite of 90 degree angle).
We can use the pythagorean theorem to find x. The pythagorean theorem tells us to square each leg (height and base) of the triangle and add it. It should be equal to the hypotenuse square.
For this triangle it means, we square 6 and 3 and add it. It should be equal to x squared. Then we can solve. Shown below:
<em>Now we can use property of radical to simplify:</em>
Correct answer is C
The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule . The next number would then be fourth power of 7 plus 1, or 2402.
And the harder way: Denote the <em>n</em>-th term in this sequence by , and denote the given sequence by
.
Let denote the <em>n</em>-th term in the sequence of forward differences of
, defined by
for <em>n</em> ≥ 1. That is, is the sequence with
and so on.
Next, let denote the <em>n</em>-th term of the differences of
, i.e. for <em>n</em> ≥ 1,
so that
etc.
Again: let denote the <em>n</em>-th difference of
:
etc.
One more time: let denote the <em>n</em>-th difference of
:
etc.
The fact that these last differences are constant is a good sign that for all <em>n</em> ≥ 1. Assuming this, we would see that
is an arithmetic sequence given recursively by
and we can easily find the explicit rule:
and so on, up to
Use the same strategy to find a closed form for , then for
, and finally
.
and so on, up to
Recall the formula for the sum of consecutive integers:
and so on, up to
Recall the formula for the sum of squares of consecutive integers: