What is the graph of the function rule? y = |3x| - 1
2 answers:
You might be interested in
Answer:
is the sum of positive integers between
(inclusive) and
(inclusive) that are not multiples of
and not multiples
.
Step-by-step explanation:
For an arithmetic series with:
as the first term,
as the last term, and
as the common difference,
there would be terms, where as the sum would be
.
Positive integers between (inclusive) and
(inclusive) include:
.
The common difference of this arithmetic series is . There would be
terms. The sum of these integers would thus be:
.
Similarly, positive integers between (inclusive) and
(inclusive) that are multiples of
include:
.
The common difference of this arithmetic series is . There would be
terms. The sum of these integers would thus be:
Positive integers between (inclusive) and
(inclusive) that are multiples of
include:
.
The common difference of this arithmetic series is . There would be
terms. The sum of these integers would thus be:
Positive integers between (inclusive) and
(inclusive) that are multiples of
(integers that are both multiples of
and multiples of
) include:
.
The common difference of this arithmetic series is . There would be
terms. The sum of these integers would thus be:
.
The requested sum will be equal to:
- the sum of all integers from
to
,
- minus the sum of all integer multiples of
between
and
, and the sum integer multiples of
between
- plus the sum of all integer multiples of
between
That is:
.
Let's find out the gradient (Slope " m ") of line q ;
Now, since we already know the gradient let's find of the equation of line by using its Slope and one of the points using point slope form of line :
Now, plug in the value of gradient ~
here we can clearly observe that, the Area under the curve can easily be represented as :
Since, all the values of y that lies in the shaded region is smaller than the actual value of y for the corresponding values of x in the equation of line q