Answer:
a) The table of values represents the ordered pairs formed by the elements of the sequence (
) (range) and their respective indexes (
) (domain):
1 6
2 11
3 16
4 21
5 26
b) The algebraic expression for the general term of the sequence is 
.
c) The 25th term in the sequence is 126.
Step-by-step explanation:
a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...
The table of values represents the ordered pairs formed by the elements of the sequence () (range) and their respective indexes () (domain):
1 6
2 11
3 16
4 21
5 26
b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:
(1)
Where:
- First element of the sequence.
- Arithmetic difference.
- Index.
If we know that 
and 
, then the algebraic expression for the general term of the sequence is:
c) If we know that and 
, then the 25th term in the sequence is:
The 25th term in the sequence is 126.
Answer:
Where are the questions....?
Answer: 3/20
Step-by-step explanation:
12/80 is simplified to 3/20
Answer:
Maximum volume = 649.519 cubic inches
Step-by-step explanation:
A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).
Volume is given by
V = 
First, we differentiate V(x) with respect to x, to get,
Equating the first derivative to zero, we get,
Solving, with the help of quadratic formula, we get,
,
Again differentiation V(x), with respect to x, we get,
At x =
,
Thus, by double derivative test, the maxima occurs at
x = for V(x).
Thus, largest volume the box can have occurs when 
.
Maximum volume =
