What is the area of this trapezoid? units 2
2 answers:
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Answer:
a₁ = - 24
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₇ = 2a₅ , then
a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )
- a₁ - 2d = 0 → (1)
The sum to n terms of an AP is
=
[ 2a₁ + (n - 1)d ]
Given = 84 , then
(2a₁ + 6d) = 84
3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )
2a₁ + 6d = 24 → (2)
Thus we have 2 equations
- a₁ - 2d = 0 → (1)
2a₁ + 6d = 24 → (2)
Multiplying (1) by 3 and adding to (2) will eliminate d
- 3a₁ - 6d = 0 → (3)
Add (2) and (3) term by term to eliminate d
- a₁ = 24 ( multiply both sides by - 1 )
a₁ = - 24
First of all, find a program or a calculator that will give you the answer. Then you'll know how to make your table. I recommend Desmos. I have inserted the final graph for you.
Make up a table for this graph. Put the lowest point as the central entry in your graph.
x y
-4
-3
-2
-1
0
Now fill in the y values.
x y
-4 1
-3 -3.5
-2 -5
-1 -3.5
0 1
You can use the outline of the parabola and then mark the outline with the points in the table.
Make up a table for this graph. Put the lowest point as the central entry in your graph.
x y
-4
-3
-2
-1
0
Now fill in the y values.
x y
-4 1
-3 -3.5
-2 -5
-1 -3.5
0 1
You can use the outline of the parabola and then mark the outline with the points in the table.