As you increase the subintervals the area will be closer and closer to the real value. In other words your approximation gets better.
As you increase the intervals, there will be more rectanagles and the added area of these rectangles are converging towards the actual area under the curve.
You can write both numbers as fractions:
Dividing by a fraction is the same as multiplying by its inverse, so we have
We can cross-simplify the 10's and we have
1+68
2+67
3+66
4+65
5+64
6+63
7+62
8+61
9+60
Step-by-step explanation:
parallelogram area is:h×base
10×14=140
we have two so
140×2=280
traingle is:h×base/2
18-10=8=h
8×14/2=56
56×3=168
168+280=448
Solve for x in -7x - 8y = 9
x = -9 + 8y/7
Substitute x = -9 + 8y/7 into -4x + 9y = -22
4(9 + 8y)/7 + 9y = -22
Solve for y in 4(9 + 8y)/7 + 9y = -22
y = -2
Substitute y = -2 into x = -9 + 8y/7
x = 1
Thus,
<u>x = 1</u>
<u>y = -2</u>
