The farmers wife baked 9 pies on Monday and 5 on Tuesday. How many more pies did she bake on Monday?
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Hi there!
Our interval is from 0 to 3, with 6 intervals. Thus:
3 ÷ 6 = 0.5, which is our width for each rectangle.
Since n = 6 and we are doing a right-riemann sum, the points we will be plugging in are:
0.5, 1, 1.5, 2, 2.5, 3
Evaluate:
(0.5 · f(0.5)) + (0.5 · f(1)) + (0.5 · f(1.5)) + (0.5 · f(2)) + (0.5 · f(2.5)) + (0.5 · f(3)) =
Simplify:
0.5( -2.75 + (-3) + (-.75) + 4 + 11.25 + 21) = 14.875
We must find the area of each cake's top.
Formula for area of a circle:
where r is the radius.
<span>small cake:
</span>Plug in 4 for r because the radius is 4. (They give us the diameter, which is 8, and the radius is half that)
A = 16π
<span>big cake:
</span>Repeat the process:
Plug in 12 for r because the radius is 12. (They give us the diameter, which is 24, and the radius is half that)
A = 144π
So our two radii are 144π and 16π.
The large cake's top is not 3 times the area of the small cake's.
This makes sense because you are squaring the radius, which makes the fact that the larger cake's diameter is triple the smaller cake diameter irrelevant.
Hope this helped! ^-^
Formula for area of a circle:
<span>small cake:
</span>Plug in 4 for r because the radius is 4. (They give us the diameter, which is 8, and the radius is half that)
A = 16π
<span>big cake:
</span>Repeat the process:
Plug in 12 for r because the radius is 12. (They give us the diameter, which is 24, and the radius is half that)
A = 144π
So our two radii are 144π and 16π.
The large cake's top is not 3 times the area of the small cake's.
This makes sense because you are squaring the radius, which makes the fact that the larger cake's diameter is triple the smaller cake diameter irrelevant.
Hope this helped! ^-^