A) division cause you divide 12 and -6
Hope it helps.
Answer:
D
Step-by-step explanation:
11/3 = 3.66
so it must be D
Answer:
45 pound plate = 4
10 pound plate = 8
Step-by-step explanation:
x = 45 pound plate
y = 10 pound plate
x + y = 12 - - - (1)
45x + 10y = 260 - - (2)
x = 12 - y
45(12 - y) + 10y = 260
540 - 45y + 10y = 260
540 - 35y = 260
-35y = 260 - 540
-35y = - 280
y = 280 / 35
y = 8
x = 12 - y
x = 12 - 8
x = 4
Formula for Riemann Sum is:
![\frac{b-a}{n} \sum_{i=1}^n f(a + i \frac{b-a}{n})](https://tex.z-dn.net/?f=%5Cfrac%7Bb-a%7D%7Bn%7D%20%5Csum_%7Bi%3D1%7D%5En%20f%28a%20%2B%20i%20%5Cfrac%7Bb-a%7D%7Bn%7D%29)
interval is [1,3] so a = 1, b = 3
f(x) = 3x , sub into Riemann sum
![\frac{2}{n} \sum_{i=1}^n 3(1 + \frac{2i}{n})](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bn%7D%20%5Csum_%7Bi%3D1%7D%5En%203%281%20%2B%20%5Cfrac%7B2i%7D%7Bn%7D%29)
Continue by simplifying using properties of summations.
![= \frac{2}{n}\sum_{i=1}^n 3 + \frac{2}{n}\sum_{i=1}^n \frac{6i}{n} \\ \\ = \frac{6}{n}\sum_{i=1}^n 1 + \frac{12}{n^2}\sum_{i=1}^n i \\ \\ =\frac{6}{n} (n) + \frac{12}{n^2}(\frac{n(n+1)}{2}) \\ \\ =6+\frac{6}{n}(n+1) \\ \\ =12 + \frac{6}{n}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5En%203%20%2B%20%20%5Cfrac%7B2%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5En%20%5Cfrac%7B6i%7D%7Bn%7D%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B6%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5En%201%20%2B%20%20%5Cfrac%7B12%7D%7Bn%5E2%7D%5Csum_%7Bi%3D1%7D%5En%20i%20%5C%5C%20%20%5C%5C%20%3D%5Cfrac%7B6%7D%7Bn%7D%20%28n%29%20%2B%20%5Cfrac%7B12%7D%7Bn%5E2%7D%28%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%29%20%5C%5C%20%20%5C%5C%20%3D6%2B%5Cfrac%7B6%7D%7Bn%7D%28n%2B1%29%20%5C%5C%20%20%5C%5C%20%3D12%20%2B%20%5Cfrac%7B6%7D%7Bn%7D%20)
Now you have an expression for the summation in terms of 'n'.
Next, take the limit as n-> infinity.
The limit of
![\frac{6}{n}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7Bn%7D)
goes to 0, therefore the limit of the summation is 12.
The area under the curve from [1,3] is equal to limit of summation which is 12.