Average is the sum divideided by the number of numbers added together
so avarage of 3 number is 15 means
three numbers represented as x+y+z so
= 15
(x+y+z)/3=15
multiply both sides by 3 to clear fraction
x+y+z=45
45 is the sum of the 3 numbesr
double of that is
45 times 2=90
Formula for Riemann Sum is:
interval is [1,3] so a = 1, b = 3
f(x) = 3x , sub into Riemann sum
Continue by simplifying using properties of summations.
Now you have an expression for the summation in terms of 'n'.
Next, take the limit as n-> infinity.
The limit of
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.
Answer:
feldspar, because it has a higher number then gypsum and apatite, and it can be scratched by quartz because it has a lower number.
1. 58,072
2. 16,926
Hope this helps you!
I think it might be, 29.58 but I'm not entirely sure.