In order to get $5 per pound, you need a ratio of 1:2. One $9 for every two $3 will get you $5 per pound, since 9 + 3 + 3 is 15, divided by 3 pounds is $5. For 240 pounds, divide by three (since there is one $9 and two $3). This is 80 times the 3 pounds at $5.
Therefore, 1 × 80 is 80 pounds of $9 coffee, and 2 × 80 is 160 pounds if $3 coffee. which totals 240 pounds at $5 per pound.
The first one is 0,5 the second one is 1,3 last one is 2,1
The expression of integral as a limit of Riemann sums of given integral
is 4
∑
from i=1 to i=n.
Given an integral
.
We are required to express the integral as a limit of Riemann sums.
An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.
A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.
Using Riemann sums, we have :
=
∑f(a+iΔx)Δx ,here Δx=(b-a)/n
=f(x)=
⇒Δx=(5-1)/n=4/n
f(a+iΔx)=f(1+4i/n)
f(1+4i/n)=![[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}](https://tex.z-dn.net/?f=%5Bn%5E%7B2%7D%28n%2B4i%29%5D%2F2n%5E%7B3%7D%2B%28n%2B4i%29%5E%7B3%7D)
∑f(a+iΔx)Δx=
∑
=4
∑
Hence the expression of integral as a limit of Riemann sums of given integral
is 4
∑
from i=1 to i=n.
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