HURRY I DONT HAVE TIME ( I WILL GIVE 50 POINTS )

1 answer:

4 0

John just hired a new employee to work in your bakeshop. In one day, the employee burned 150
chocolate chip cookies out of 1,000 cookies made. What percent of the day's production, did
John's new employee burn?
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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

8 0

2 years ago

Mind explaining anyone?

8090 [49]

Do 45/225 and simplify and that’s your answer

7 0

2 years ago

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Use the table to determine the average rate of change from 3 to 6 storms

skelet666 [1.2K]

Answer:

Step-by-step explanation: