Can someone help me ‼️

Mathematics

1 answer:

vazorg [7]3 years ago

8 0

Answer:

A) 6

Step-by-step explanation:

The angle 12x is the same angle as the one below 108 degrees. They are supplementary angles so they add up to 180 degrees. 180-108 = 72, 12x = 72 divide each side by 12, x = 6 :)

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Anettt [7]

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

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

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
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so our sum becomes

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

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