Need help with this math that I don’t know

Mathematics

2 answers:

denis23 [38]2 years ago

6 0

Answer:

$129.00

Step-by-step explanation:

First, we find out the area of the window

(2+6)/2 =4

4*1.5= 6 ft ^2

6*21.5= $129.00

FromTheMoon [43]2 years ago

5 0

Answer:

6 sqft × $21.5 = $129

Step-by-step explanation:

Area of a trapezoid is just average the top and bottom 2 + 6 = 8÷2 = 4 the times this by the height. So toss out those 2.5 sides (the not-parallel sides) we don't need them; we don't care about them. Use the straight up and down height measurement.

4 × 1.5

= 6 ft^2

Then times by 21.50 to find the cost. 6×21.5=129

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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

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

so our sum becomes

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

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