If you'd graph this function, you'd see that it's positive on [-1.5,0], and that it's possible to inscribe 3 rectangles on the intervals [-1.5,-1), (-1,-0.5), (-0.5, 1].
The width of each rect. is 1/2.
The heights of the 3 inscribed rect. are {-2.25+6, -1+6, -.25+6} = {3.75,5,5.75}.
The areas of these 3 inscribed rect. are (1/2)*{3.75,5,5.75}, which come out to:
{1.875, 2.5, 2.875}
Add these three areas together; you sum will represent the approx. area under the given curve on the given interval: 1.875+2.5+2.875 = ?
Answer:
Step-by-step explanation:
<h3>Given</h3>
<u>Quadratic function </u>
with the roots:
<h3>To find </h3>
<h3>Solution</h3>
<u>As we know the sum of the roots is -b/a and the product of the roots is c/a. Substituting values and solving for b and c:</u>
- (-5 + 9i) + (-5 - 9i) = -b/-1
- -10 = b
- b = -10
And
- (-5 + 9i)(-5 - 9i) = c/-1
- (-5)² - (9i)² = -c
- 25 - 81(-1) = -c
- - c = 25 + 81
- - c = 106
- c = -106
g(x) = -x² -10x - 106
The first one is 9/25
The second one is 29.44
The last one is 8
so, what we do is, we multiply the value by a power of 10, that moves the recurring numbers to the left of the dot, in this case we want moved the "15", so we'll need two zeros, so we'll be using 100.
![\bf 0.151515\overline{15}~\hspace{7em}x=0.151515\overline{15} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{array}{|lll|ll} \cline{1-3} &&\\ 100\cdot x&=&15.1515\overline{15}\\ &&15+0.1515\overline{15}\\ &&15+x \\&&\\ \cline{1-3} \end{array}\implies 100x=15+x \\\\\\ 99x=15\implies x=\cfrac{15}{99}\implies \stackrel{simplified}{x=\cfrac{5}{33}}](https://tex.z-dn.net/?f=%5Cbf%200.151515%5Coverline%7B15%7D~%5Chspace%7B7em%7Dx%3D0.151515%5Coverline%7B15%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Clll%7Cll%7D%20%5Ccline%7B1-3%7D%20%26%26%5C%5C%20100%5Ccdot%20x%26%3D%2615.1515%5Coverline%7B15%7D%5C%5C%20%26%2615%2B0.1515%5Coverline%7B15%7D%5C%5C%20%26%2615%2Bx%20%5C%5C%26%26%5C%5C%20%5Ccline%7B1-3%7D%20%5Cend%7Barray%7D%5Cimplies%20100x%3D15%2Bx%20%5C%5C%5C%5C%5C%5C%2099x%3D15%5Cimplies%20x%3D%5Ccfrac%7B15%7D%7B99%7D%5Cimplies%20%5Cstackrel%7Bsimplified%7D%7Bx%3D%5Ccfrac%7B5%7D%7B33%7D%7D)
