The result of the division of polynomial <em>3.23 + 8x2 + 9x + 10</em> by <em>x + 2</em> is; 3x² + 2x +5
<h3>Long division of polynomials</h3>
According to the question given;
- The result of the long division of polynomials can be evaluated as in the attached image.
By observation of the procedures in the attached image, we may conclude that the expressions (x+2) and (3x² + 2x +5) are factors of; 3x³ + 8x2 + 9x + 10
Learn more on polynomials division;
brainly.com/question/24662212
Answer:
answer is point d. circumcentre is the center of the circle inscribed inside the triangle
By de Moivre's theorem,

![\implies \sqrt[4]{(1 - i)^2} = \sqrt[4]{2}\,e^{i(2\pi k-\pi/2)/4} = \sqrt[4]{2}\,e^{i(4k-1)\pi/8}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%5B4%5D%7B%281%20-%20i%29%5E2%7D%20%3D%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi%282%5Cpi%20k-%5Cpi%2F2%29%2F4%7D%20%3D%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi%284k-1%29%5Cpi%2F8%7D)
where
. The fourth roots of
are then
![k = 0 \implies \sqrt[4]{2}\,e^{-i\pi/8}](https://tex.z-dn.net/?f=k%20%3D%200%20%5Cimplies%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7B-i%5Cpi%2F8%7D)
![k = 1 \implies \sqrt[4]{2}\,e^{i3\pi/8}](https://tex.z-dn.net/?f=k%20%3D%201%20%5Cimplies%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi3%5Cpi%2F8%7D)
![k = 2 \implies \sqrt[4]{2}\,e^{i7\pi/8}](https://tex.z-dn.net/?f=k%20%3D%202%20%5Cimplies%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi7%5Cpi%2F8%7D)
![k = 3 \implies \sqrt[4]{2}\,e^{i11\pi/8}](https://tex.z-dn.net/?f=k%20%3D%203%20%5Cimplies%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi11%5Cpi%2F8%7D)
or more simply
![\boxed{\pm\sqrt[4]{2}\,e^{-i\pi/8} \text{ and } \pm\sqrt[4]{2}\,e^{i3\pi/8}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cpm%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7B-i%5Cpi%2F8%7D%20%5Ctext%7B%20and%20%7D%20%5Cpm%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi3%5Cpi%2F8%7D%7D)
We can go on to put these in rectangular form. Recall


Then




and the roots are equivalently
![\boxed{\pm\sqrt[4]{2}\left(\sqrt{\dfrac12 + \dfrac1{2\sqrt2}} - i\sqrt{\dfrac12 - \dfrac1{2\sqrt2}}\right) \text{ and } \pm\sqrt[4]{2}\left(\sqrt{\dfrac12 + \dfrac1{2\sqrt2}} + i \sqrt{\dfrac12 - \dfrac1{2\sqrt2}}\right)}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cpm%5Csqrt%5B4%5D%7B2%7D%5Cleft%28%5Csqrt%7B%5Cdfrac12%20%2B%20%5Cdfrac1%7B2%5Csqrt2%7D%7D%20-%20i%5Csqrt%7B%5Cdfrac12%20-%20%5Cdfrac1%7B2%5Csqrt2%7D%7D%5Cright%29%20%5Ctext%7B%20and%20%7D%20%5Cpm%5Csqrt%5B4%5D%7B2%7D%5Cleft%28%5Csqrt%7B%5Cdfrac12%20%2B%20%5Cdfrac1%7B2%5Csqrt2%7D%7D%20%2B%20i%20%5Csqrt%7B%5Cdfrac12%20-%20%5Cdfrac1%7B2%5Csqrt2%7D%7D%5Cright%29%7D)
Answer:
18 feet
Step-by-step explanation:
The difference in elevations is ...
-12 -(-30) = -12 +30 = 30 -12 = 18 . . . feet
The ray is 18 feet above the whale.