5^11 + 5^10
------------------- =
5^10 - 5^8
48,828,125 + 5^10
-------------------------- =
5^10 - 5^8
48,828,125 + 9,765,625
--------------------------------- =
5^10 - 5^8
48,828,125 + 9,765,625
----------------------------------- =
9,765,625 - 5^8
48,828,125 + 9,765,625
--------------------------------- =
9,765,625 - 390,625
58,593,750
------------------------------ =
9,765,625 - 390,625
58,593,750
------------------ =
9,375,000
answer: 6.25
![\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}\\\\ -----------------------------\\\\ \textit{so, let's find the missing side} \\\\\\ c=\sqrt{2.7^2+3.4^2-2(2.7)(3.4)cos(40^o)} \\\\\\ c=\sqrt{4.78542402433556327368}\implies c\approx 2.187561204706182220](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BLaw%20of%20Cosines%7D%5C%5C%20%5Cquad%20%5C%5C%0Ac%5E2%20%3D%20%7B%7B%20a%7D%7D%5E2%2B%7B%7B%20b%7D%7D%5E2-%282%7B%7B%20a%7D%7D%7B%7B%20b%7D%7D%29cos%28C%29%5Cimplies%20%0Ac%20%3D%20%5Csqrt%7B%7B%7B%20a%7D%7D%5E2%2B%7B%7B%20b%7D%7D%5E2-%282%7B%7B%20a%7D%7D%7B%7B%20b%7D%7D%29cos%28C%29%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bso%2C%20let%27s%20find%20the%20missing%20side%7D%0A%5C%5C%5C%5C%5C%5C%0Ac%3D%5Csqrt%7B2.7%5E2%2B3.4%5E2-2%282.7%29%283.4%29cos%2840%5Eo%29%7D%0A%5C%5C%5C%5C%5C%5C%0Ac%3D%5Csqrt%7B4.78542402433556327368%7D%5Cimplies%20c%5Capprox%202.187561204706182220)
or we can round it, to say c = 2.19, so hmm that's the missing side
now, we use Heron's Formula, which uses all 3 sides only
![\bf \textit{Heron's Area Formula}\\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} a=2.7\\ b=3.4\\ c\approx 2.19\\\\ s=\cfrac{a+b+c}{2} \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BHeron%27s%20Area%20Formula%7D%5C%5C%5C%5C%0AA%3D%5Csqrt%7Bs%28s-a%29%28s-b%29%28s-c%29%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Aa%3D2.7%5C%5C%0Ab%3D3.4%5C%5C%0Ac%5Capprox%202.19%5C%5C%5C%5C%0As%3D%5Ccfrac%7Ba%2Bb%2Bc%7D%7B2%7D%0A%5Cend%7Bcases%7D)
and that'd be the area of it
I think that you have wrong u-substitution ( partial integration ):
![\int {u} \, dv= uv- \int {v} \, du](https://tex.z-dn.net/?f=%20%5Cint%20%7Bu%7D%20%5C%2C%20dv%3D%20uv-%20%5Cint%20%7Bv%7D%20%5C%2C%20du%20%20)
u=x, dv=cos 5x dx
du=dx, v=1/5 * sin 5x
Integral becomes:
Is it OK now?
Answer:
Blue (the first)
Step-by-step explanation:
The answer would be -8, idk of the picture will show. hope this helped.