Split the integrand into partial fractions.
![\dfrac{9x+2}{x^2+x-6} = \dfrac{9x+2}{(x-2)(x+3)} = \dfrac a{x-2} + \dfrac b{x+3}](https://tex.z-dn.net/?f=%5Cdfrac%7B9x%2B2%7D%7Bx%5E2%2Bx-6%7D%20%3D%20%5Cdfrac%7B9x%2B2%7D%7B%28x-2%29%28x%2B3%29%7D%20%3D%20%5Cdfrac%20a%7Bx-2%7D%20%2B%20%5Cdfrac%20b%7Bx%2B3%7D)
![\implies 9x+2 = a(x+3) + b(x-2) = (a+b)x + (3a-2b)](https://tex.z-dn.net/?f=%5Cimplies%209x%2B2%20%3D%20a%28x%2B3%29%20%2B%20b%28x-2%29%20%3D%20%28a%2Bb%29x%20%2B%20%283a-2b%29)
![\implies \begin{cases}a+b=9 \\ 3a-2b=2\end{cases} \implies a=4,b=5](https://tex.z-dn.net/?f=%5Cimplies%20%5Cbegin%7Bcases%7Da%2Bb%3D9%20%5C%5C%203a-2b%3D2%5Cend%7Bcases%7D%20%5Cimplies%20a%3D4%2Cb%3D5)
Then we have
![\displaystyle \int \frac{9x+2}{x^2+x-6} \, dx = 4 \int \frac{dx}{x-2} + 5 \int \frac{dx}{x+3} \\\\ = \boxed{4\ln|x-2| + 5\ln|x+3| + C}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7B9x%2B2%7D%7Bx%5E2%2Bx-6%7D%20%5C%2C%20dx%20%3D%204%20%5Cint%20%5Cfrac%7Bdx%7D%7Bx-2%7D%20%2B%205%20%5Cint%20%5Cfrac%7Bdx%7D%7Bx%2B3%7D%20%5C%5C%5C%5C%20%3D%20%5Cboxed%7B4%5Cln%7Cx-2%7C%20%2B%205%5Cln%7Cx%2B3%7C%20%2B%20C%7D)
which follows from the result
![\displaystyle \int \frac{dx}x = \ln|x|+C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7Bdx%7Dx%20%3D%20%5Cln%7Cx%7C%2BC)
Answer:
£13,268.35 (sorry if this is incorrect :P)
Step-by-step explanation:
16.5% = 0.165
15890.23 x 0.165 ≈ 2621.88
15890.23 - 2621.88 = 13,268.35
Answer:
Step-by-step explanation:
not sure sorryyyy
Answer:
A = 160 cm²
Step-by-step explanation:
The area (A ) of a rhombus is calculated as
A = 0.5 × product of diagonals, that is
A = 0.5 × 16 × 20 = 160