You just convert it into a fraction , decimal or precent from the given number given to you .Hope this helps!
Answer:
![\large\boxed{\int\left(1+\dfrac{4}{3x-1}+\dfrac{3}{x+2}\right)\ dx=x+\dfrac{4}{3}\ln(3x-1)+3\ln(x+2)}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cint%5Cleft%281%2B%5Cdfrac%7B4%7D%7B3x-1%7D%2B%5Cdfrac%7B3%7D%7Bx%2B2%7D%5Cright%29%5C%20dx%3Dx%2B%5Cdfrac%7B4%7D%7B3%7D%5Cln%283x-1%29%2B3%5Cln%28x%2B2%29%7D)
Step-by-step explanation:
![\large{\int}\normal\left(1+\dfrac{4}{3x-1}+\dfrac{3}{x+2}\right)\ dx=\int1\ dx+\int\dfrac{4}{3x-1}\ dx+\int\dfrac{3}{x+2}\ dx\\\\(1)\int1\ dx=x\\\\(2)\int\dfrac{4}{3x-1}\ dx\Rightarrow\left|\begin{array}{ccc}3x-1=t\\3dx=dt\\dx=\frac{1}{3}dt\end{array}\right|\Rightarrow\int\dfrac{4}{3t}\ dt=\dfrac{4}{3}\int\dfrac{1}{t}\ dt=\dfrac{4}{3}\ln(t)=\dfrac{4}{3}\ln(3x-1)\\\\(3)\int\dfrac{3}{x+2}\ dx\Rightarrow\left|\begin{array}{ccc}x+2=u\\dx=du\end{array}\right|\Rightarrow\int\dfrac{3}{t}\ dt=3\int\dfrac{1}{t}\ dt=3\ln(t)=3\ln(x+2)](https://tex.z-dn.net/?f=%5Clarge%7B%5Cint%7D%5Cnormal%5Cleft%281%2B%5Cdfrac%7B4%7D%7B3x-1%7D%2B%5Cdfrac%7B3%7D%7Bx%2B2%7D%5Cright%29%5C%20dx%3D%5Cint1%5C%20dx%2B%5Cint%5Cdfrac%7B4%7D%7B3x-1%7D%5C%20dx%2B%5Cint%5Cdfrac%7B3%7D%7Bx%2B2%7D%5C%20dx%5C%5C%5C%5C%281%29%5Cint1%5C%20dx%3Dx%5C%5C%5C%5C%282%29%5Cint%5Cdfrac%7B4%7D%7B3x-1%7D%5C%20dx%5CRightarrow%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D3x-1%3Dt%5C%5C3dx%3Ddt%5C%5Cdx%3D%5Cfrac%7B1%7D%7B3%7Ddt%5Cend%7Barray%7D%5Cright%7C%5CRightarrow%5Cint%5Cdfrac%7B4%7D%7B3t%7D%5C%20dt%3D%5Cdfrac%7B4%7D%7B3%7D%5Cint%5Cdfrac%7B1%7D%7Bt%7D%5C%20dt%3D%5Cdfrac%7B4%7D%7B3%7D%5Cln%28t%29%3D%5Cdfrac%7B4%7D%7B3%7D%5Cln%283x-1%29%5C%5C%5C%5C%283%29%5Cint%5Cdfrac%7B3%7D%7Bx%2B2%7D%5C%20dx%5CRightarrow%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7Dx%2B2%3Du%5C%5Cdx%3Ddu%5Cend%7Barray%7D%5Cright%7C%5CRightarrow%5Cint%5Cdfrac%7B3%7D%7Bt%7D%5C%20dt%3D3%5Cint%5Cdfrac%7B1%7D%7Bt%7D%5C%20dt%3D3%5Cln%28t%29%3D3%5Cln%28x%2B2%29)
![\Downarrow\\\\\int\left(1+\dfrac{4}{3x-1}+\dfrac{3}{x+2}\right)\ dx=x+\dfrac{4}{3}\ln(3x-1)+3\ln(x+2)](https://tex.z-dn.net/?f=%5CDownarrow%5C%5C%5C%5C%5Cint%5Cleft%281%2B%5Cdfrac%7B4%7D%7B3x-1%7D%2B%5Cdfrac%7B3%7D%7Bx%2B2%7D%5Cright%29%5C%20dx%3Dx%2B%5Cdfrac%7B4%7D%7B3%7D%5Cln%283x-1%29%2B3%5Cln%28x%2B2%29)
1) To calculate maximum of f(t) function we first need to find derivative of it:
f(t)' = 10(e^(-t/8) + t*e^(-t/8)*(-1/8)) = 10(e^(-t/8) -t/8*e^(-t/8)) = 10e^(-t/8)(1-t/8)
the condition is:
f(t)' = 0 that means:
0 = 10e^(-t/8)(1-t/8)
10t/8*e*(-t/8) = 10*e^(-t/8)
t/8 = 1
t = 8
The answer is 8 days.
2) that percent we will get simply by expressing t=8 in our equation.
f(8) = 10*8*e^(-1) = 80/e = 29.43%
You did all of them wornv but i ciuld help you
Answer:
0.18
Step-by-step explanation:
Find the probability that both independent events occur by multiplying the individual probabilities by each other:
0.2(0.9)
= 0.18
So, the probability is 0.18