The solution for l4 is mathematically given as
L_{4}=0.5431
<h3>What is the solution for l4?</h3>
![&\text { Given } f(x)=a \cos ^{2}(x) \quad\left[\frac{\pi}{8}, \frac{\pi}{2}\right] \text { \& } n=4\\\\&\Delta a=\frac{b-a}{n}=\frac{\pi / 2-\pi / 8}{9}=\frac{3 \pi}{32}\\\\&x_{0}=\pi / 8, x_{1}=\frac{\pi}{8}+\frac{3 \pi}{32}=\frac{7 \pi}{32}\\\\&x_{2}=\frac{5 \pi}{16}, \quad x_{3}=\frac{13 \pi}{32}, x_{4}=\pi / 2\\\\&f\left(x_{0}\right)=f(1 / 8)=0.8535\\](https://tex.z-dn.net/?f=%26%5Ctext%20%7B%20Given%20%7D%20f%28x%29%3Da%20%5Ccos%20%5E%7B2%7D%28x%29%20%5Cquad%5Cleft%5B%5Cfrac%7B%5Cpi%7D%7B8%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cright%5D%20%5Ctext%20%7B%20%5C%26%20%7D%20n%3D4%5C%5C%5C%5C%26%5CDelta%20a%3D%5Cfrac%7Bb-a%7D%7Bn%7D%3D%5Cfrac%7B%5Cpi%20%2F%202-%5Cpi%20%2F%208%7D%7B9%7D%3D%5Cfrac%7B3%20%5Cpi%7D%7B32%7D%5C%5C%5C%5C%26x_%7B0%7D%3D%5Cpi%20%2F%208%2C%20x_%7B1%7D%3D%5Cfrac%7B%5Cpi%7D%7B8%7D%2B%5Cfrac%7B3%20%5Cpi%7D%7B32%7D%3D%5Cfrac%7B7%20%5Cpi%7D%7B32%7D%5C%5C%5C%5C%26x_%7B2%7D%3D%5Cfrac%7B5%20%5Cpi%7D%7B16%7D%2C%20%5Cquad%20x_%7B3%7D%3D%5Cfrac%7B13%20%5Cpi%7D%7B32%7D%2C%20x_%7B4%7D%3D%5Cpi%20%2F%202%5C%5C%5C%5C%26f%5Cleft%28x_%7B0%7D%5Cright%29%3Df%281%20%2F%208%29%3D0.8535%5C%5C)
![&f\left(x_{1}\right)=f\left(\frac{7 \pi}{32}\right)=0.5975\\\\\&f\left(x_{2}\right)=f\left(\frac{5 \pi}{16}\right)=0.3086\\\\\&f\left(a_{3}\right)=f\left(\frac{13 \pi}{32}\right)=0.0842\\\\\&L_{4}=\sum_{k_{0}^{=0}}^{3} f\left(x_{k}\right) \Delta x\\\\&=\Delta \\\\x\left[f\left(x_{0}\right)+f\left(x_{1}\right)+f\left(x_{2}\right)+f\left(x_{3}\right)\right]\\\\\&=\frac{3 \pi}{32}[0.8535+0.5975+0.3056+0.0842]\\\\&L_{4}=0.5431](https://tex.z-dn.net/?f=%26f%5Cleft%28x_%7B1%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B7%20%5Cpi%7D%7B32%7D%5Cright%29%3D0.5975%5C%5C%5C%5C%5C%26f%5Cleft%28x_%7B2%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B5%20%5Cpi%7D%7B16%7D%5Cright%29%3D0.3086%5C%5C%5C%5C%5C%26f%5Cleft%28a_%7B3%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B13%20%5Cpi%7D%7B32%7D%5Cright%29%3D0.0842%5C%5C%5C%5C%5C%26L_%7B4%7D%3D%5Csum_%7Bk_%7B0%7D%5E%7B%3D0%7D%7D%5E%7B3%7D%20f%5Cleft%28x_%7Bk%7D%5Cright%29%20%5CDelta%20x%5C%5C%5C%5C%26%3D%5CDelta%20%5C%5C%5C%5Cx%5Cleft%5Bf%5Cleft%28x_%7B0%7D%5Cright%29%2Bf%5Cleft%28x_%7B1%7D%5Cright%29%2Bf%5Cleft%28x_%7B2%7D%5Cright%29%2Bf%5Cleft%28x_%7B3%7D%5Cright%29%5Cright%5D%5C%5C%5C%5C%5C%26%3D%5Cfrac%7B3%20%5Cpi%7D%7B32%7D%5B0.8535%2B0.5975%2B0.3056%2B0.0842%5D%5C%5C%5C%5C%26L_%7B4%7D%3D0.5431)
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The complete Question is attached below
Answer:
A
Step-by-step explanation:
BECAUSE THERE IS ONLI ONE VARIABLE
Answer: 8.75$
Step-by-step explanation: to find the answer to this problem, you would divide his total amount of cash earned by the number of hours he worked to see how the cash is split between each hour. By doing this, you should get 8.75$ and hour.