Answer:
Step-by-step explanation:
![f(x)=\frac{1}{\sqrt{x} }\\f'(x)=-\frac{1}{2} x^{-\frac{3}{2}}\\\\f'(4)=-\frac{1}{2} 4^{-\frac{3}{2} }=-\frac{1}{2} \frac{1}{4^\frac{3}{2} } \\=-\frac{1}{2} *\frac{1}{8}=-\frac{1}{16} \\when x=4\\y=f(x)=\frac{1}{\sqrt{4} } =\frac{1}{2} \\\\eq.~ of ~tangent ~line~is\\y=-\frac{1}{2} -\frac{1}{16} (x-4)](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%7D%20%7D%5C%5Cf%27%28x%29%3D-%5Cfrac%7B1%7D%7B2%7D%20x%5E%7B-%5Cfrac%7B3%7D%7B2%7D%7D%5C%5C%5C%5Cf%27%284%29%3D-%5Cfrac%7B1%7D%7B2%7D%204%5E%7B-%5Cfrac%7B3%7D%7B2%7D%20%7D%3D-%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7B1%7D%7B4%5E%5Cfrac%7B3%7D%7B2%7D%20%7D%20%5C%5C%3D-%5Cfrac%7B1%7D%7B2%7D%20%2A%5Cfrac%7B1%7D%7B8%7D%3D-%5Cfrac%7B1%7D%7B16%7D%20%20%5C%5Cwhen%20x%3D4%5C%5Cy%3Df%28x%29%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B4%7D%20%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%5C%5Ceq.~%20of%20~tangent%20~line~is%5C%5Cy%3D-%5Cfrac%7B1%7D%7B2%7D%20-%5Cfrac%7B1%7D%7B16%7D%20%28x-4%29)
We presume your cost function is
c(p) = 124p/((10 +p)(100 -p))
This can be rewritten as
c(p) = (124/11)*(10/(100 -p) -1/(10 +p))
The average value of this function over the interval [50, 55] is given by the integral
![\frac{1}{55-50} \times \frac{-124}{11} \int\limits^{55}_{50} {(\frac{1}{x+10}+\frac{10}{x-100})} \, dx](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B55-50%7D%20%5Ctimes%20%5Cfrac%7B-124%7D%7B11%7D%20%5Cint%5Climits%5E%7B55%7D_%7B50%7D%20%7B%28%5Cfrac%7B1%7D%7Bx%2B10%7D%2B%5Cfrac%7B10%7D%7Bx-100%7D%29%7D%20%5C%2C%20dx)
This evaluates to
(-124/55)*(ln(65/60)+10ln(45/50)) ≈ 2.19494
The average cost of removal of 50-55% of pollutants is about
$2.19 hundred thousand = $219,000
Answer:
B : -2
Step-by-step explanation:
![3(2) \div ( - 3) \\ 6 \div ( - 3) \\ - 2](https://tex.z-dn.net/?f=3%282%29%20%5Cdiv%20%28%20-%203%29%20%5C%5C%206%20%5Cdiv%20%28%20-%203%29%20%5C%5C%20%20-%202)