Answer:
k = 96
Step-by-step explanation:
![f(x) = x\sqrt{(6 -x^{2}) } \\\\ = x(6 - x^{2})^{\frac{1}{2} }](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5Csqrt%7B%286%20-x%5E%7B2%7D%29%20%7D%20%5C%5C%5C%5C%20%3D%20x%286%20-%20x%5E%7B2%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
![V = \int\limits^2_ {-2}\pi (f(x))^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} (f(x))^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} (x(6 - x^{2})^{\frac{1}{2} })^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} x^{2}(6 - x^{2}) \, dx \\\\ = \pi \int\limits^2_{-2} 6x^{2} - x^{4} \, dx \\\\ = \pi [\frac{6x^{3} }{3} -\frac{x^{5}}{5} ]\limits^2_{-2} \\\\ = \pi [(2(2)^{3}-\frac{(2)^{5}}{5})-(2(-2)^{3} - \frac{(-2)^{-5}}{5}) ] \\\\ = \pi[(16 - \frac{32}{5}) - (-16-(-\frac{32}{5}))] \\\\ = \pi[\frac{48}{5} - (-\frac{48}{5})]](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%5Climits%5E2_%20%7B-2%7D%5Cpi%20%28f%28x%29%29%5E%7B2%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%20%3D%20%5Cpi%20%5Cint%5Climits%5E2_%20%7B-2%7D%20%28f%28x%29%29%5E%7B2%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%20%3D%20%5Cpi%20%5Cint%5Climits%5E2_%20%7B-2%7D%20%28x%286%20-%20x%5E%7B2%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B2%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%20%3D%20%5Cpi%20%5Cint%5Climits%5E2_%20%7B-2%7D%20x%5E%7B2%7D%286%20-%20x%5E%7B2%7D%29%20%5C%2C%20dx%20%5C%5C%5C%5C%20%3D%20%5Cpi%20%5Cint%5Climits%5E2_%7B-2%7D%206x%5E%7B2%7D%20-%20x%5E%7B4%7D%20%20%5C%2C%20dx%20%5C%5C%5C%5C%20%3D%20%5Cpi%20%5B%5Cfrac%7B6x%5E%7B3%7D%20%7D%7B3%7D%20-%5Cfrac%7Bx%5E%7B5%7D%7D%7B5%7D%20%5D%5Climits%5E2_%7B-2%7D%20%5C%5C%5C%5C%20%3D%20%5Cpi%20%5B%282%282%29%5E%7B3%7D-%5Cfrac%7B%282%29%5E%7B5%7D%7D%7B5%7D%29-%282%28-2%29%5E%7B3%7D%20-%20%5Cfrac%7B%28-2%29%5E%7B-5%7D%7D%7B5%7D%29%20%5D%20%5C%5C%5C%5C%20%3D%20%5Cpi%5B%2816%20-%20%5Cfrac%7B32%7D%7B5%7D%29%20-%20%28-16-%28-%5Cfrac%7B32%7D%7B5%7D%29%29%5D%20%5C%5C%5C%5C%20%3D%20%5Cpi%5B%5Cfrac%7B48%7D%7B5%7D%20-%20%28-%5Cfrac%7B48%7D%7B5%7D%29%5D)
= π[⁴⁸/₅ + ⁴⁸/₅]
= π(⁹⁶/₅)
It’s a reflection over the x axis So the answer is C
Answer:
Step-by-step explanation:
Lands on C on 8 out of 30 times = 4/15= .26666 times
we expected to land on C using theoretical probability 1/5 =.2 times
for 1,000 times it will be expect to land on C, 200 times because,
1*200 = 200 C : 5*200 =1,000 spins
we do not expected to land on C exactly 200 times yet we expected something close to that 200 number.
Answer:
37.584
Step-by-step explanation:
Hope this helps