For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:
![\displaystyle 2\pi \int_0^5 (5-x)(x^2+2)\,\mathrm dx=2\pi\int_0^5 (10-2x+5x^2-x^3)\,\mathrm dx=\boxed{\frac{925\pi}6}](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5Cpi%20%5Cint_0%5E5%20%285-x%29%28x%5E2%2B2%29%5C%2C%5Cmathrm%20dx%3D2%5Cpi%5Cint_0%5E5%20%2810-2x%2B5x%5E2-x%5E3%29%5C%2C%5Cmathrm%20dx%3D%5Cboxed%7B%5Cfrac%7B925%5Cpi%7D6%7D)
Answer: ok boomer :3
Step-by-step explanation:
Answer: c. 0.0778
Step-by-step explanation:
Let X is the number of non-authentic names in her sample with parameter :
n= 5 and p=40% = 0.40
Binomial probability distribution, the probability of getting success in x trials :-
![P(X=x)=^nC_xp^x(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%3D%5EnC_xp%5Ex%281-p%29%5E%7Bn-x%7D)
We have ,
![P(X=0)=^{5}C_0(0.40)^0(1-0.40)^{5}\\\\=(1)(0.60)^{5}\\\\=0.07776\approx0.0778](https://tex.z-dn.net/?f=P%28X%3D0%29%3D%5E%7B5%7DC_0%280.40%29%5E0%281-0.40%29%5E%7B5%7D%5C%5C%5C%5C%3D%281%29%280.60%29%5E%7B5%7D%5C%5C%5C%5C%3D0.07776%5Capprox0.0778)
Thus , the correct answer is option c. 0.0778
Answer:
<em>see</em><em> </em><em>explanation</em>
Step-by-step explanation:
f(x)= -2(x²+8x+16)-5
![-2 {x}^{2} - 16x - 32 - 5 \\ f(x)= - 2 {x}^{2} - 16x - 37](https://tex.z-dn.net/?f=%20-2%20%7Bx%7D%5E%7B2%7D%20%20-%2016x%20-%2032%20-%205%20%5C%5C%20%20f%28x%29%3D%20-%202%20%7Bx%7D%5E%7B2%7D%20%20-%2016x%20-%2037)
Answer:
a
Step-by-step explanation: