Answer:
The answer is "
".
Step-by-step explanation:
please find the complete question in the attached file.
Let the sphere center be (0,0,0) and then let the intersection diameter lie all along the z-axis.
So one of the collision plans is the xz-plane the other is the path via an xz-plane angle.

All appropriate region could then be indicated in spherical coordinates

Calculating the volume:
![=\int_{0}^{\frac{\pi}{6}} \int_{0}^{\pi} \int_{0}^{a} \rho^2 \sin \phi d \rho d \phi d \theta\\\\ =\int_{0}^{\frac{\pi}{6}} d \theta \int_{0}^{\pi} \sin \phi d \int_{0}^{a} \rho^2 d \rho\\\\= [\theta]^{\frac{\pi}{6}}_{0} [-\cos \phi]^{\pi}_{0} [\frac{\rho^3}{3}]^{a}_{0}\\\\= \frac{\pi}{6} [1+1] \frac{a^3}{3}\\\\=\frac{\pi a^3}{9}](https://tex.z-dn.net/?f=%3D%5Cint_%7B0%7D%5E%7B%5Cfrac%7B%5Cpi%7D%7B6%7D%7D%20%5Cint_%7B0%7D%5E%7B%5Cpi%7D%20%5Cint_%7B0%7D%5E%7Ba%7D%20%5Crho%5E2%20%5Csin%20%5Cphi%20d%20%5Crho%20d%20%5Cphi%20d%20%5Ctheta%5C%5C%5C%5C%20%3D%5Cint_%7B0%7D%5E%7B%5Cfrac%7B%5Cpi%7D%7B6%7D%7D%20d%20%5Ctheta%20%5Cint_%7B0%7D%5E%7B%5Cpi%7D%20%5Csin%20%5Cphi%20d%20%5Cint_%7B0%7D%5E%7Ba%7D%20%5Crho%5E2%20d%20%5Crho%5C%5C%5C%5C%3D%20%5B%5Ctheta%5D%5E%7B%5Cfrac%7B%5Cpi%7D%7B6%7D%7D_%7B0%7D%20%5B-%5Ccos%20%5Cphi%5D%5E%7B%5Cpi%7D_%7B0%7D%20%5B%5Cfrac%7B%5Crho%5E3%7D%7B3%7D%5D%5E%7Ba%7D_%7B0%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%5B1%2B1%5D%20%5Cfrac%7Ba%5E3%7D%7B3%7D%5C%5C%5C%5C%3D%5Cfrac%7B%5Cpi%20a%5E3%7D%7B9%7D)
Answer:
Step-by-step explanation:use a calculator then press 4.32 divided by 12 whatever you get that is the answer
The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series
The sigma notation of the series is: 
<h3>How to write the series in sigma notation?</h3>
The series is given as:
7 + 16 + 25 +34 +43 +52 + 61
The above series is an arithmetic series, with the following parameters
- First term, a = 7
- Common difference, d = 9
- Number of terms, n = 7
Start by calculating the nth term using:
a(n) = a + (n - 1) * d
This gives
a(n) = 7 + (n - 1) * 9
Evaluate the product
a(n) = 7 - 9 + 9n
Evaluate the difference
a(n) = 9n - 2
So, the sigma notation is:

Read more about arithmetic series at:
brainly.com/question/6561461
Answer: -8
Step-by-step explanation: negative numbers are below zero in this case its 8 below zero which the keyword is below which means less than negative integers are less than zero so its -8
For a circle with center (h,k) and radius, r
the equaiton is

so
center=(5,2), radius=3
