Answer:
The volume of the hemisphere is 496741.6 m³
Step-by-step explanation:
The volume of an sphere is given by:
![V_{s} = \frac{4\pi r^{3}}{3}](https://tex.z-dn.net/?f=V_%7Bs%7D%20%3D%20%5Cfrac%7B4%5Cpi%20r%5E%7B3%7D%7D%7B3%7D)
In which
and r is the radius.
An hemisphere is half of an sphere, so it's volume is half the sphere's volume. So
![V_{h} = \frac{V_{s}}{2} = \frac{2\pi r^{3}}{3}](https://tex.z-dn.net/?f=V_%7Bh%7D%20%3D%20%5Cfrac%7BV_%7Bs%7D%7D%7B2%7D%20%3D%20%5Cfrac%7B2%5Cpi%20r%5E%7B3%7D%7D%7B3%7D)
In this question:
. So
![V_{h} = \frac{2\pi (61.9)^{3}}{3} = 496741.6](https://tex.z-dn.net/?f=V_%7Bh%7D%20%3D%20%5Cfrac%7B2%5Cpi%20%2861.9%29%5E%7B3%7D%7D%7B3%7D%20%3D%20496741.6)
The volume of the hemisphere is 496741.6 m³
Answer:
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Solution of the given system of equations
x = 3 and y= 2
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given system of equations are
4x - y = 10 ...(i)
8x +5y = 34...(ii)
The matrix form
A X = B
![\left[\begin{array}{ccc}4&-1\\8&5\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}10\\34\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%26-1%5C%5C8%265%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%5C%5C34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Step(ii):-</em></u>
<u><em>By using matrix inversion method</em></u>
<u><em></em></u>
<u><em></em></u>
<u><em></em></u>
|A| = ad-b c = 4(5) - 8(-1) = 20+8 = 28
Given matrix
![A = \left[\begin{array}{ccc}4&-1\\8&5\\\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%26-1%5C%5C8%265%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![AdjA = \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=AdjA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![A djA = \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]](https://tex.z-dn.net/?f=A%20djA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Inverse of the matrix
<u><em></em></u>
![A^{-1} = \frac{1}{|A|} A djA =\frac{1}{28} \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7B%7CA%7C%7D%20A%20djA%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Step(iii)</em></u>:-
The solution of the given system of equations by using matrix inversion method
X = A⁻¹ B
![X = A^{-1}B =\frac{1}{28} \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]\left[\begin{array}{ccc}10\\34\\\end{array}\right]](https://tex.z-dn.net/?f=X%20%3D%20A%5E%7B-1%7DB%20%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%5C%5C34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![X = A^{-1}B =\frac{1}{28} \left[\begin{array}{ccc}5X10+1X34\\-8X10+4X34\\\end{array}\right]](https://tex.z-dn.net/?f=X%20%3D%20A%5E%7B-1%7DB%20%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5X10%2B1X34%5C%5C-8X10%2B4X34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] =\frac{1}{28} \left[\begin{array}{ccc}84\\56\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D84%5C%5C56%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Final answer</em></u>:-
Solution of the given system x = 3 and y= 2
Answer:
hi
Step-by-step explanation:
The answer is just 24.3 miles.
The questions asked "How long was the ride from Kiley's house to the airport?"
The first sentence of the problem reads "They drove 24.3 miles from their house to the airport in an hour". The rest of the information isn't necessary to find this answer.