Answer: Volume of the cylinder is 75π or 235.62 cm³
Volume of cylinder =πr²h
where r is radius and h is height.
Here given radius = 5 and height = 3
Using the formula: πr²h
: π * 5² * 3
: π * 5 * 5 * 3
: 75π or 235.62 cm³
I believe there’s 52 weeks in a year besides leap year so it would be 52 divided by 2 times 10 and you’d have your answer
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The question is missing. Here is the complete question.
Let y = ![\left[\begin{array}{ccc}2\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
and u = ![\left[\begin{array}{ccc}7\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
. Write y as the sum of a vector in Span(u) and a vector orthogonal to u.
Answer: y = ![\left[\begin{array}{ccc}\frac{21}{10} \\ \frac{3}{10} \end{array}\right] + \left[\begin{array}{ccc}\frac{-1}{10}\\ \frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%20%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B-1%7D%7B10%7D%5C%5C%20%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation: The sum of vectors is given by
y = 
+ z
where is in Span(u);
vector z is orthogonal to it;
First you have to compute the orthogonal projection of y:
= proj y = 
Calculating orthogonal projection:
![\left[\begin{array}{c}2\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
.![\left[\begin{array}{c}7\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D7%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{c}9\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
. = ![\left[\begin{array}{c}49\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D49%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
![y_{1} = \frac{3}{10}.\left[\begin{array}{c}7\\1\end{array}\right]](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%20%5Cfrac%7B3%7D%7B10%7D.%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D7%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
![y_{1} = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right]](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Calculating vector z:
z = y -
z = ![\left[\begin{array}{c}2\\6\end{array}\right] - \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C6%5Cend%7Barray%7D%5Cright%5D%20-%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
z = ![\left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-1%7D%7B10%7D%20%5C%5C%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Writing y as the sum:
![y = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right] + \left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-1%7D%7B10%7D%20%5C%5C%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
