If she only had 1 hour sessions she had 8 sessions in the first week because if you do 35 times 8 you get 280.
Answer:
65°
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360 degrees.
65+115+115=295
360-295=65
Answer: 65°
<span>(x-h)^2 + (y-k)^2 = r^2
(h, k) = (-5, -1)
r = 5
</span><span>(x+5)^2 + (y+1)^2 = 5^2
</span><span>(x+5)^2 + (y+1)^2 = 25</span>
Part (a)
The radius is r = 42 because OA = 42.
The circumference, aka distance around the circle, is
C = 2*pi*r
C = 2*(22/7)*42
C = 264
We're told that arc AB is 110 mm which is 110/264 = 5/12 of the full distance around the circle.
So we'll apply 5/12 to the full rotation 360 to get (5/12)*360 = 150
<h3>
Answer: 150 degrees</h3>
==============================================================
Part (b)
Compute the area of the full circle
A = pi*r^2
A = (22/7)*(42)^2
A = 5544
Then take 5/12 of this because we only want 5/12 of the full circle area (to get the area of the shaded pizza slice)
(5/12)*(5544) = 2310
<h3>Answer: 2310 square mm</h3>
==============================================================
Side note: Both answers are approximate because pi = 22/7 is approximate.
Answer:
a) ![A=\left[\begin{array}{ccc}1&2&3\\1&-1&1\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%263%5C%5C1%26-1%261%5Cend%7Barray%7D%5Cright%5D)
![b=\left[\begin{array}{ccc}0\\1\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
b) 
c) ![A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%266%5Csqrt%7B2%7D%20%260%5C%5C%5Csqrt%7B3%7D%20%263%5Csqrt%7B3%7D%20%260%5C%5C2%26-16%260%5Cend%7Barray%7D%5Cright%5D)
![x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]](https://tex.z-dn.net/?f=x%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B1%7D%20%5C%5Cx_%7B2%7D%20%5C%5Cx_%7B3%7D%20%5Cend%7Barray%7D%5Cright%5D)
![b=\left[\begin{array}{ccc}-\sqrt{2} \\\sqrt{3} \\6\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Csqrt%7B2%7D%20%5C%5C%5Csqrt%7B3%7D%20%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
a) considering the equation:
Minimize 
(matrix A)
vector b
![b=\left[\begin{array}{ccc}0\\1\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
b) If Pxn is matrix B and p-vector d, we have:
minimize 
![Ax=\left[\begin{array}{ccc}0&-6&0\\-4&3&0\\1&8&0\end{array}\right]](https://tex.z-dn.net/?f=Ax%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-6%260%5C%5C-4%263%260%5C%5C1%268%260%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B1%7D%20%5C%5Cx_%7B2%7D%20%5C%5Cx_%7B3%7D%20%5Cend%7Barray%7D%5Cright%5D)
![b=\left[\begin{array}{ccc}-4\\1\\3\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%5C%5C1%5C%5C3%5Cend%7Barray%7D%5Cright%5D)
![Ax-b=\left[\begin{array}{ccc}-bx_{2}+4 \\-4x_{1}+3x_{2}-1 \\x_{1}+8x_{2}-3 \end{array}\right] =1](https://tex.z-dn.net/?f=Ax-b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-bx_%7B2%7D%2B4%20%5C%5C-4x_%7B1%7D%2B3x_%7B2%7D-1%20%20%5C%5Cx_%7B1%7D%2B8x_%7B2%7D-3%20%20%5Cend%7Barray%7D%5Cright%5D%20%3D1)

c) minimize 
in matrix:
![A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%266%5Csqrt%7B2%7D%20%260%5C%5C%5Csqrt%7B3%7D%20%263%5Csqrt%7B3%7D%20%260%5C%5C2%26-16%260%5Cend%7Barray%7D%5Cright%5D)
![x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]](https://tex.z-dn.net/?f=x%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B1%7D%20%5C%5Cx_%7B2%7D%20%5C%5Cx_%7B3%7D%20%5Cend%7Barray%7D%5Cright%5D)
![b=\left[\begin{array}{ccc}-\sqrt{2} \\\sqrt{3} \\6\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Csqrt%7B2%7D%20%5C%5C%5Csqrt%7B3%7D%20%5C%5C6%5Cend%7Barray%7D%5Cright%5D)