<h3>Given</h3>
three numbers: a, b, c
a+b+c = 11
2a +5b +6c = 32
3a -b = 22
<h3>Find</h3>
a, b, c
<h3>Solution</h3>
The equations can be represented by the augmented matrix
![\left[\begin{array}{ccc|c}1&1&1&11\\2&5&6&32\\3&-1&0&22\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%261%2611%5C%5C2%265%266%2632%5C%5C3%26-1%260%2622%5Cend%7Barray%7D%5Cright%5D)
A graphing calculator gives the solution
(a, b, c) = (8, 2, 1)
The three numbers are 8, 2, and 1.
_____
If you want to solve this by hand, you could use Cramer's rule, or you could do the row operations by and. For example, subtract twice the first equation from the second to get
... 3b +4c = 10
Subtract 3 times the first equation from the third to get
... -4b -3c = -11
These two equations can be solved by your favorite method to find
... b = (-44 +30)/(-16 +9) = -14/-7 = 2 . . . . . using Cramer's rule
... c = (-40 +33)/-7 = 1
Then the first equation can be used to find <em>a</em>.
... a + 2 + 1 = 11
... a = 8 . . . . . . . . . . . as above
Answer:
1 or more than 1
Step-by-step explanation:
This is your answer
Answer:
Step-by-step explanation:
The length of an arc is given by θ/360×2πr, where θ is angle subtended by the arc to the center and r is the radius of the circle.
The length is 12 units, and θ/360 is 1/3
Therefore, 12 = 1/3 × 3.142 ×r
r = 12× 3/3.142
r = 11.457 units
≈ 11 units
63 two-course meals can be made.