Answer:
Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.
If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.
Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.
Reorder 2 cos (2y) and sin (2y)
= sin (2y)(2 cos(2y))
Remove parenthesis
= sin (2y) * 2 cos (2y)
Reorder sin (2y) and 2
= 2 * sin (2y) cos (2y)
Apply the sine double-angle identity
= sin (2(2y))
Now multiply 2 by 2
<u>= sin (4y) </u>
Let the number of green apples bought be x
Green apples = x
Red apples = 2x
Yellow apples = 1/3 (2x) = 2/3 x
Total = 22 apples
x + 2x + 2/3 x = 22
11/3 x = 22
11x = 66
x = 6
Green apples = x = 6
Red apples = 2x = 2(6) = 12
Yellow apples = 2/3 (2x) = 2/3 (6) = 4
Answer: Green = 6, Red = 12, Yellow = 4
Answer:
7/10
Step-by-step explanation:
3/10+2/5
You have to make like denominators
So you multiply 2/5 by 2 since 1/ is the common denominator.
Then you add them
Hope this helped
