X=1/30
Reduce 6/9 to 2/3, take 2/3 from both sides, then subtract the fractions
When you multiply two complex numbers given in polar form, the argument of the product is the sum of the arguments of the factors. Meanwhile, the modulus of the product is the product of the moduli of the factors.
In this case, you'd have
and the modulus would simply be
. Since
we would expect the final product to fall in the first quadrant.
Answer:
see explanation
Step-by-step explanation:
(a)
Given
2k - 6k² + 4k³ ← factor out 2k from each term
= 2k(1 - 3k + 2k²)
To factor the quadratic
Consider the factors of the product of the constant term ( 1) and the coefficient of the k² term (+ 2) which sum to give the coefficient of the k- term (- 3)
The factors are - 1 and - 2
Use these factors to split the k- term
1 - k - 2k + 2k² ( factor the first/second and third/fourth terms )
1(1 - k) - 2k(1 - k) ← factor out (1 - k) from each term
= (1 - k)(1 - 2k)
1 - 3k + 2k² = (1 - k)(1 - 2k) and
2k - 6k² + 4k³ = 2k(1 - k)(1 - 2k)
(b)
Given
2ax - 4ay + 3bx - 6by ( factor the first/second and third/fourth terms )
= 2a(x - 2y) + 3b(x - 2y) ← factor out (x - 2y) from each term
= (x - 2y)(2a + 3b)
When a question is asking you for the y-intercept based on a graph, all you have to do is look to see at what point does the function cross/intersect the y-axis. The x-value will always be zero in a y-intercept. By looking at the graph you see that the function crosses the y-axis at the point (0, -1), which is your answer.
Answer: (0, -1)
