Let u = (1,2), v = (−3,4), and w = (5,0)
1 answer:
Answer:
w-2u-v
Step-by-step explanation:
Given are three vectors u, v and w.
In R^2 we treat first element as x coordinate and 2nd element as y coordinate.
Thus we mark (1,2) in the I quadrant, (-3,4) in II quadrant and (5,0) on positive x axis 5 units form the origin.
b)
We have to find the values of a and b
]
Equate the corresponding terms
Divide II equation by 2 to get
Eliminate a
-5 = 5b: b=-1
a=-2
Hence
w = 2u-v
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Answer:
(-5, 0) ∪ (5, ∞)
Step-by-step explanation:
I find a graph convenient for this purpose. (See below)
__
When you want to find where a function is increasing or decreasing, you want to look at the sign of the derivative. Here, the derivative is ...
f'(x) = 4x^3 -100x = 4x(x^2 -25) = 4x(x +5)(x -5)
This has zeros at x=-5, x=0, and x=5. The sign of the derivative will be positive when 0 or 2 factors have negative signs. The signs change at the zeros. So, the intervals of f' having a positive sign are (-5, 0) and (5, ∞).
