Answer:
<30,-20>
Step-by-step explanation:
4u + 2v
4< 6,-4> + 2< 3,-2>
<24,-16> + < 6,-4>
<30,-20>
We can rewrite the expression under the radical as
then taking the fourth root, we get
Why the absolute value? It's for the same reason that
since both and return the same number , and captures both possibilities. From here, we have
The absolute values disappear on all but the term because all of , and are positive, while could potentially be negative. So we end up with
Answer:
1. Vertex: (4,26)
X-intercept: (9.09,0)(-1.09)
2. Vertex: (-4,-6)
X-intercept: (-1.55,0)(-6.44,0)
Step-by-step explanation:
The rate of change of the size of the diagonal is; 25.2 ft/s
By Pythagoras theorem;
The length, l of a diagonal of a rectangle whose sides have lengths x and y is;
In essence; the length of the diagonal is dependent on the length, x and y of the sides.
Therefore;
(dl/dt)² = (dx/dt)² + (dy/dt)²
where;
- (dx/dt) = 19 ft/s
- (dy/dt) = -15 ft/s
Therefore,
(dl/dt)² = 19² + (-15)²
(dl/dt)² = 361 + 225
dl/dt = √586
dl/dt = 25.2
Therefore, the size of the diagonal is changing at a rate of; 25.2 ft/s.
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