9514 1404 393
Answer:
(-4√494)/13i +(6√494)/13k ≈ -6.8388i +0j +10.2585k
Step-by-step explanation:
To answer this question, you need to know two things:
1) the direction of vector v
2) the magnitude of vector u
__
<u>direction of v</u>
A direction is specified by a "unit vector", one with the proper ratio of components, and a magnitude of 1. It is found from a given vector by dividing that vector by its magnitude.
The unit vector in the v direction is ...
v/|v| = (-2i +3k)/(√((-2)² +3²) = (-2i +3k)/√13
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<u>magnitude of u</u>
The magnitude of vector u is ...
|u| = √(5² +(-2)² +3²) = √38
__
Then the desired vector is ...
(2|u|)(v/|v|) = 2√38(-2i+3k)/√13 = (-4√494)/13i +(6√494)/13k
_____
<em>Additional comment</em>
We have chosen to "rationalize the denominator" by writing √(38/13) as (√494)/13.
Answer:
C
Step-by-step explanation:
Answer:
Jenna sold 280 boxes, Becca sold 105 boxes.
Step-by-step explanation:
For every 3 boxes B sold, J sold 8 boxes and ended with a total of 385 boxes sold.
3b+8j=385
From how the question is asked, we can assume that each round of sales would equal 11 total sales. (3b+8j=11)
Knowing the sales take place in intervals of 11, we can solve the problem by doing 385/11.
385/11=35
Finally, with 35 rounds of sales happening and knowing Jenna sells 8 while Becca sells 3 at each one, all that's left to do is multiply.
8x35=280
3x35=105
To be sure we can check our answer by adding them together, 280+105=385.
Answer:
5.5 units
Step-by-step explanation:
Arc length is given by ...
s = rθ
s = (3.5)(π/2) ≈ 5.5 . . . units
