Answer:
The relation or y = seven-halves x is a direct variation that contains the ordered pair (2,7).
Step-by-step explanation:
Given:
The ordered pair = (2, 7).
Now, to get the direct variation:
As (2,7) lies on it.
So, direct variation means
Now,
Now, to get the direct variation:
or y = seven-halves x.
Therefore, the relation or y = seven-halves x is a direct variation that contains the ordered pair (2,7).
Answer:
(a) 53.451∠163°
Step-by-step explanation:
The sum of the vectors is the sum of their components:
v1 +v2 = (-55i +3j) +(4i +13j) = (-55 +4)i +(3 +13)j = -51i +16j
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<h3>conversion to polar form</h3>This is converted to magnitude and direction by ...
|ai +bj| = √(a² +b²)
|-51i +16j| = √((-51)² +16²) = √(2601 +256) = √2857 ≈ 53.451
and
∠(ai +bj) = arctan(b/a) = arctan(16/-51) ≈ -17° +180° = 163°
note that 180° is added because the components indicate the angle is in the 2nd quadrant.
The object's speed and direction are ...
53.451 ∠163°
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<em>Additional comment</em>
If you're doing a lot of vector calculations, the process is simplified immensely by a suitable calculator. (See attached.) 2-dimensional vectors are handled nicely using the complex number functions of the calculator.
