Let u = <-4, 3>. Find the unit vector in the direction of u, and write your answer in component form. (2 points)
1 answer:
Answer: < -4/5, 3/5>
This is equivalent to writing < -0.8, 0.6 >
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Explanation:
Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.
We have a right triangle with legs of 4 and 3. The hypotenuse is through use of the pythagorean theorem.
We have a 3-4-5 right triangle.
Therefore, the vector is 5 units long. This is the magnitude of the vector.
Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.
Therefore, we go from < -4, 3 > to < -4/5, 3/5 >
This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6
Side note: Unit vectors are useful in computer graphics.
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Answer:
Therefore he invested $60,000 at 9% per year and $(210,000-60,000)=$150,000 at 4% per year.
Step-by-step explanation:
Given John plans to invest $210,000 in two different funds. He projects that the moderately high risk investments should return, overtime 9% per year,while low risk investments should return about 4% per year.
He wants a supplemental income of$11,400 a year.
Let , he invested $x at 9% per year and $(210,000-x) at 4% per year.
p = principle , r = rate of interest and t = time
The interest earns at 9% per year=
The interest earns at 4% per year=
According to the problem,
Therefore he invested $60,000 at 9% per year and $(210,000-60,000)=$150,000 at 4% per year.