Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 4 feet and
a height of 17 feet. Container B has a radius of 6 feet and a height of 11 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is full after the pumping is complete?
To the nearest tenth, what is the percent of Container B that is full after the pumping is complete?
1 answer:
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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.
