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12345 [234]
3 years ago
5

Johnny rode his bike to a friends house 4 blocks down the street in his neighborhood. He Immediately rode back home once he real

ized his friend was unable to play. What was his displacement for the total bike ride trip? What could you use as a reference point ? Show the steps to solve this problem.
Mathematics
1 answer:
Aneli [31]3 years ago
7 0

Answer:

Total displacement = 0 blocks

Step-by-step explanation:

Displacement : It is defined as the total distance between the initial and the final positions of the moving object or a body. The total displacement can be 0 in case the initial and the final positions of the body are same.

The distance traveled by Johnny from his house to his friends house = 4 blocks

Then he immediately returns to his house, so the total distance then covered = 4 blocks

Total distance traveled = 4 + 4

                                        = 8 blocks

But the initial position of Johnny is his house and the final position of Johnny is also his house

Therefore, the initial and the final position of Johnny is same and this can be used as a reference point for the given problem.

⇒ Total displacement = 0 blocks

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Express the function graphed on the axes below as a piecewise function.
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Answer:

  f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

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<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

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<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

  y -(-1) = -3(x -5)

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The second piece can be written ...

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<h3>Whole function</h3>

Putting these pieces together, we have ...

  \boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}

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<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

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