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Zanzabum
3 years ago
5

On any given day, the number of users, u, that access a certain website can be represented by the inequality 125-4530

Mathematics
1 answer:
Masteriza [31]3 years ago
4 0

Answer:

Step-by-step explanation:

Our inequality is |125-u| ≤ 30. Let's separate this into two. Assuming that (125-u) is positive, we have 125-u ≤ 30, and if we assume that it's negative, we'd have -(125-u)≤30, or u-125≤30.

Therefore, we now have two inequalities to solve for:

125-u ≤ 30

u-125≤30

For the first one, we can subtract 125 and add u to both sides, resulting in

0 ≤ u-95, or 95≤u. Therefore, that is our first inequality.

The second one can be figured out by adding 125 to both sides, so u ≤ 155.

Remember that we took these two inequalities from an absolute value -- as a result, they BOTH must be true in order for the original inequality to be true. Therefore,

u ≥ 95

and

u ≤ 155

combine to be

95 ≤ u ≤ 155, or the 4th option

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Vectors: Find the vector from the point A=(−1,−7,3) to the point B=(3,−2,9).
devlian [24]

Answer:

\overrightarrow {AB} = (4,5,6)

1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉 F

2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉 F

3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉 T

4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉 F

5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉 F

Step-by-step explanation:

The vector AB is the vectorial difference between point A and B, that is:

\overrightarrow {AB} = \vec B - \vec A

Given that \vec A = (-1,-7,3) and \vec B = (3,-2,9), the vector AB is:

\overrightarrow {AB} = (3,-2,9)-(-1,-7,3)

\overrightarrow{AB} = (3-(-1),-2-(-7),9-3)

\overrightarrow {AB} = (4,5,6)

The vectorial equation of the line is represented by:

\langle x, y, z\rangle = \vec A + t \cdot \overrightarrow {AB}

Where t is the parametric variable, dimensionless. Given that \vec A = (-1,-7,3) and \overrightarrow {AB} = (4,5,6)

\langle x,y,z \rangle = \langle -1,-7,3 \rangle + t\cdot \langle 4,5,6 \rangle

Finally, the list of questions are now checked:

1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉 F

2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉 F

3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉 T

4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉 F

5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉 F

4 0
3 years ago
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