Question

help me please if you canTable:interval of time (t-2) (t-1) 4(t-2)(t-1) less than 1 hour 1 hourbetween 1 and 2 hours2 hoursmore than 2 hours

Answer 1

To complete the table, we want to choose any value on the given intervals and test its sign on each columns, (t - 2) and (t - 1). If both have + signs, the las column will also have + sign. If both have - sign, the last column will have + sign. If one has + sign and the other has - sign, the last column will have - sign.

The first internal is "less than 1 hour".

One easi pick here is t = 0:

`\begin{gathered} (t-2)=0-2=-2\longrightarrow- \\ (t-1)=0-1=-1\longrightarrow- \end{gathered}`

Since both are negative, we have:

`4(t-2)(t-1)\longrightarrow+`

So, the first row is:

less than 1 hour - - +

The second is not an interval it is "1 hour", so:

`\begin{gathered} (t-2)=1-2=-1\longrightarrow- \\ (t-1)=1-1=0\longrightarrow0 \end{gathered}`

Since any number multiplied by 0 is also 0, the result on the third column will also be 0:

`4(t-2)(t-1)\longrightarrow0`

So, the second row is:

1 hour - 0 0

The third interval is "between 1 and 2 hours", so we can pick 1.5, for example. We have:

`\begin{gathered} (t-2)=1.5-2=-0.5\longrightarrow- \\ (t-1)=1.5-1=0.5\longrightarrow+ \end{gathered}`

Since one is - and the other is +, the third column will be negative:

`4(t-2)(t-2)\longrightarrow-`

So, the third row is:

between 1 and 2 hours - + -

In the fourth, we have a value of 2 hours, so:

`\begin{gathered} (t-2)=2-2=0\longrightarrow0 \\ (t-1)=2-1=1\longrightarrow+ \end{gathered}`

Since one of them is 0, the third column will also be 0, so:

`4(t-2)(t-1)\longrightarrow0`

So, the fourth row is:

2 hours 0 + 0

The last interval is "more than 2 hours", so we can pick 3, for example:

`\begin{gathered} (t-2)=3-2=1\longrightarrow+ \\ (t-1)=3-1=2\longrightarrow+ \end{gathered}`

Since both are +, the third column will also be +:

`4(t-2)(t-1)\longrightarrow+`

So, the fifth row is:

more than 2 hours + + +

So, we have:

interval of time (t-2) (t-1) 4(t-2)(t-1)

less than 1 hour - - +

1 hour - 0 0

between 1 and 2 hours - + -

2 hours 0 + 0

more than 2 hours + + +