Get the answers you've been looking for with the help of IDNLearn.com's expert community. Find the solutions you need quickly and accurately with help from our knowledgeable community.
Sagot :
To solve for the values of [tex]\( a \)[/tex] through [tex]\( e \)[/tex] that make these two relations inverses of each other, let's proceed step by step.
### Understanding Relations and Their Inverses
Given two sets of pairs, a relation and its inverse share a specific property: if a pair [tex]\((x, y)\)[/tex] is in the first relation, then the pair [tex]\((y, x)\)[/tex] should be in the inverse relation.
### Relations Given
1. First Relation:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3.8 & -3.1 \\ b & 3.2 \\ -1.4 & c \\ -0.2 & 4.4 \\ 1.0 & 5.0 \\ \hline \end{array} \][/tex]
2. Second Relation (Inverse):
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3.1 & a \\ 3.2 & -2.6 \\ 1.7 & -1.4 \\ d & -0.2 \\ 5.0 & e \\ \hline \end{array} \][/tex]
### Solving for Each Variable
#### [tex]\( a \)[/tex]
It’s given that the pair [tex]\((-3.8, -3.1)\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((-3.1, -3.8)\)[/tex].
So, [tex]\( a = -3.8 \)[/tex].
#### [tex]\( b \)[/tex]
It’s given that the pair [tex]\(( b, 3.2 )\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((3.2, b )\)[/tex].
Since [tex]\((3.2, -2.6)\)[/tex] is a pair in the inverse relation, it corresponds to [tex]\( b = -2.6 \)[/tex].
#### [tex]\( c \)[/tex]
It's given that [tex]\((-1.4, c)\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((c, -1.4)\)[/tex].
Since [tex]\((1.7, -1.4)\)[/tex] is a pair in the inverse relation, it corresponds to [tex]\( c = 1.7 \)[/tex].
#### [tex]\( d \)[/tex]
It’s given that the pair [tex]\((-0.2, 4.4)\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((4.4, -0.2)\)[/tex].
Since there is no pair [tex]\( (d, 4.4) \)[/tex] included in the given relations, [tex]\( d\)[/tex] includes no value, hence [tex]\( d = None \)[/tex].
#### [tex]\( e \)[/tex]
It’s given that the pair [tex]\((1.0, 5.0)\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((5.0, 1.0)\)[/tex].
Since [tex]\((5.0, 1.0)\)[/tex] is a pair in the inverse relation, thus we find:
Hence, [tex]\( e = 1.0 \)[/tex].
### Summary of Values:
[tex]\[ a = -3.8 \\ b = -2.6 \\ c = 1.7 \\ d = None \\ e = 1.0 \][/tex]
Thus, the values of [tex]\( a \)[/tex] through [tex]\( e \)[/tex] that make the relations inverses of each other are:
[tex]\[ a = -3.8, \quad b = -2.6, \quad c = 1.7, \quad d = None, \quad e = 1.0 \][/tex]
### Understanding Relations and Their Inverses
Given two sets of pairs, a relation and its inverse share a specific property: if a pair [tex]\((x, y)\)[/tex] is in the first relation, then the pair [tex]\((y, x)\)[/tex] should be in the inverse relation.
### Relations Given
1. First Relation:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3.8 & -3.1 \\ b & 3.2 \\ -1.4 & c \\ -0.2 & 4.4 \\ 1.0 & 5.0 \\ \hline \end{array} \][/tex]
2. Second Relation (Inverse):
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3.1 & a \\ 3.2 & -2.6 \\ 1.7 & -1.4 \\ d & -0.2 \\ 5.0 & e \\ \hline \end{array} \][/tex]
### Solving for Each Variable
#### [tex]\( a \)[/tex]
It’s given that the pair [tex]\((-3.8, -3.1)\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((-3.1, -3.8)\)[/tex].
So, [tex]\( a = -3.8 \)[/tex].
#### [tex]\( b \)[/tex]
It’s given that the pair [tex]\(( b, 3.2 )\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((3.2, b )\)[/tex].
Since [tex]\((3.2, -2.6)\)[/tex] is a pair in the inverse relation, it corresponds to [tex]\( b = -2.6 \)[/tex].
#### [tex]\( c \)[/tex]
It's given that [tex]\((-1.4, c)\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((c, -1.4)\)[/tex].
Since [tex]\((1.7, -1.4)\)[/tex] is a pair in the inverse relation, it corresponds to [tex]\( c = 1.7 \)[/tex].
#### [tex]\( d \)[/tex]
It’s given that the pair [tex]\((-0.2, 4.4)\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((4.4, -0.2)\)[/tex].
Since there is no pair [tex]\( (d, 4.4) \)[/tex] included in the given relations, [tex]\( d\)[/tex] includes no value, hence [tex]\( d = None \)[/tex].
#### [tex]\( e \)[/tex]
It’s given that the pair [tex]\((1.0, 5.0)\)[/tex] is in the first relation.
Thus, the inverse relation should include [tex]\((5.0, 1.0)\)[/tex].
Since [tex]\((5.0, 1.0)\)[/tex] is a pair in the inverse relation, thus we find:
Hence, [tex]\( e = 1.0 \)[/tex].
### Summary of Values:
[tex]\[ a = -3.8 \\ b = -2.6 \\ c = 1.7 \\ d = None \\ e = 1.0 \][/tex]
Thus, the values of [tex]\( a \)[/tex] through [tex]\( e \)[/tex] that make the relations inverses of each other are:
[tex]\[ a = -3.8, \quad b = -2.6, \quad c = 1.7, \quad d = None, \quad e = 1.0 \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.
