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b.  Diketahui vektor dan vektor dan vektor . dan . Tentukan nilai

Pertanyaan

b.  Diketahui vektor begin mathsize 14px style x with rightwards arrow on top equals open parentheses table row 12 row 16 end table close parentheses end style dan vektor begin mathsize 14px style y with rightwards arrow on top equals open parentheses table row a row 8 end table close parentheses end style dan vektor begin mathsize 14px style straight z with rightwards arrow on top equals open parentheses table row 9 row straight b end table close parentheses end style. begin mathsize 14px style vertical line x with rightwards arrow on top vertical line plus vertical line y with rightwards arrow on top vertical line equals 30 end style dan begin mathsize 14px style vertical line y with rightwards arrow on top vertical line minus vertical line z with rightwards arrow on top vertical line equals negative 5 end style . Tentukan nilai a squared minus 3 a plus 2 b

Pembahasan Soal:

Ingat!

v with rightwards arrow on top equals open parentheses table row x row y end table close parentheses open vertical bar v with rightwards arrow on top close vertical bar equals square root of x squared plus y squared end root

Pertama kita mencari nilai a:

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line x with rightwards arrow on top vertical line plus vertical line y with rightwards arrow on top vertical line end cell equals 30 row cell square root of 12 squared plus 16 squared end root plus square root of a squared plus 8 squared end root end cell equals 30 row cell square root of 144 plus 256 end root plus square root of a squared plus 64 end root end cell equals 30 row cell square root of 400 plus square root of a squared plus 64 end root end cell equals 30 row cell square root of a squared plus 64 end root end cell equals 10 row cell a squared plus 64 end cell equals cell 10 squared end cell row cell a squared end cell equals cell 100 minus 64 end cell row cell a squared end cell equals 36 row a equals cell plus-or-minus 6 end cell end table

Kemudain kita tentukan nilai b:

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line y with rightwards arrow on top vertical line minus vertical line z with rightwards arrow on top vertical line end cell equals cell negative 5 end cell row cell square root of 6 squared plus 8 squared end root minus square root of 9 squared plus b squared end root end cell equals cell negative 5 end cell row cell square root of 100 minus square root of 81 plus b squared end root end cell equals cell negative 5 end cell row cell 10 plus negative square root of 81 plus b squared end root end cell equals cell negative 5 end cell row cell negative square root of 81 plus b squared end root end cell equals cell negative 15 end cell row cell square root of 81 plus b squared end root end cell equals 15 row cell 81 plus b squared end cell equals cell 15 squared end cell row cell b squared end cell equals cell 225 minus 81 end cell row cell b squared end cell equals 144 row b equals cell plus-or-minus 12 end cell end table 

Maka nilai dari a squared minus 3 a plus 2 b

Untuk a equals 6 comma space b equals 12

table attributes columnalign right center left columnspacing 0px end attributes row cell a squared minus 3 a plus 2 b end cell equals cell open parentheses 6 close parentheses squared minus 3 open parentheses 6 close parentheses plus 2 open parentheses 12 close parentheses end cell row blank equals cell 36 minus 18 plus 24 end cell row blank equals 42 end table

Untuk a equals negative 6 comma space b equals 12

table attributes columnalign right center left columnspacing 0px end attributes row cell a squared minus 3 a plus 2 b end cell equals cell open parentheses negative 6 close parentheses squared minus 3 open parentheses negative 6 close parentheses plus 2 open parentheses 12 close parentheses end cell row blank equals cell 36 plus 18 plus 24 end cell row blank equals 78 end table

Untuk a equals 6 comma space b equals negative 12

table attributes columnalign right center left columnspacing 0px end attributes row cell a squared minus 3 a plus 2 b end cell equals cell open parentheses 6 close parentheses squared minus 3 open parentheses 6 close parentheses plus 2 open parentheses negative 12 close parentheses end cell row blank equals cell 36 minus 18 minus 24 end cell row blank equals cell negative 6 end cell end table

Untuk a equals negative 6 comma space b equals negative 12

table attributes columnalign right center left columnspacing 0px end attributes row cell a squared minus 3 a plus 2 b end cell equals cell open parentheses negative 6 close parentheses squared minus 3 open parentheses negative 6 close parentheses plus 2 open parentheses negative 12 close parentheses end cell row blank equals cell 36 plus 18 minus 24 end cell row blank equals 30 end table


Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table memiliki empat nilai yang mungkin yaitu 42 comma space 78 comma space minus 6 comma dan 30

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 30 Juli 2021

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