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Diketahui a = ⎝ ⎛ ​ 3 − 2 1 ​ ⎠ ⎞ ​ dan b = ⎝ ⎛ ​ 2 y 2 ​ ⎠ ⎞ ​ jika z adalah proyeksi a terhadap dan ∣ z ∣ ​ = 2 1 ​ ∣ ∣ ​ b ∣ ∣ ​ , maka nilai y yang memenuhi adalah ...

Diketahui  jika  adalah proyeksi  terhadap dan , maka nilai y yang memenuhi adalah ...

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A. Rahmawati

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai y yang memenuhi adalah .

nilai y yang memenuhi adalah negative 2 plus square root of 10 space da n minus 2 minus square root of 10.

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Pembahasan

Diketahui : Ditanya : nilai y yang memenuhi Penyelesaian akan dicari nilai dari Akan dicari nilai dari AKan dicari nilai dari y Dengan menggunakan rumus ABC maka, Jadi, nilai y yang memenuhi adalah .

Diketahui :

table attributes columnalign right center left columnspacing 0px end attributes row cell stack straight a space with rightwards arrow on top end cell equals cell open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses end cell row cell straight b with rightwards arrow on top end cell equals cell open parentheses table row 2 row straight y row 2 end table close parentheses end cell row cell open vertical bar straight z with rightwards arrow on top close vertical bar end cell equals cell 1 half open vertical bar straight b with rightwards arrow on top close vertical bar end cell end table

Ditanya :

nilai y yang memenuhi

Penyelesaian 

z with rightwards arrow on top equals fraction numerator a with rightwards arrow on top space b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction

akan dicari nilai dari a with rightwards arrow on top space b with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top straight b with rightwards arrow on top end cell equals cell open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses open parentheses table row 2 row straight y row 2 end table close parentheses end cell row blank equals cell open parentheses 3 close parentheses open parentheses 2 close parentheses plus open parentheses straight y close parentheses open parentheses negative 2 close parentheses plus open parentheses 1 close parentheses open parentheses 2 close parentheses end cell row blank equals cell 6 minus 2 straight y plus 2 end cell row blank equals cell 8 minus 2 straight y end cell end table

Akan dicari nilai dari open vertical bar b with rightwards arrow on top close vertical bar

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight b with rightwards arrow on top close vertical bar end cell equals cell square root of 2 squared plus straight y squared plus 2 squared end root end cell row blank equals cell square root of 4 plus straight y squared plus 4 end root end cell row blank equals cell square root of 8 plus straight y squared end root end cell end table

AKan dicari nilai dari y

table attributes columnalign right center left columnspacing 0px end attributes row cell straight z with rightwards arrow on top end cell equals cell fraction numerator straight a with rightwards arrow on top straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar end fraction end cell row cell 1 half open vertical bar straight b with rightwards arrow on top close vertical bar end cell equals cell fraction numerator straight a with rightwards arrow on top straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar end fraction end cell row cell 1 half open parentheses stack open vertical bar straight b close vertical bar with rightwards arrow on top close parentheses squared end cell equals cell straight a with rightwards arrow on top straight b with rightwards arrow on top end cell row cell 1 half open parentheses square root of 8 plus straight y squared end root close parentheses squared end cell equals cell 8 minus 2 straight y end cell row cell 1 half open parentheses 8 plus straight y close parentheses end cell equals cell 8 minus 2 straight y end cell row cell 8 plus straight y squared end cell equals cell 16 minus 4 straight y end cell row cell straight y squared plus 4 straight y minus 8 end cell equals 0 row blank blank blank end table

Dengan menggunakan rumus ABC maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell straight y squared plus 4 straight y minus 8 end cell equals 0 row cell straight x subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative straight b plus-or-minus square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction end cell row blank equals cell fraction numerator negative 4 plus-or-minus square root of 4 squared minus 4 open parentheses 1 close parentheses open parentheses negative 8 close parentheses end root over denominator 2 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator negative 4 plus-or-minus square root of 16 plus 32 end root over denominator 2 end fraction end cell row blank equals cell fraction numerator negative 4 plus-or-minus 2 square root of 10 over denominator 2 end fraction end cell row cell straight x subscript 1 comma 2 end subscript end cell equals cell negative 2 plus-or-minus square root of 10 end cell end table

Jadi, nilai y yang memenuhi adalah negative 2 plus square root of 10 space da n minus 2 minus square root of 10.

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