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begin mathsize 14px style open curly brackets table attributes columnalign left end attributes row cell x equals cos space A minus 2 space sin space B end cell row cell y equals sin space A plus 2 space cos space B end cell end table close end style 

Nilai minimum dari begin mathsize 14px style x squared plus y squared equals.... end style 

  1. 1undefined 

  2. 2undefined 

  3. 3undefined 

  4. 5undefined 

  5. 7undefined 

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Dapat ditentukan begin mathsize 14px style x squared end style dan begin mathsize 14px style y squared end style sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared end cell equals cell open parentheses cos space A minus 2 space sin space B close parentheses squared end cell row blank equals cell cos squared space A minus 4 space cos space A space sin space B plus 4 space sin squared B end cell row cell y squared end cell equals cell open parentheses sin space A plus 2 space cos space B close parentheses squared end cell row blank equals cell sin squared space A plus 4 space sin space A space cos space B plus 4 space cos squared B end cell end table end style 

Selanjutnya dapat undefined ditentukan sebagai berikut.

begin mathsize 14px style table row cell table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space 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 space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank B 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 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank B end table end cell space row cell table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table squared table attributes columnalign right center left columnspacing 0px end attributes row blank blank space 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 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space 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 space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank B 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 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table squared table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell space B end cell end table end cell plus row cell table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 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 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis sin space A space cos space B minus sin space B space cos space A right parenthesis end cell 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 4 end table end cell space end table end style 

Sehingga dapat disederhanakan menjadi:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals cell 1 plus 4 left parenthesis sin space A space cos space B minus sin space B space cos space A right parenthesis plus 4 end cell row blank equals cell 5 plus 4 open parentheses sin space left parenthesis A minus B right parenthesis close parentheses end cell end table end style

Bentuk undefined akan mencapai minimum ketika nilai begin mathsize 14px style sin space open parentheses A minus B close parentheses equals negative 1 end style sehingga diperoleh nilai minimumnya sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell min space left parenthesis x squared plus y squared right parenthesis end cell equals cell 5 plus 4 space open parentheses negative 1 space close parentheses end cell row blank equals cell 5 minus 4 end cell row blank equals 1 end table end style 

Jadi, jawaban yang benar adalah A.

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