Roboguru

Diketahui: . Jika  adalah sudut antara  serta , maka nilai konstanta positif k adalah ....

Pertanyaan

Diketahui: begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 2 row k end table close parentheses space dan space c with rightwards arrow on top equals open parentheses table row 6 row 10 end table close parentheses end style. Jika alpha adalah sudut antara begin mathsize 14px style a with italic rightwards arrow on top italic space dan italic space c with italic rightwards arrow on top end style serta begin mathsize 14px style tan alpha equals 1 end style, maka nilai konstanta positif k adalah ....

  1. ...space 

  2. ...undefined 

Pembahasan Soal:

Nilai tan sama dengan 1 terjadi saat sudut alpha sebesar 45 derajat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan alpha end cell equals 1 row cell tan alpha end cell equals cell tan 45 degree end cell row blank rightwards arrow cell alpha equals 45 degree end cell end table end style

Vektor  begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 2 row k end table close parentheses space dan space c with rightwards arrow on top equals open parentheses table row 6 row 10 end table close parentheses end style

 ingat rumus dot product pada vektor begin mathsize 14px style straight a times c equals vertical line a vertical line vertical line c vertical line cross times cos alpha end style,maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times c with rightwards arrow on top end cell equals cell vertical line a with rightwards arrow on top vertical line vertical line c with rightwards arrow on top vertical line cos 45 degree end cell row cell open parentheses table row 2 row k end table close parentheses times open parentheses table row 6 row 10 end table close parentheses end cell equals cell square root of 2 squared plus k squared end root square root of 6 squared plus 10 squared end root cross times 1 half square root of 2 end cell row cell 12 plus 10 k end cell equals cell square root of 4 plus k squared end root square root of 136 cross times square root of 1 half end root end cell row blank equals cell square root of 4 plus k squared end root square root of 68 end cell row blank equals cell square root of 272 plus 68 k squared end root end cell row cell 144 plus 240 k plus 100 k squared end cell equals cell 272 plus 68 k squared end cell row cell 32 k squared plus 240 k minus 128 end cell equals 0 row cell 2 k squared plus 15 k minus 8 end cell equals 0 row cell left parenthesis 2 k minus 1 right parenthesis left parenthesis k plus 8 right parenthesis end cell equals 0 row blank rightwards arrow cell k equals negative 8 space logical or k equals 1 half end cell end table end style

Jadi, nilai konstanta positif begin mathsize 14px style k equals 1 half end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 2021

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