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Persamaan garis singgung kurva yang tegak lurus dengan garis  adalah ....

Pertanyaan

Persamaan garis singgung kurva Error converting from MathML to accessible text. yang tegak lurus dengan garis table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 y 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 equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table adalah ....

Pembahasan Soal:

Diketahui :Error converting from MathML to accessible text. yang tegak lurus dengan garis table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 y 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 equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table.

Ditanya : persamaan garis singgung kurva ?

Jawab :
Dengan menggunakan konsep perrsamaan garis singgung kurva yang tegak lurus dengan garis, diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 x cubed minus 3 x squared minus 61 over 5 x end cell row cell y apostrophe end cell equals cell m equals 6 x squared minus 6 x minus 61 over 5 end cell row cell 5 x minus y plus 2 end cell equals 0 row cell negative y end cell equals cell negative 5 x minus 2 end cell row y equals cell 5 x plus 2 end cell row m equals 5 end table

Karena tegak lurus maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m subscript 1 end cell equals cell negative 1 over straight m end cell row blank equals cell negative 1 fifth end cell end table

Kemudian subtitusikan pada m,

table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript 1 end cell equals cell 6 x squared minus 6 x minus 61 over 5 end cell row cell negative 1 fifth end cell equals cell 6 x squared minus 6 x minus 61 over 5 end cell row cell 6 x squared minus 6 x minus 61 over 5 plus 1 fifth end cell equals 0 row cell 6 x squared minus 6 x minus 60 over 5 end cell equals 0 row cell 6 left parenthesis x plus 1 right parenthesis left parenthesis x minus 2 right parenthesis end cell equals 0 row x equals cell negative 1 space dan space x equals 2 end cell end table

Masing-masing subtitusikan pada Error converting from MathML to accessible text.

Untuk table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank 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 1 end table,

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 x cubed minus 3 x squared minus 61 over 5 x end cell row blank equals cell 2 left parenthesis negative 1 right parenthesis cubed minus 3 left parenthesis negative 1 right parenthesis squared minus 61 over 5 left parenthesis negative 1 right parenthesis end cell row blank equals cell 2 left parenthesis negative 1 right parenthesis minus 3 plus 61 over 5 end cell row blank equals cell 36 over 5 end cell end table

Untuk table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank 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 y equals cell 2 x cubed minus 3 x squared minus 61 over 5 x end cell row blank equals cell 2 left parenthesis 2 right parenthesis cubed minus 3 left parenthesis 2 right parenthesis squared minus 61 over 5 left parenthesis 2 right parenthesis end cell row blank equals cell 16 minus 12 minus 122 over 5 end cell row blank equals cell negative 102 over 5 end cell end table

Didapat titik open parentheses negative 1 comma space 36 over 5 close parentheses dan open parentheses 2 comma space minus 102 over 5 close parentheses.

Persamaan garis singgung 1 :

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell m subscript 1 open parentheses x minus x subscript 1 close parentheses end cell row cell y minus 36 over 5 end cell equals cell negative 1 fifth open parentheses x plus 1 close parentheses end cell row y equals cell negative 1 fifth x minus 1 fifth plus 36 over 5 end cell row y equals cell negative 1 fifth x plus 7 end cell end table

Persamaan garis singgung 2 :

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell m subscript 1 open parentheses x minus x subscript 1 close parentheses end cell row cell y plus 102 over 5 end cell equals cell negative 1 fifth open parentheses x minus 2 close parentheses end cell row y equals cell negative 1 fifth x plus 2 over 5 minus 102 over 5 end cell row y equals cell negative 1 fifth x minus 20 end cell end table

Jadi, persamaan garis singgung kurva Error converting from MathML to accessible text. yang tegak lurus dengan garis table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 y 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 equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank 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 cell 1 fifth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 7 end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank 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 cell 1 fifth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 20 end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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