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Tentukan persamaan garis singgung lingkaran yang melewati titik !

Pertanyaan

Tentukan persamaan garis singgung lingkaran left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 16 yang melewati titik left parenthesis negative 6 comma 5 right parenthesis!

Pembahasan Soal:

Persamaan garis singgung ditentukan sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x subscript 1 minus a close parentheses open parentheses x minus a close parentheses plus open parentheses y subscript 1 minus b close parentheses open parentheses y minus b close parentheses end cell equals cell r squared end cell row cell open parentheses negative 6 plus 2 close parentheses left parenthesis x plus 2 right parenthesis plus left parenthesis 5 minus 1 right parenthesis left parenthesis y minus 1 right parenthesis end cell equals 16 row cell negative 4 left parenthesis x plus 2 right parenthesis plus 4 left parenthesis y minus 1 right parenthesis end cell equals 16 row cell negative 4 x minus 8 plus 4 y minus 4 end cell equals 16 row cell negative 4 x plus 4 y minus 28 end cell equals 0 row cell x minus y plus 7 end cell equals 0 end table

Jadi, persamaan garis singgung lingkaran tersebut adalah x minus y plus 7 equals 0.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Janatu

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 07 Juni 2021

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Pertanyaan yang serupa

Diketahui matriks invers dari adalah...

Pembahasan Soal:

Ingat operasi perkalian matriks : open square brackets table row a b row c d end table close square brackets open square brackets table row e f row g h end table close square brackets equals open square brackets table row cell a e plus b g end cell cell a f plus b h end cell row cell c e plus d g end cell cell c f plus d h end cell end table close square brackets

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell A times B end cell equals cell open square brackets table row 3 2 row 2 cell negative 1 end cell end table close square brackets open square brackets table row cell negative 2 end cell 1 row 1 cell negative 1 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 3 left parenthesis negative 2 right parenthesis plus 2 left parenthesis 1 right parenthesis end cell cell 3 left parenthesis 1 right parenthesis plus 2 left parenthesis negative 1 right parenthesis end cell row cell 2 left parenthesis negative 2 right parenthesis plus left parenthesis negative 1 right parenthesis 1 end cell cell 2 left parenthesis 1 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 1 right parenthesis end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 4 end cell 1 row cell negative 5 end cell 3 end table close square brackets end cell end table

ingat invers matriks: open square brackets table row a b row c d end table close square brackets to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets

invers matriks A times B adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets table row cell negative 4 end cell 1 row cell negative 5 end cell 3 end table close square brackets to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator negative 4 left parenthesis 3 right parenthesis minus 1 left parenthesis negative 5 right parenthesis end fraction open square brackets table row 3 cell negative 1 end cell row 5 cell negative 4 end cell end table close square brackets end cell row blank equals cell negative 1 over 7 open square brackets table row 3 cell negative 1 end cell row 5 cell negative 4 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 3 over 7 end cell cell 1 over 7 end cell row cell negative 5 over 7 end cell cell 4 over 7 end cell end table close square brackets end cell end table.

Jadi, tidak ada jawaban yang tepat pada pilihan jawaban.

0

Roboguru

Diketahui matriks dan matriks .  Invers matriks AB adalah =.......

Pembahasan Soal:

A B equals open parentheses table row 1 2 1 row 1 cell negative 1 end cell cell negative 1 end cell end table close parentheses open parentheses table row 1 cell negative 1 end cell row 1 1 row cell negative 1 end cell cell negative 2 end cell end table close parentheses  A B equals open parentheses table row cell 1 plus 2 minus 1 end cell cell negative 1 plus 2 minus 2 end cell row cell 1 minus 1 plus 1 end cell cell negative 1 minus 1 plus 2 end cell end table close parentheses  A B equals open parentheses table row 2 cell negative 1 end cell row 1 0 end table close parentheses  I n g a t space b a h w a space i n v e r s space d a r i space m a t r i k s space P equals open parentheses table row a b row c d end table close parentheses space a d a l a h space P to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses comma space m a k a  open parentheses A B close parentheses to the power of negative 1 end exponent equals fraction numerator 1 over denominator 2 open parentheses 0 close parentheses minus open parentheses 1 close parentheses open parentheses negative 1 close parentheses end fraction open parentheses table row 0 1 row cell negative 1 end cell 2 end table close parentheses  open parentheses A B close parentheses to the power of negative 1 end exponent equals open parentheses table row 0 1 row cell negative 1 end cell 2 end table close parentheses

0

Roboguru

Jika  maka matriks

Pembahasan Soal:

Hasil kali dari matriks P dan Q dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row PQ equals cell open parentheses table row 2 5 row 1 3 end table close parentheses open parentheses table row 4 5 row 1 1 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 times 4 plus 5 times 1 end cell cell 2 times 5 plus 5 times 1 end cell row cell 1 times 4 plus 3 times 1 end cell cell 1 times 5 plus 3 times 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 13 15 row 7 8 end table close parentheses end cell end table end style 

Invers dari matriks PQ dapat dinyatakan sebagai berikut.

begin mathsize 14px style open parentheses PQ close parentheses to the power of negative 1 end exponent equals straight Q to the power of negative 1 end exponent straight P to the power of negative 1 end exponent end style

sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight Q to the power of negative 1 end exponent straight P to the power of negative 1 end exponent end cell equals cell open parentheses PQ close parentheses to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 1 over denominator 13 times 8 minus 15 times 7 end fraction open parentheses table row 8 cell negative 15 end cell row cell negative 7 end cell 13 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 104 minus 105 end fraction open parentheses table row 8 cell negative 15 end cell row cell negative 7 end cell 13 end table close parentheses end cell row blank equals cell negative 1 open parentheses table row 8 cell negative 15 end cell row cell negative 7 end cell 13 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 8 end cell 15 row 7 cell negative 13 end cell end table close parentheses end cell end table end style

Jadi, jawaban yang benar adalah E.

0

Roboguru

Jika , maka  adalah ....

Pembahasan Soal:

0

Roboguru

Diketahui matriks berikut ini:   Tentukan: c.      d.

Pembahasan Soal:

c.   Menentukan A B

table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals cell open square brackets table row 2 6 row 3 8 end table close square brackets times open square brackets table row 1 3 row 1 4 end table close square brackets end cell row blank equals cell open square brackets table row cell 2 times 1 plus 6 times 1 end cell cell space space 2 times 3 plus 6 times 4 end cell row cell 3 times 1 plus 8 times 1 end cell cell space space 3 times 3 plus 8 times 4 end cell end table close square brackets end cell row blank equals cell open square brackets table row 8 30 row 11 41 end table close square brackets end cell end table 

Jadi, 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 B 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 cell open square brackets table row 8 30 row 11 41 end table close square brackets end cell end table.

d.   Menentukan open parentheses A B close parentheses to the power of negative 1 end exponent

table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals cell open square brackets table row 8 30 row 11 41 end table close square brackets end cell row cell A B to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator det space A B end fraction cross times Adj space open parentheses A B close parentheses end cell row blank equals cell fraction numerator 1 over denominator 8 times 41 minus 30 times 11 end fraction open square brackets table row 41 cell negative 30 end cell row cell negative 11 end cell 8 end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator 328 minus 330 end fraction open square brackets table row 41 cell negative 30 end cell row cell negative 11 end cell 8 end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator negative 2 end fraction open square brackets table row 41 cell negative 30 end cell row cell negative 11 end cell 8 end table close square brackets end cell row blank equals cell open square brackets table row cell negative 41 over 2 end cell 15 row cell 11 over 2 end cell cell negative 4 end cell end table close square brackets end cell end table 

Jadi, Error converting from MathML to accessible text. 

0

Roboguru

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