Michael plays 1/5 of a song in 1/15 pf a minute. How many minutes will it take to play whole song

1 answer:

6 0

Well, a whole will be five fifths or 5/5.

now, he only plays 1/5 in 1/15, how many minutes will it take to play the whole 5/5 of the song?

$\bf \begin{array}{ccll}
\stackrel{part}{song}&\stackrel{part}{minutes}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
\frac{1}{5}&\frac{1}{15}\\\\
\frac{5}{5}&m
\end{array}\implies \cfrac{\frac{1}{5}}{\frac{5}{5}}=\cfrac{\frac{1}{15}}{m}\implies \cfrac{\frac{1}{5}}{\frac{5}{5}}=\cfrac{\frac{1}{15}}{\frac{m}{1}}\implies \cfrac{1}{5}\cdot \cfrac{5}{5}=\cfrac{1}{15}\cdot \cfrac{1}{m}$

$\bf \cfrac{1}{5}=\cfrac{1}{15m}\implies 15m=5\implies m=\cfrac{5}{15}\implies m=\stackrel{\textit{minutes}}{\cfrac{1}{3}}$

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Help me. I don't understand. Please help me find X and IK

sertanlavr [38]

Answer:

$x=4\\\\y=6\\\\IK=47$

Step-by-step explanation:

Two Tangent Theorem: Tangents which meet at same point are equal in length.

Here tangents at J and H meet at I.

$Hence\ HI=IJ\\\\y^2-10=4y+2\\\\y^2-4y-12=0\\\\y^2-6y+2y-12=0\\\\y(y-6)+2(y-6)=0\\\\(y-6)(y+2)\\\\y\ can\ not\ be\ negative\ as\ in\ that\ case\ IJ\ will\ be\ negative.\\\\Hence\ y=6\\\\IJ=4y+2=4\times 6+2=26\\\\\\\\Tangents\ at\ J\ and\ L\ meet\ at\ K.\ Use\ two\ tangent\ theorem.\\\\JK=KL\\\\5x+1=6x-3\\\\6x-5x=1+3\\\\x=4\\\\JK=5x+1=5\times 4+1=21\\\\\\IK=IJ+JK=26+21\\\\IK=47$