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tatiyna
4 years ago
15

Y varies directly as x. If x = 5 when y = 12 find x when y = 30

Mathematics
1 answer:
Rzqust [24]4 years ago
4 0
Direct Variation. The equation is y=k(x). So 12=k(5), divide by 5 on both sides coming up with k=2.4. Plug 2.4 in as k in the original equation, making it 30=2.4(x), divide both sides by 2.4, 30 divided by 2.4 is 12.5, making x=12.5
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\bf \begin{array}{ccll}
n&term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
2&a_2&20\\
3&a_3&20r\\
4&a_4&20rr\\
&&20r^2\\\\
&&\frac{45}{4}
\end{array}\implies \stackrel{4^{th}~term}{20r^2=\cfrac{45}{4}}\implies r^2=\cfrac{45}{80}
\\\\\\
r^2=\stackrel{simplified}{\cfrac{9}{16}}\implies r=\sqrt{\cfrac{9}{16}}\implies r=\cfrac{\sqrt{9}}{\sqrt{16}}\implies r=\cfrac{3}{4} 
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