Suppose that $p$ and $q$ are positive numbers for

Ответ:

Jasten

13.03.2022

Given p,q0 and $\log_9p=\log_{12}q=\log_{16}(p+q)=x$ (say).

Then,

$p=9^x\\ q=12^x\\ p+q=16^x$

From the above 3 equations,

$\frac{q}{p} =(\frac{12}{9} )^x\\ \frac{q}{p} =(\frac{4}{3} )^x\\ \frac{p+q}{p} =(\frac{16}{9} )^x\\ \frac{p+q}{p} =(\frac{4}{3} )^{2x}\\$

From the equations, we get

$\frac{p+q}{p}=(\frac{q}{p})^2\\ 1+\frac{q}{p}=(\frac{q}{p})^2\\ (\frac{q}{p})^2-\frac{q}{p}-1=0\\ \frac{q}{p}=\frac{1 \pm \sqrt{5}}{2}$

Since p,q0 , the negative value is rejected.

$\frac{q}{p}=\frac{1 + \sqrt{5}}{2}$

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Baby010391

27.05.2022

0.3 galloons of water.

Step-by-step explanation:

We know that 1/5 galloons of water fills 2/3 of the bin.

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