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marshall27 [118]
3 years ago
14

Suppose that $p$ and $q$ are positive numbers for which \[\log_9 p = \log_{12} q = \log_{16} (p + q).\] what is the value of $q/

p$?
Mathematics
1 answer:
SVEN [57.7K]3 years ago
3 0

Given p,q>0 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,q>0, the negative value is rejected.

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

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Natasha_Volkova [10]
The correct answers are:
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Explanation:
Given:
cos(x) =  \frac{1}{2}

Step 1:
Since, according to the Trigonometric identity:
sin^2(x) + cos^2(x) = 1 -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
sin^2(x) + ( \frac{1}{2} )^2 = 1 \\ sin^2(x) + \frac{1}{4} = 1 \\ sin^2(x)  =  \frac{3}{4}

Step 3:
Take square-root on both sides:
\sqrt{sin^2(x)} =  \sqrt{\frac{3}{4}}

sin(x) = \frac{ \sqrt{3} }{2}

Now to find the tan(x), we would use the following formula:

tan(x) = \frac{sin(x)}{cos(x)} --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = \frac{ \frac{ \sqrt{3} }{2} }{ \frac{1}{2} }

Hence tan(x) = \sqrt{3}
6 0
3 years ago
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four-fifths of the senior class went to prom. if 324 seniors went to prom, how many are there in the senior class
romanna [79]

The answer to your question is 405, because look divide 324 by 4 becasue thats how many fifths are being used then multiply the answer which is 81 by 405

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Step-by-step explanation:

The garden is 4 yards = 12 feet by 3 yards = 9 feet. The area of it is the product of these dimensions, ...

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Write an expression that represents the area of the rectangle. Remember A = LW
Iteru [2.4K]

Answer:

b) 9x² - 3x

Step-by-step explanation:

Area of a  rectangle = Length × Width

Area for the rectangle = 3x - 1 × 3x

Area = (3x-1)(3x)

Step 1. Multiply by combining like terms

3x · 3x = 9x²

Step 2. Multiply -1 by 3x

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Step 3. Combine 9x² and -3x

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jonny [76]

Answer:

  • A. f(n) = (n + 1)^2 – 1

Step-by-step explanation:

Figure 1

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Figure 2

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Figure 3

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<u>The function is:</u>

  • f(n) = (n + 1)² - 1
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