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nydimaria [60]
3 years ago
7

Help can some one do number 10 please

Mathematics
1 answer:
marissa [1.9K]3 years ago
6 0
Download Socratic it'll do everything
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Let $f(x)$ be a function defined for all positive real numbers satisfying the conditions $f(x) > 0$ for all $x > 0$ and $f
algol [13]
Suppose we choose x=1 and y=\dfrac12. Then

f(x-y)=\sqrt{f(xy)+1}\implies f\left(\dfrac12\right)=\sqrt{f\left(\dfrac12\right)+1}\implies f\left(\dfrac12\right)=\dfrac{1+\sqrt5}2


Now suppose we choose x,y such that

\begin{cases}x-y=\dfrac12\\\\xy=2009\end{cases}


where we pick the solution for this system such that x>y>0. Then we find

\dfrac{1+\sqrt5}2=\sqrt{f(2009)+1}\implies f(2009)=\dfrac{1+\sqrt5}2

Note that you can always find a solution to the system above that satisfies x>y>0 as long as x>\dfrac12. What this means is that you can always find the value of f(x) as a (constant) function of f\left(\dfrac12\right).
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Sally has eight-teen books.
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4 years ago
MULTIPLE CHOICE PLEASE HELP ME
Nonamiya [84]

Step-by-step explanation:

vol =πr²h

22/7×8×8×3

= 603.2

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The answer would be 3
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A line has a slope of 7 and contains the point (5, −9).
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Your answer would come out to be y=7x-44 
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Those match up to that answer.
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