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qwelly [4]
4 years ago
13

Simplest form for 3/36 or is it already simplified???? HELP ME

Mathematics
1 answer:
larisa [96]4 years ago
5 0
3/36    3 into 3 is 1, and 3 into 36 is 12

= 1/12    is the simplified form.
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If f(x)=2x+sinx and the function g is the inverse of f then g'(2)=
Alexxx [7]
\bf f(x)=y=2x+sin(x)
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inverse\implies x=2y+sin(y)\leftarrow f^{-1}(x)\leftarrow g(x)
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\textit{now, the "y" in the inverse, is really just g(x)}
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\textit{so, we can write it as }x=2g(x)+sin[g(x)]\\\\
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\bf \textit{let's use implicit differentiation}\\\\
1=2\cfrac{dg(x)}{dx}+cos[g(x)]\cdot \cfrac{dg(x)}{dx}\impliedby \textit{common factor}
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1=\cfrac{dg(x)}{dx}[2+cos[g(x)]]\implies \cfrac{1}{[2+cos[g(x)]]}=\cfrac{dg(x)}{dx}=g'(x)\\\\
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g'(2)=\cfrac{1}{2+cos[g(2)]}

now, if we just knew what g(2)  is, we'd be golden, however, we dunno

BUT, recall, g(x) is the inverse of f(x), meaning, all domain for f(x) is really the range of g(x) and, the range for f(x), is the domain for g(x)

for inverse expressions, the domain and range is the same as the original, just switched over

so, g(2) = some range value
that  means if we use that value in f(x),   f( some range value) = 2

so... in short, instead of getting the range from g(2), let's get the domain of f(x) IF the range is 2

thus    2 = 2x+sin(x)

\bf 2=2x+sin(x)\implies 0=2x+sin(x)-2
\\\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}\implies g'(2)=\cfrac{1}{2+cos[2x+sin(x)-2]}

hmmm I was looking for some constant value... but hmm, not sure there is one, so I think that'd be it
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Step-by-step explanation:

If you just divide 200/12.54, you get about 15.9 which rounds to 16.

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Step-by-step explanation: 5x-9y=17

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You can’t go any further than that because you can’t combine unlike Terms on the right side of the equation.

6 0
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LenaWriter [7]

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Step-by-step explanation:

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The answer is 103 because it’s in the “middle”

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