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2 years ago

Please solve this question fast.

Mathematics

1 answer:

Alexxandr [17]2 years ago

3 0

Answer:

See Explanation

Step-by-step explanation:

${a} = {6}^{x}, \: \: b = {6}^{y} ...(given) \\ {a}^{y}. {b}^{x} = 36..(1) \\ pluggig \: the \: values \: of \: a \: and \: b \: in \: (1) \\ ({6}^{x}) ^{y} . ({6}^{y}) ^{x} = {6}^{2} \\ {6}^{xy}.{6}^{xy} = {6}^{2} \\ {6}^{xy + xy} = {6}^{2} \\ {6}^{2xy} = {6}^{2} \\ bases \: are \: equal \: so \: exponentes \: will \: also \: be\\ \: equal \\ \therefore \: 2xy = 2 \\ xy = \frac{2}{2} \\ \huge \red { \boxed{ xy = 1}} \\ hence \: proved \\$

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Step-by-step explanation:

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3 years ago

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$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see, it went to the right 2 units, and then up 3 units.

that simply means, C = -2, D = 3.

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2 years ago