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3 years ago

Refering to the equation, tell how

Mathematics

1 answer:

Ugo [173]3 years ago

5 0

Answer:

the scale factor is the vertical expansion factor.

Step-by-step explanation:

The scale factor of 2 in

g(x) = 2·F(x)

means g(x) is a <em>vertical expansion</em> (not shrink) of F(x) — by a factor of 2.

_____

<em>Additional comment</em>

The equation g(x) could be considered to be ...

g(x) = F(x·√2)

in which case g(x) could be interpreted as a <em>horizontal shrink</em> by a factor of (√2)/2. Squeezing a parabola horizontally has the same effect on its appearance as stretching it vertically.

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loris [4]

To solve the problem we must know the Basic Rules of Exponentiation.

<h2>Basic Rules of Exponentiation</h2>

$x^ax^b = x^{(a+b)}$
$\dfrac{x^a}{x^b} = x^{(a-b)}$
$(a^a)^b =x^{(a\times b)}$
$(xy)^a = x^ay^a$

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The solution of the expression is $\dfrac{4x^4}{y^6}$ .

<h2>Explanation</h2>

Given to us

$(16x^8y^{12})^{\frac{1}{2}}$

Solution

We know that 16 can be reduced to $2^4$ ,

$=(2^4x^8y^{12})^{\frac{1}{2}}$

Using identity $(xy)^a = x^ay^a$ ,

$=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}$

Using identity $(a^a)^b =x^{(a\times b)}$ ,

$=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})$

Solving further

$=2^2x^4y^{-6}$

Using identity $\dfrac{x^a}{x^b} = x^{(a-b)}$ ,

$=\dfrac{2^2x^4}{y^6}$

$=\dfrac{4x^4}{y^6}$

Hence, the solution of the expression is $\dfrac{4x^4}{y^6}$ .

Learn more about Exponentiation:

brainly.com/question/2193820

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