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3 years ago

Determine whether each equation represents a proportional relationship

Mathematics

2 answers:

Dmitriy789 [7]3 years ago

6 0

Answer:

2,4 and 5 are proportional the rest are not

wlad13 [49]3 years ago

4 0

Hey there! I'm happy to help!

A proportional equation follows the form y=kx, where k is the constant of proportionality.

Answer 1 is wrong because there is something added.

2 is correct as it follows this format.

3 is incorrect as it does not follow this format.

4 is correct as it follows the format (k is 1)

5 Is correct because it follows this format.

6 is not correct because there is a 1 added, which does not follow the format.

Therefore, the correct answers are 2, 4, and 5.

Have a wonderful day! :D

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Answer:

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Step-by-step explanation:

To solve the question we refresh our knowledge of the quotient rule.

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$f(x)=\frac{u(x)}{v(x)}\\$ , the derivative is express as

$\frac{df(x)}{dx}=\frac{v(x)\frac{du(x)}{dx}-u(x)\frac{dv(x)}{dx}}{v(x)^{2} }$

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we assign u(x)=lnx and v(x)=x^2

and the derivatives

$\frac{du(x)}{dx}=\frac{1}{x}\\\frac{dv(x)}{dx}=2x\\$ .

Note the expression used in determining the derivative of the logarithm function.it was obtain from the general expression of logarithm derivative i.e $y=lnx\\\frac{dy}{dx}=\frac{1}{x}$

If we substitute values into the quotient expression we arrive at

$\frac{dy}{dx}=\frac{(x^{2}*\frac{1}{x})-(2x*lnx)}{x^{4}}\\\frac{dy}{dx}=\frac{x-2xlnx}{x^{4}}\\\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

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Please consider marking this answer as Brainliest to help me advance.

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