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2 years ago

What is the image of O(1,4) after two reflections, first across the line y = 4, and then across

Mathematics

1 answer:

natulia [17]2 years ago

6 0

Answer:

A. (-5,4)

Step-by-step explanation:

A reflect on y=4 does not affect point (1,4) since it is on y=4

So a reflect on itself is the same

A reflection of x= -2 is trickier

Since the distance between x=-2 and (1,4) is 3 (I am only counting x-axis the distance between -2 and 1 is 3)

So we have to start at (-2,4) (Since the y-axis, "4" didn't change) and move it 3 points to the left

Which is (-5,4)

Thus A

Hope this helps!

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wlad13 [49]

Answer:

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Step-by-step explanation:

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

For a function f(x) express as a ratio of another functions u(x) and v(x) i.e

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

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

from $y=lnx/x^{2}$

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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Answer:

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