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2 years ago

A parabola is represented by the equation y2 = 5x. which equation represents the directrix?

Mathematics

1 answer:

ivann1987 [24]2 years ago

7 0

The value of the directrix is -5/4.

According to the statement

we have given that the equation of parabola is y2 = 5x. And we have to find that the which equation represents the directrix.

We know that the general equation of parabola is

(y - k)2 = 4a(x - h) -(1)

and given parabola equation is

y2 = 5x. -(2)

After comparing the both equations we get k=0 and h=0

And the formula to find the directrix is

x = h - a

Substitute the values of h and a in it then

x = 0-5/4

x = -5/4.

Here the directrix is -5/4.

So, The value of the directrix is -5/4.

Learn more about the Parabola here brainly.com/question/4061870

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Answer:

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Step-by-step explanation:

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For example, [2]3/4 = 2*4 + 3 = 11 => the fraction is 11/4.

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How do you solve this limit of a function math problem?

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If you know that

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then it's possible to rewrite the given limit so that it resembles the one above. Then the limit itself would be some expression involving $e$ .

For starters, we have

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Now use some of the properties of limits: the above is the same as

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To see why this is the case, replace $y=-z$ , so that $z\to-\infty$ as $y\to\infty$ , and

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# # #

Another way to do this without knowing the definition of $e$ as given above is to take apply exponentials and logarithms, but you need to know about L'Hopital's rule. In particular, write

$\left(\dfrac{3x-1}{3x+3}\right)^{2x-1}=\exp\left(\ln\left(\frac{3x-1}{3x+3}\right)^{2x-1}\right)=\exp\left((2x-1)\ln\frac{3x-1}{3x+3}\right)$

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$\displaystyle\lim_{x\to\infty}\left(\frac{3x-1}{3x+3}\right)^{2x-1}=\exp\left(\lim_{x\to\infty}(2x-1)\ln\frac{3x-1}{3x+3}\right)$

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and our original limit comes out to the same value as before, $\exp\left(-\frac83\right)=\boxed{e^{-8/3}}$ .

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<h3>How to determine the equation?</h3>

An exponential function is represented as:

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Where b represents the base.

The base is given as:

b = 12

So, we have:

y = (12)^x

It is vertically compressed by a factor of 1/8.

So, we have:

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When reflected across the y-axis, we have:

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