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4 years ago

What is x^3=8/27? pls help

Mathematics

1 answer:

yaroslaw [1]4 years ago

4 0

Answer:x=2/3 =0.6667

Step-by-step explanation:

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Find the points on x^2+3(y-2)^2 = 27 which are closest to and farthest from the origin

maria [59]

$(-4.89, 3)$ and $(4.89, 3)$ are the farthest from the origin and $(0, -1)$ is the closest from the origin.

Let be a curve of the form $x^{2}+3\cdot (y-2)^{2} = 27$ . The distance with respect to origin is found by using the following Pythagorean identity:

$r = x^{2}+y^{2}$ (1)

Where $r$ is the square distance function.

We can modify (1) as following:

$r = [27-3\cdot (y-2)^{2}]+y^{2}$

$r = 27-3\cdot (y^{2}-4\cdot y +4)+y^{2}$

$r = 27-3\cdot y^{2}+12\cdot y -12 + y^{2}$

$r = -2\cdot y^{2}+12\cdot y+27$ (1b)

Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:

First derivative test

$-4\cdot y +12 = 0$

$y = 3$

Second derivative test

$r'' = -4$

The y-component represents a maximum.

Now we graph the function with the ressource of a graphing tool, we find the following points:

Farthest points: $(-4.89, 3)$ , $(4.89, 3)$ .

Closest points: $(0, -1)$ .

$(-4.89, 3)$ and $(4.89, 3)$ are the farthest from the origin and $(0, -1)$ is the closest from the origin.

To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943

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olasank [31]

Answer:

its s

Step-by-step explanation:

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Alchen [17]

Answer:

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Step-by-step explanation:

sorry if those are the only answer choices then I do not know how to help

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3 years ago

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aniked [119]

Your answer is 123.3 because the hundreths (4) is under 5, so you round down.

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4 years ago

What is the slope of the line y = 3x + 5? -3 -5 5 3

melomori [17]

Answer:

The slope is 3

Step-by-step explanation:

The number before the x is always the slope

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3 years ago