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2 years ago

What is the radius of this circle if the circumference is 18 pi cm? A circle. C = 18 pi cm 3 cm 9 cm 18 cm 36 cm

Mathematics

2 answers:

nirvana33 [79]2 years ago

7 0

Answer:

the answer is 9 cm

Step-by-step explanation:

Afina-wow [57]2 years ago

6 0

Answer:

9 cm

Step-by-step explanation:

$\because \: C = 2\pi \: r \\ \\ \therefore \: 18\pi = 2\pi \times r \\ \\ \therefore \: r = \frac{18\pi}{2\pi} \\ \\ \therefore \: r =9 \: cm$

Hence, radius of circle is 9 cm.

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2 years ago

Find the standard form of the equation for the conic section represented by x^2 + 10x + 6y = 47.

Levart [38]

Answer:

The standard form of the equation for the conic section represented by $x^2\:+\:10x\:+\:6y\:=\:47$ is:

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

Step-by-step explanation:

We know that:

$4p\left(y-k\right)=\left(x-h\right)^2$ is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.

Given the equation

$x^2\:+\:10x\:+\:6y\:=\:47$

Rewriting the equation in the standard form

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

Thus,

The vertex (h, k) = (-5, 12)

Please also check the attached graph.

Therefore, the standard form of the equation for the conic section represented by $x^2\:+\:10x\:+\:6y\:=\:47$ is:

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

where

vertex (h, k) = (-5, 12)

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natta225 [31]

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$(xy)'=x^5$

Integrating both sides with respect to $x$ yields

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Since $y(1)=1$ ,

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so that

$\boxed{y(x)=\dfrac{x^5}6+\dfrac5{6x}}$

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2 years ago