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3 years ago

The equation of a circle is x^2+y^2-12y+27=0

Mathematics

1 answer:

Ksivusya [100]3 years ago

3 0

The equation in graphing form:

$(x-h)^2+(y-k)^2=r^2$

Use: $(*)\ a\pm b)^2=a^2\pm2ab+b^2$

$x^2+y^2-12y+27=0\\\\x^2+y^2-2\cdot y\cdot6+27=0\\\\x^2+\underbrace{y^2-2\cdot y\cdot6+6^2}_{(*)}-6^2+27=0\\\\x^2+(y-6)^2-36+27=0\\\\x^2+(y-6)^2-9=0\ \ \ \ |+9\\\\x^2+(y-6)^2=9$

Answer: d) x^2+(y-6)^2=9

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We can solve this by drawing a triangle with three points. The first point at Fort Collins (F), the second at Cheyenne (C) and the third at Laramie (L).

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3 years ago

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X=24

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Cube A has a volume of 9 in3. Cube B has a volume of 5 in3. Which of the following expresses the ratio of the side length of Cub

Troyanec [42]

Using the formula for the volume of a cube, it is found that the expression which gives the ratio of the side length of Cube A to the side length of Cube B is:

$r = \frac{3^{\frac{2}{3}}}{5^{\frac{1}{3}}}$

Which means that option E is correct.

The <em>volume of a cube</em> of side length l is given by:

$V = l^3$

For Cube A, the volume is of 9 cubic inches, hence:

$l_a^3 = 9$

$l_a = \sqrt[3]{9}$

$l_a = 9^{\frac{1}{3}}$

$l_a = 3^{\frac{2}{3}}$

For Cube B, the volume is of 5 cubic inches, hence:

$l_b^3 = 5$

$l_b = \sqrt[3]{5}$

$l_b = 5^{\frac{1}{3}}$

Then, the ratio is:

$r = \frac{l_a}{l_b} = \frac{3^{\frac{2}{3}}}{5^{\frac{1}{3}}}$

To learn more about the volume of a cube, you can take a look at brainly.com/question/13030328

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