3 years ago

Convert the following common fractions to decimals. round to three decimal places if necessary. you may use a calculator.3/5 =

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

7 0

0.6 is the correct answer

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What is the standard form of the equation of the circle x2 - 2x + y2 - 8y + 1 = 0

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The standard equation of a circle is $\displaystyle{ (x-a)^2+(y-b)^2=r^2$ ,

where (a, b) is the center of the circle, and r is the radius.

So, if we write $x^2 - 2x + y^2 - 8y + 1 = 0$ in the above form, the center and the radius will be obvious to us.

Note that $x^2-2x$ is very close to $(x-1)^2=x^2-2x+1$ except for the 1.

Similarly, we notice that $y^2-8y$ is like $(y-4)^2=x^2-8x+16$ , without the 16.

So,

$x^2 - 2x + y^2 - 8y + 1 = 0\\\\(x^2 - 2x) + (y^2 - 8y) + 1 = 0\\\\(x^2 - 2x+1)-1 + (y^2 - 8y+16)-16 + 1 = 0\\\\(x-1)^2+(y-4)^2-16=0\\\\(x-1)^2+(y-4)^2=16=4^2$ .

Answer:

$(x-1)^2+(y-4)^2=4^2$

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