Mathematics: The equation x ^ 2 - 2x + y ^ 2 - 4y = 20 defines a circle in the xy-coordinate plane What is the radius of the circle?

Step-by-step explanation:RequiredThis is calculated as:Where:So:...

The equation x ^ 2 - 2x + y ^ 2 - 4y = 20 defines - id22242013776053, isabelperez063

Ответ:

dmaxbexkham

17.07.2021

Mathematics

I'll set up the problem and you can do the calculation

Step-by-step explanation:

we need to complete the squares to get the equation in the general form:

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

where h = the x coordinate of the center

k = the y coordinate of the center

r = the radius

so looking at

${x}^{2} - 2x$

we can see that if use -1 as the constant we have

${(x - 1)}^{2} = {x}^{2} - 2x + 1$

doing the same for y

${y}^{2} - 4y$

we can use -2 as the constant (basically you that the s

quare of the y coefficient )

${(y - 2)}^{2} = {y}^{2} - 4y + 4$

so now we have to add or subtract the constant on the RHS to see what the square of the radius is according to the general form of the equation at the top

20 +1+4=25

Take the square root and you have the radius

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Ответ:

cbawesome8

10.11.2020

Mathematics

(f + g)(2) = 21

Step-by-step explanation:

f(x) = -x^2 - 4x +2

g(x) = 4x^2 + 5x + 5

Required

(f + g)(2)

This is calculated as:

(f + g)(2) = f(2) + g(2)

Where:

f(2) = -2^2 - 4*2 +2 = -10

g(2) = 4*2^2 + 5*2 + 5 = 31

So:

(f + g)(2) = f(2) + g(2)

(f + g)(2) = -10 + 31

(f + g)(2) = 21

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The equation x ^ 2 - 2x + y ^ 2 - 4y = 20 defines a circle in the xy-coordinate plane What is the radius of the circle?

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