Mathematics, 30.06.2019 09:00 ghazanfarwaheed7967

Acircle with center c(4,-20 contains point d(8,1) what is the equation of a line perpendicular to the radius of a circle passing through point c

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Answer from: sallylove03

$y=-\frac{4}{21}x-\frac{404}{21}$

Step-by-step explanation:

we know that

the segment CD is the radius of the circle

Step 1

Find the slope of the segment CD

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$C(4,-20)\ D(8,1)$

Substitute the values

$m=\frac{1+20}{8-4}$

$m=\frac{21}{4}$

Step 2

Find the slope of the line perpendicular to the radius of the circle

we know that

If two lines are perpendicular. then the product of their slopes is equal to minus one

m1*m2=-1

we have

$m1=\frac{21}{4}$

substitute and solve for m2

$\frac{21}{4}*m2=-1$

$m2=-\frac{4}{21}$

Step 3

Find the equation of the line perpendicular to the radius of a circle passing through point c

we have

$m2=-\frac{4}{21}$

C(4,-20)

The equation of the line into point-slope form is equal to

y-y1=m(x-x1)

substitute the values

$y+20=-\frac{4}{21}(x-4)$

$y=-\frac{4}{21}x+\frac{16}{21}-20$

$y=-\frac{4}{21}x-\frac{404}{21}$

Answer from: Quest

Suredude why not right

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

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Acircle with center c(4,-20 contains point d(8,1) what is the equation of a line perpendicular to th...