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noname [10]
3 years ago
9

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

Mathematics
1 answer:
Sedbober [7]3 years ago
8 0

Answer:

The equation of the circle is (x + -5)² + (y + 4)² = 100

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- If the center of the circle is point (h , k) and the length of its radius is r,

 then the equation of the circle is (x - h)² + (y - k)² = r² in standard form

* Now lets solve the problem

- The center of the circle is point (5 , -4)

∴ h = 5 and k = -4

∴ The equation of the circle is (x - 5)² + (y - -4)² = r²

∴ The equation of the circle is (x - 5)² + (y + 4)² = r²

- The circle passes through the point (-3 , 2)

- To find r substitute the x-coordinate and the y-coordinate of the

  point in the equation of the circle

∵ Point (-3 , 2) is on the circle

∴ x = -3 and y = 2

∴ (-3 - 5)² + (2 + 4)² = r² ⇒ simplify it

∴ (-8)² + (6)² = r² ⇒ solve power 2

∴ 64 + 36 = r² ⇒ add the like terms

∴ 100 = r²

∵ The equation of the circle is (x - 5)² + (y + 4)² = r²

∴ The equation of the circle is (x - 5)² + (y + 4)² = 100

- To complete the form

∴ The equation of the circle is (x + -5)² + (y + 4)² = 100

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Answer:

3/25

Step-by-step explanation:

Simplify the fraction by using common factors of numerator and denominator. Now, 12% can be written as 12/100.

4 0
3 years ago
Write an equation of the line that is parallel to 5x + 20y = 10 and passes through the point (8, 3).
Serga [27]
20y=-5x+10
y=-1/4x+1/2
y-3=-1/4(x-8)
y-3=-1/4x+2
d. y = -1/4x + 5
6 0
3 years ago
Read 2 more answers
1 + tanx / 1 + cotx =2
Lera25 [3.4K]

Answer:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 + cot(x) + tan(x) = 2

Multiply both sides of 1 + cot(x) + tan(x) = 2 by tan(x):

1 + tan(x) + tan^2(x) = 2 tan(x)

Subtract 2 tan(x) from both sides:

1 - tan(x) + tan^2(x) = 0

Subtract 1 from both sides:

tan^2(x) - tan(x) = -1

Add 1/4 to both sides:

1/4 - tan(x) + tan^2(x) = -3/4

Write the left hand side as a square:

(tan(x) - 1/2)^2 = -3/4

Take the square root of both sides:

tan(x) - 1/2 = (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

tan(x) = 1/2 + (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Take the inverse tangent of both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) = 1/2 - (i sqrt(3))/2

Take the inverse tangent of both sides:

Answer:  x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

4 0
3 years ago
Help plz i really dont understand how to do this
Svetlanka [38]

74 cause an absolute value of any number will always be positive.

7 0
3 years ago
3/2-x + 5/4-2x - 1/x-2 =4
dimaraw [331]
Is there like a question???
3 0
3 years ago
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