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kolbaska11 [484]
2 years ago
9

What is the center and radius of x^2+6x+y^2-4y =-4?​

Mathematics
1 answer:
Nat2105 [25]2 years ago
7 0

Answer:

The center of this circle is at (-3,\, 2). The radius of this circle is 3.

Step-by-step explanation:

A circle with center (a,\, b) and a radius of r (r > 0) could be expressed as:

(x - a)^{2} + (y - b)^{2} = r^{2}.

(In other words, a point is on this circle if and only if the distance between that point and the center is equal to the radius.)

Rearrange this equation using binomial expansion to match the equation given in this question:

(x^{2} - 2\, a\, x + a^{2}) + (y^{2} - 2\, b\, y + b^{2}) = r^{2}.

x^{2} + (-2\, a)\, x + y^{2} + (-2\, b)\, y = -a^{2} - b^{2} + r^{2}.

The equation in this question is:

x^{2} + 6\, x + y^{2} + (-4)\, y = -4.

Match up the coefficients of x and y in the two equations.:

  • Coefficient of x: (-2\, a) = 6.
  • Coefficient of y: (-2\, b) = (-4).

Thus, a = (-3) and b = 2.

The constants of the two equations should also match up:

(-a^{2} - b^{2} + r^{2}) = (-4).

Substitute in a = (-3) as well as b = 2 and solve for r:

r^{2} = 9.

r = 3 (since r > 0.)

Therefore, the center of this circle is (-3,\, 2). The radius of this circle is 3.

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Answer:

Step-by-step explanation:

Total cake shared=1/2

Pete share=x

Bill= twice as much as Pete

=2x

Pete's share+ Bill's share=total share

x+2x=1/2

3x=1/2

x=1/2÷3

x=1/2×1/3

=1/6

Pete's share=x=1/6

Bill's share=2x

=2(1/6)

=2/6

=1/3

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3 years ago
Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle encl
katovenus [111]

Answer:

The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units

Step-by-step explanation:

The given parameters in the question are;

The radius of the circle, r = 11

The length of the chord PL = 16

The measure of angle ∠PAL = 93°

The segment of the circle for which the area is required = Minor segment PL

The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL

The area of a segment of a circle is given by the following formula;

Area of segment = Area of the sector - Area of the triangle

In detail, we have;

Area of segment = Area of the sector of the circle that contains the segment) - (Area of the isosceles triangle in the sector)

Area of a sector = (θ/360)×π·r²

Where;

r = The radius of the circle

θ = The angle of the sector of the circle

Plugging in the the values of <em>r</em> and <em>θ</em>, we get;

The area of the sector enclosed by arc PL and radii AP and AL = (93°/360°) × π × 11² ≈ 98.2 square units

Area of a triangle = (1/2) × Base length × Height

Therefore;

The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units

∴ The area of the segment PL ≈ (98.2 - 60.58) square units = 37.62 square units

Therefore, the area of the shaded segment PL ≈ 37.62 square units

More examples on area of a shaded segment can be found here:

brainly.com/question/22599425

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2 years ago
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Marta_Voda [28]

Answer:

B

Step-by-step explanation:

the question is asking to name any point, B is a point that falls on the graph

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