1 Point The circle below is centered at (-3, 2) and has a radius of 3. What is its equation?

Mathematics

1 answer:

arlik [135]3 years ago

8 0

Answer:

(x + 3)^2 + (y - 2)^2 = 9

Step-by-step explanation:

Equation for a circle: (x – h)^2 + (y – k)^2 = r^2

Step 1: Determine what h, k, and r are

h is the x value of the point: -3

k is the y value of the point: 2

r is the radius of the circle: 3

Step 2: Plug in and solve

(x – h)^2 + (y – k)^2 = r^2

(x – (-3))^2 + (y – (2))^2 = (3)^2

(x + 3)^2 + (y - 2)^2 = 9

Answer: (x + 3)^2 + (y - 2)^2 = 9

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State whether the given measurements determine zero, one, or two triangles. b=86, b=21, c=18

hammer [34]

Answer: 1

Step-by-step explanation:

I assume you meant to type $B=86^{\circ}, b=21, c=18$ .

By the Law of Sines,

$\frac{\sin C}{c}=\frac{\sin B}{b} \\ \\ \frac{\sin C}{18}=\frac{\sin 86^{\circ}}{21} \\ \\ \sin C=\frac{18 \sin 86^{\circ}}{21} \\ \\ C=\sin^{-1} \left(\frac{18 \sin 86^{\circ}}{21} \right), 180^{\circ}-\sin^{-1} \left(\frac{18 \sin 86^{\circ}}{21} \right) \\ \\ C \approx 58.77^{\circ}, 121.23^{\circ}$

Since only one of these values will make a triangle (the obtuse possibility for C will mean $B+C > 180^{\circ}$ , which violates the condition that the angles of a triangle add to 180 degrees), 1 triangle can be formed.