15.09.2020

A circle centered at the origin has a radius of 12. What is the equation of the circle

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Mathematics

A circle centered at the origin has a radius of 13. The terminal side of an angle x, intercepts the circle in quadrant IV at point C. The x coordinate of point C is 12. What is the value of sin x

Step-by-step answer

P Answered by Master

$sin x=-\frac{5}{13}$

Step-by-step explanation:

From the question we are told that:

Radius r=13

Co-ordinate of x axis at C x'=12

Let

x' represent the x axis

y' represent the y axis

Since the intercept across the radius has values on the x' and y' axis

Therefore

Generally the Trigonometric equation for cos x is mathematically given by

$cos x=\frac{x'_c}{r}$

$cos x=\frac{12}{13}$

Generally the Trigonometric equation for sin x is mathematically given by

$sin x=\sqrt{1-cos^2x}$

$sin x=\sqrt{1-(\frac{12}{13})^2}$

$sin x=\frac{5}{13}$

Since x is in the IV quadrant sin x is negative

$sin x=-\frac{5}{13}$

Mathematics

What is the equation of a circle centered about the origin with a radius of 6? Select one: A. (x)2 + (y)2 = 6 B. (x)2 − (y)2 = 6 C. (x)2 + (y)2 = 36 D. (x)2 − (y)2 = 36 E. (x)2 + (y)2 = 12

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

Given that a centre has an origin (0,0) and (5,7) at the edge.

What is the radius of the circle

This is a direct question, we can apply coordinate geometry by finding the distance between two point, .

From co-ordinate geometry, the distance between two points is

d =√[(x2-x1)² + (y2-y1)²]

So, applying this

Point 1 = (x1,y1) = (0,0)

Point 2 = (x2,y2) = (5,7)

The radius of the is

r = √[(x2-x1)² + (y2-y1)²]

r = √[(5-0)² + (7-0)²]

r = √[5² + 7²]

r = √(25 + 49)

r = √74

The correct answer is D

D. √74

Mathematics

What is the equation of a circle centered about the origin with a radius of 6? Select one: A. (x)2 + (y)2 = 6 B. (x)2 − (y)2 = 6 C. (x)2 + (y)2 = 36 D. (x)2 − (y)2 = 36 E. (x)2 + (y)2 = 12

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

Given that a centre has an origin (0,0) and (5,7) at the edge.

What is the radius of the circle

This is a direct question, we can apply coordinate geometry by finding the distance between two point, .

From co-ordinate geometry, the distance between two points is

d =√[(x2-x1)² + (y2-y1)²]

So, applying this

Point 1 = (x1,y1) = (0,0)

Point 2 = (x2,y2) = (5,7)

The radius of the is

r = √[(x2-x1)² + (y2-y1)²]

r = √[(5-0)² + (7-0)²]

r = √[5² + 7²]

r = √(25 + 49)

r = √74

The correct answer is D

D. √74

Mathematics

The equation of a circle centered at the origin is x2 + y2 = 144. what is the radius of the circle? a. 14 b. 72 c. 144 d. 12

Step-by-step answer

P Answered by Specialist

The answer is D.
(x−h)2+(y−k)2=r2

Mathematics

The equation of a circle centered at the origin is x2 + y2 = 144. what is the radius of the circle? a. 14 b. 72 c. 144 d. 12

Step-by-step answer

P Answered by Master

The answer is D.
(x−h)2+(y−k)2=r2

Mathematics

Acircle has its center at the origin, and (5, -12) is a point on the circle. how long is the radius of the circle? a.5 b.12 or c.15

Step-by-step answer

P Answered by PhD

Easy peasy

a circle centered at the origin is form
x^2+y^2=r^2
r=radius

point (5,-12) is on it
sub to find r^2

(x,y)
(5,-12)
(5)^2+(-12)^2=r^2
25+144=r^2
169=r^2
sqrt both sides
13=r

the radius is 13
answer is not listed

Mathematics

Acircle has its center at the origin, and (5, -12) is a point on the circle. how long is the radius of the circle? 5 12 13

Step-by-step answer

P Answered by PhD

Hello here is a solution :
the radius of the circle is OA A(5;-12) and O (0;0)
OA=   square root ((5-0)² + (-12-0)²)
=   square root (25+144)
=   square root(169)
OA = 13

Mathematics

Acircle has its center at the origin, and (5, -12) is a point on the circle. how long is the radius of the circle? 5 12 13

Step-by-step answer

P Answered by PhD

Check the picture below.

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 0}}\quad ,&{{ 0}})\quad 
% (c,d)
&({{ 5}}\quad ,&{{ -12}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
r=\sqrt{(5-0)^2+(-12-0)^2}\implies r=\sqrt{5^2+(-12)^2}
\\\\\\
r=\sqrt{25+144}\implies r=\sqrt{169}\implies r=13$

Acircle has its center at the origin, and (5, -12) is a point on the circle. how long is the radius