Answer:
The length of the chord is 16 cm
Step-by-step explanation:
Mathematically, a line from the center of the circle to a chord divides the chord into 2 equal portions
From the first part of the question, we can get the radius of the circle
The radius form the hypotenuse, the two-portions of the chord (12/2 = 6 cm) and the distance from the center to the chord forms the other side of the triangle
Thus, by Pythagoras’ theorem; the square of the hypotenuse equals the sum of the squares of the two other sides
Thus,
r^2 = 8^2 + 6^2
r^2= 64 + 36
r^2 = 100
r = 10 cm
Now, we want to get a chord length which is 6 cm away from the circle center
let the half-portion that forms the right triangle be c
Using Pythagoras’ theorem;
10^2 = 6^2 + c^2
c^2 = 100-36
c^2 = 64
c = 8
The full
length of the chord is 2 * 8 = 16 cm
Answer:
Slope is 2/3
Step-by-step explanation:
What you can do is use the first two coordinates. This would get the formula to look like this:
From here you get ⅔ for the slope.
Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
Answer:
id say b
Step-by-step explanation:
but i mean idk really
