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
Derivitive of cosx=-sinx
dy/dx sinx=cosx
and use chain rue
2cosx=-2sinx
2cos2x=-4sin2x
so
-2sinx-4sin2x id the deritivitve
This is the formula of finding the hypotenuse: a² + b² = c².
So the legs would be a and b.
4² + 4² = c²
c² = 16 + 16
c² = 32
c = √32 (Option C)
