Answer:
Therefore r'(t) =-k sin t i + k cos t j and |r'(t)| = k so T(t) = r'(t)/|r'(t)| = -sin t i + cos t j and T'(t) = -cos t i- sin t j . This gives |T'(t)| = 1, so using this equation, we have κ(t) = |T'(t)|/|r'(t)| = 1/k.
Step-by-step explanation:
We are already given the definition of curvature and the parametrization needed to find the curvature of the circle. In genecral the curvature κ is equal to κ(t)=|T'(t)|/|r'(t)| where r(t) is a parametrization of the curve and T(t) is the normalized tangent vector respect to the parametrization, that is, T(t)=r'(t)/|r'(t)|.
Now, using the derivatives of sines and cosines, and the definition of norm, we obtain that:
r(t) = k cos t i + k sin t j ⇒ r'(t)=-k sin t i + k cos t j ⇒|r'(t)|²=sin²t+cos²t=1
T(t) = r'(t)/|r'(t)|=-sin t i +cos t j ⇒ T'(t)= -cos t i - sin t j ⇒|T'(t)|²=cos²t+sin²t=1
Answer:
x=4
Step-by-step explanation:
2x-3=5
Add 3 to both sides
2x=8
divide both sides by 2
x=4
10x+2y, this is the simplified version
Answer:
It is the hypotenuse of a right triangle with legs 5 and 12.
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. If the angle at which they meet is a right angle, then a right triangle is formed whose legs are half the length of each of the diagonals, and whose hypotenuse is the length of one side of the parallelogram (rhombus).
Here, the triangle's leg lengths are 5 and 12, so the Pythagorean theorem tells us the hypotenuse is ...
√(5²+12²) = √(25+144) = √169 = 13
Since the perpendicular diagonals are 10 and 24 inches long, the side length of the rhombus must be 13 inches long.
HK must be 13 inches because the Pythagorean theorem applies and that's what it says.
Ok rmemeber
√(a/b)=(√a)/(√b)
and
√ab=(√a)(√b)
and
(a^m)/(a^n)=a^(m-n)
so
ignore 11 for now, we will get to that at end
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