Answer:
D.) independent variable on the x-axis
Explanation:
Normally in an x-y plane, the value of x is taken as an independent variable, i.e. it is independent because it can assume any value (real number), while y depends on the value x. for example for the following equation.
y = x
Where:
x = independent value.
y = dependent value of x
This is the equation of a line, inclined with slope equal to 1.
Answer:
Explanation:
Initial kinetic energy of particle
= 1/2 m V²
= .5 x .208 x 1.26²
= .165 J
Work done by force = force x displacement
= .766 x .195
= .149 J
This energy will be added up .
Total final kinetic energy
= initial kinetic energy + work done on the particle
= .165 + .149 J
= .314 J .
Answer:
Three linear operators A,B, and C will satisfy the condition ![[[A, B],C] + [[B,C), A] + [[C, A], B] = 0](https://tex.z-dn.net/?f=%5B%5BA%2C%20B%5D%2CC%5D%20%2B%20%5B%5BB%2CC%29%2C%20A%5D%20%2B%20%5B%5BC%2C%20A%5D%2C%20B%5D%20%3D%200)
.
Explanation:
According to the question we have to prove.
Now taking Left hand side of the equation and solve.
![[[A, B],C] + [[B,C), A] + [[C, A], B]](https://tex.z-dn.net/?f=%5B%5BA%2C%20B%5D%2CC%5D%20%2B%20%5B%5BB%2CC%29%2C%20A%5D%20%2B%20%5B%5BC%2C%20A%5D%2C%20B%5D)
Now use commutator property on it as,
![=[A,B] C-C[A,B]+[B,C]A-A[B,C]+[C,A]B-B[C,A]\\=(AB-BA)C-C(AB-BA)+(BC-CA)A-A(BC-CB)+(CA-AC)B-B(CA-AC)\\=ABC-BAC-CAB+CBA+BCA-CAB-ABC+ACB+CAB-ACB-BCA+BAC\\=0](https://tex.z-dn.net/?f=%3D%5BA%2CB%5D%20C-C%5BA%2CB%5D%2B%5BB%2CC%5DA-A%5BB%2CC%5D%2B%5BC%2CA%5DB-B%5BC%2CA%5D%5C%5C%3D%28AB-BA%29C-C%28AB-BA%29%2B%28BC-CA%29A-A%28BC-CB%29%2B%28CA-AC%29B-B%28CA-AC%29%5C%5C%3DABC-BAC-CAB%2BCBA%2BBCA-CAB-ABC%2BACB%2BCAB-ACB-BCA%2BBAC%5C%5C%3D0)
Therefore, it is proved that .
The first time we read this, we think that we'll have to go look up a bunch of stuff about the gravitational constant, centripetal force, orbital mechanics, the Moon's period of revolution, and who knows whut owl !
But you know whut ? The only thing we need is Newton's 2nd law:
F = m A
Divide each side by m :
Acceleration = Force / mass
Acceleration = (2.03 x 10²⁰ Newtons) / (7.35 x 10²² kg)
Acceleration = (2.03 x 10²⁰ / 7.35 x 10²² kg) (m/s²)
<em>Acceleration = 0.00276 m/s²</em>
