<span>1) Find an equation of the plane. The plane that passes through the point (2, 3, 4) and contains the line x = 4t, y = 2 + t, z = 3 − t 2) Find an equation of the plane. The plane that passes through (6, 0, −3) and contains the line x = 2 − 4t, y = 1 + 5t, z = 2 + 2t 3) Find an equation of the plane. The plane that passes through the point (1, −1, 1) and contains the line with symmetric equations x = 2y = 5z 4) Find the point at which the line intersects the given plane. x = 2 − t, y = 1 + t, z = 3t; x − y + 5z = 14 5) Find the point at which the line intersects the given plane. x = 2 + 2t, y = 3t, z = 4 − 2t; x + 2y − z + 2 = 0 6) Find the point at which the line intersects the given plane. x = y − 2 = 2z; 2x − y + 2z = 2</span>
Answer:
An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as
x(t) = x0 + A cos(ωt + φ).
The object oscillates about the equilibrium position x0. If we choose the origin of our coordinate system such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by
x(t) = A cos(ωt + φ).
A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction. Simple harmonic motion is repetitive. The period T is the time it takes the object to complete one oscillation and return to the starting position. The angular frequency ω is given by ω = 2π/T. The angular frequency is measured in radians per second. The inverse of the period is the frequency f = 1/T. The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time. It is measured in units of Hertz, (1 Hz = 1/s).
The velocity of the object as a function of time is given by
v(t) = dx(t)/dt = -ω A sin(ωt + φ),
and the acceleration is given by
a(t) = dv(t)/dt = -ω2A cos(ωt + φ) = -ω2x.
Hello! :)
P (a or b) means
P (a+b)
So the blue side and the red side of the diagram have students so add them up:
3+2=5
Then the ratio
blue and red/total number of students
5/10
(10 students)
So simplify:
1/2
Hope I helped and answered in time!
Good luck!
~ Destiny ^_^
