A positively charged particle is at rest on the positive z-axis in reference frame S. Reference frame S′ is moving along the positive x-axis of S, reference frame S′′ is moving along the negative x-axis, and reference frame S′′′ is moving along the positive y-axis, all with speed v relative to S. The axes of all the reference frames are oriented the same way, and their origins coincide at instant t = 0, when observers in each reference frame make measurements.
In which reference frames do observers measure an electric field?
Check all that apply.

a) S b) S′ c) S′′ d) S′′′

im sorry i dont know

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.