Pand s waves from an earthquake travel at different speeds, and this difference locate the earthquake "epicenter" (where the disturbance took place). assuming typical speeds of 8.8 km/s and 5.1 km/s for p and s waves, respectively, how far away did an earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.5 min apart?

the earthquake's epicenter is L = 1091.2 km away

Explanation:

if the P and S waves start from the same place (x=0) :

P would travel the distance L in , L = vP * tP

P would travel the distance L in , L = vS * tS

therefore

vP * tP= vS * tS

if the difference in time d= tS-tP → tS=d+tP , then

vS * tS= vP * tP

vS *(d+tP) = vP * tP

vS*d + vS*tP = vP * tP

vS*d = vP * tP - vS*tP = (vP - vS) * tP

tP = vS*d / (vP - vS)

replacing values

tP = vS*d / (vS - vP) = 5.1 km/s * 1.5 min*60 s/min / ( 8.8 km/s - 5.1 Km/s) = 124 s

therefore

L = vP*tP = 8.8 km/s * 124 s =  1091.2 km

lol

explanation:

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 .