101. consider two wave functions that differ only by a phase shift, y1(x, t)=acos(kx−ωt)y1(x, t)=acos(kx−ωt) and y2(x, t)=acos(kx−ωt+ϕ).y2(x, t)=acos(kx−ωt+ϕ). use the trigonometric identities cosu+cosv=2cos(u−v2)cos(u+v2)cosu+c osv=2cos(u−v2)cos(u+v2) and cos(−θ)=cos(θ)cos(−θ)=cos(θ) to find a wave equation for the wave resulting from the superposition of the two waves. does the resulting wave function come as a surprise to you?

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

70 years.

step-by-step explanation: