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?

Expresa commuter train leaves downtown sation and travels at a average speed of 55 miles per hour towards the north side sation, which is 50miles away. thirty minutes later, express commuter train #7 leaves north side and travels at a average speed of 35miles per hour towards downtown sation. at the moment the two trains pass each other, how far(in miles) is train #12 from the downtown sation and how long(in minutes) has the #12 train been traveling

If the discriminant if a quadratic equation is 4 which statement describes the roots?

Atriangle has side lengths of x, x+11, and 3x+5. what is the perimeter? a. 3x^2 + 38x + 55 b. 4x + 16 c. 5x + 16 d. 3x^3 + 38x^2 + 55x