Using principles from physics it can be shown that when a cable is hung between two poles, it takes the shape of a curve y = f(x) that satisfies the differential equation d'y pg dy 2 1 + dx dx2 where p is the linear density of the cable, g is the accelera- tion due to gravity, T is the tension in the cable at its lowest point, and the coordinate system is chosen appro- priately. Verify that the function T cosh Pg pgx y = f(x) T is a solution of this differential equation.

A force vector has components given by F = -7.45 N and F. = 4.40 N. Find the following. y (a) the magnitude of the force (b) the direction of the force, measured counterclockwise from the positive x-axis O counterclockwise from the +x-axis Nond H n

1.Given the diagram of vectors v and w below (a) Use the graph to geometrically find v + w (b) Use the graph to geometrically find v – w (c) Write v in component form: _____________ (d) Write w in component form: _____________ (e) Algebraically calculate the sum v + w

Answer must be in standard form scientific notation with SI units that do not have prefixes ( except for kg.) all angles and directions must be calculated to the nearest 0.1 deg. (Tenth of a degree) and entered in standard form scientific notation.

Imagine that you take the cross product A x B, where A=2x + 74 and B=2x + € + 1ŷ. What is the z-component of the resulting vector?

Vector a = <-1,4,0> and vector b =<4,-4,1>. Find the cross product of a X b

check answers pls

A graph of x vs. t4, with x on the vertical axis and t4 on the horizontal axis, is linear. Its slope is 51 m/s4 and its vertical-axis intercept is 8 m. Write an equation for x as a function of t. x = (8 m )t 4 − 51 m/s 4    x = (51 m/s 4 )t 4 + 8 m    x=(51 m/s48 m)t4x=51 m/s48 mt4     x = (8 m )t 4 + 51 m/s 4