The cosh function can be used to describe the curve that a rope hanging between two poles assumes (called a catenary, it is also the shape of the st. louis archa ). suppose a hanging cable is parameterized by `(x) = hx,(28.46) cosh(x/(28.46))i for x ∈ [−50, 50] where x is measured in meters. determine the length of the cable.

Suppose that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?

Identify some abiotic characteristics of the tundra biome.

Objects a and b are visible in the night sky. six months later they are still visible, but object b shows less parallax than object a. which object is closer? a. a b. b c. you would need to wait another six months in order to figure this out. d. you would need to know the objects' angular diameters in order to figure this out.