How many balls are there in a ski ball machine?

The position of a dragonfly that is flying parallel to the ground is given as a function of time by r⃗ =[2.90m+(0.0900m/s2)t2]i^− (0.0150m/s3)t3j^. a: at what value of t does the velocity vector of the insect make an angle of 34.0 degree clockwise from the x-axis? b: at the time calculated in part (a), what is the magnitude of the acceleration vector of the insect? c : at the time calculated in part (a), what is the direction of the acceleration vector of the insect?

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)

What sort of waves exhibit the doppler effect?