At takeoff, the horizontal and vertical velocity of long jumper are 57.8 m/s and 5.6 m/s respectively. what is the resultant velocity

  58.071 m/s @ 5.53°

Step-by-step explanation:

The magnitude of the velocity vector can be found using the Pythagorean theorem:

  |v| = √(57.8² +5.6²) m/s ≈ 58.071 m/s

The angle of the velocity vector with respect to the horizontal can be found using the arctangent function:

  ∠v = arctan(5.6/57.8) ≈ 5.53°

So, the velocity vector is ...

  58.071∠5.53° m/s

_____

In the attached graph, the vertical scale is exaggerated, so the take-off angle looks to be greater than it actually is. "Hang time" is about 1143 milliseconds.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

111

step-by-step explanation: