Simplify Derivation + Integration

A spelunker is surveying a cave. She follows a passage 160 m straight west, then 230 m in a direction 45degree east of south, and then 280 m at 30 degree east of north. After a fourth unmeasured displacement, she finds herself back where she started.

Suppose a person walks so that their displacement is represented by a vector that has a magnitude of 52m (vector A). The direction of that initial displacement is 31 degrees north of east. After that, the person then walks 15 m due west (vector B).  Use trig to calculate the east and north components of the first displacement, vector A.

In the next sets, you are given the magnitude and one component. There is an ambiguity in determining the vector, because you can only determine the absolute value of the other component and not its sign; therefore, there are two possibilities. In these tables, you must enter the absolute value of the component and provide two angles for the vector, the first one assuming the other component is positive and the other assuming the component is negative. You must also provide two angles for the antiparallel vector in the same order. Set Set 5a 5b 6a 6b Ax |Axl 32 -26 Ayl Ay SENECIENTE 42 -21 Magnitude of A 62 62 Magnitude of A 72 64 Angle of A Angle of A 0 0 (pos A) (neg Ay) (pos Ay) (neg Ay) (pos A) (neg Ax) (pos A) (neg Ax) Angle of -A Angle of -A 0 0 (pos Ay) (neg A,) (pos Ay) (neg Ay) (pos A) (neg Ax) (pos A) (neg A₂)

Please solve correctly. Thank you!

d²y Let 4 - 5y = 0, suppose the solution has the form y = e1x. - dx2 dx Find the Characteristic Equation of å and find the roots of the equation.

Suppose you walk 14.5 m in a direction exactly 19° south of west then you walk 22 m in a direction exactly 39° west of north. How far are you from your starting point in m? Please explain how you got your answer in detail.

A bear, searching for honey wanders 30 meters south, then 15 meters west. Frustrated, he wanders another 14 meters north and then 5 meters east. Calculate the magnitude of bear's displacement. Round the answer to three significant figures.

A woman walks 229m in the direction 39 degrees east of north, then 170m directly east. Find (a) the magnitude and (b) the angle (from due east) of her final displacement from the starting point. (c) Find the distance she walks.             Needs Complete typed solution with 100 % accuracy.

bn nas set his GPS to track his route. At the end of his hike, his GPS indicates that he walked 3.50 miles north, 1.00 miles at 45 degrees north of east, and 1.50 miles south. How far away is Bill from his starting position? And in what direction is he? Provide the direction in number of degrees in reference to the cardinal directions (North of East, South of West, etc.).