a student walks 50m on a bearing 0.25 degrees and then 200m due east how far is she from her starting point.​

Step-by-step explanation:

I'm going to use Physics here for this concept of vectors. Here are some stipulations I have set for the problem (aka rules I set and then followed throughout the problem):

** I am counting the 50 m as 2 significant digits even though it is only 1, and I am counting 200 as 3 significant digits even though it is only 1. 1 sig dig doesn't really give us enough accuracy, in my opinion.

** A bearing of .25 degrees is measured from the North and goes clockwise; that means that measured from the x axis, the angle is 89.75 degrees. This is the angle that is used in place of the bearing of .25 degrees.

** Due east has an angle measure of 0 degrees

Now let's begin.

We need to find the x and y components of both of these vectors. I am going to call the first vector A and the second B, while the resultant vector will be C. Starting with the x components of A and B:

so

so

and we need to add those results together. Due to the rules for adding significant digits properly, the answer is

(and remember I am counting that as 3 sig fig's even though it's only 1).

Now for the y components:

so

(which I'm counting as 2 sig fig's)

so

and we need to add those results together.

Now for the resultant magnitude:

 and that gives us a final magnitude of

m

Now for the angle:

Since both the x and y components of the resultant vector are in quadrant 1, we don't need to add anything to the angle to get it right, so

The girl is 206 meters from her starting point at an angle of 14 degrees

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.

using pemdas, (order of operations) you'll see the answer is 24.