A boy walks 40m from a city X on a bearing of 040° to a city Y. She then walks 40m on a bearing of 140° to a city Z. Find the bearing of Z from city X.
a) 35°
b) 50°
c)90°

option C.

Step-by-step explanation:

If city X is in the point (0,0)

Now, we can use that a displacement of L in distance with an angle A, gives us that the components of the displacement are:

X = L*cos(A)

Y = L*sin(A)

So we know that the city Y is located in:

(40m*cos(40°), 40m*sin(40°))

Now, from this point he moves other 40m with an angle of 140°.

The new position is

(40m*cos(40°) + 40m*cos(140°), 40m*sin(40°) + 40m*sin(140°))

this is:

40m*(cos(40°) + cos(140°), sin(40°) + sin(140°)) = 40m*( 0, 1.28)

the new position is (0, 51.2m)

This means that for a new displacement L and angle A we have:

X = L*cos(A) = 0

Y = L*sin(A) = 51.2m

Cos(A) is only 0 when A = 90° or 270°,

and we know that sin(90°) = 1 and sin(270°) = -1

As we have a positive number in the Y equation, we can conclude that A must be 90°.

Then

Y = L*sin(90°) = L = 51.2m

Here we finded that the bearing of Z from city X is 90°

why do wages differ across industries

step-by-step explanation :

micro economists are concerned with economics on an industry or individual firm basis.

macro economists are concerned with national and international level

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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