The vectors x and y are unit vectors that make and angle of 30 degrees with each other. Calculate the value of | 2x + y | and the direction of 2x + y

the value of | 2x + y | = 1.39

the direction of 2x + y = 21° 

Step-by-step explanation:

Given that the vectors x and y are unit vectors that make and angle of 30 degrees with each other.

Let assume that unit vector x is along the positive x-axis, and unit vector y is at +30°.

Therefore 

2x-y=

2< 1,0 > - < cos(30),sin(30) >

=<2-(√2)/2, 0-1/2>

and

|2x-y|=√((2-(√2)/2)² + (-1/2)^2)

=1.3862 

Therefore the value of | 2x + y | = 1.39

=atan((-1/2)÷(2-(√2)/2))

=atan(1.29289/-0.5)

=-0.369 radians

= -21.143° 

Therefore the direction of 2x + y is

21° 

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

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