Answer
(3x-3)
Step-by-step explanation:
First, tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>), so if cos(<em>θ</em>) = 3/5 > 0 and tan(<em>θ</em>) < 0, then it follows that sin(<em>θ</em>) < 0.
Recall the Pythagorean identity:
sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1
Then
sin(<em>θ</em>) = -√(1 - cos²(<em>θ</em>)) = -4/5
and so
tan(<em>θ</em>) = (-4/5) / (3/5) = -4/3
The remaining trig ratios are just reciprocals of the ones found already:
sec(<em>θ</em>) = 1/cos(<em>θ</em>) = 5/3
csc(<em>θ</em>) = 1/sin(<em>θ</em>) = -5/4
cot(<em>θ</em>) = 1/tan(<em>θ</em>) = -3/4
Answer:
Step-by-step explanation:
Let 
. We have that 
if and only if we can find scalars 
such that 
. This can be translated to the following equations:
1. 
2.
3. 
Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for 
and check if the third equationd is fulfilled.
Case (2,6,6)
Using equations 1 and 2 we get
whose unique solutions are 
, but note that for this values, the third equation doesn't hold (3+2 = 5 
6). So this vector is not in the generated space of u and v.
Case (-9,-2,5)
Using equations 1 and 2 we get
whose unique solutions are 
. Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.
Answer:
50
Step-by-step explanation:
Let's drag the x line to the other side with the 14 and 48.
Then we do the Pythagorean theorem like 14^2 + 48^2 = x^2.
So then we get that x^2 is 2500
then we clearly know the square root of 2500 is 50
So 50 is our answer.
Answer:
V220 should be the answer
