Answer:
Solution : 6 + 6i
Step-by-step explanation:
This is the expression we have to solve for. Now normally we could directly apply trivial identities and convert this into standard complex form, but as the expression is too large, it would be easier to convert into trigonometric form first ----- ( 1 )
( Multiply both expressions )
( Simplify for both and )
=
( Substitute )
Now that we have this in trigonometric form, let's convert into standard form by applying the following identities ----- ( 2 )
sin(π / 4) = √2 / 2 = cos(π / 4)
( Substitute )
= =
= =
= - Therefore our solution is option a.
Note that when two lines have slopes of m₁ and m₂, then
(i) If m₁ = m₂, then the lines are parallel.
(ii) If m₁*m₂ = -1, then the lines are perpendicular.
Let us evaluate the given lines.
a. y = 4x - 1 and 12x = 3y + 7
y = 4x - 1 => m₁ = 4
Write the second equation in standard form.
3y = 12x - 7
y = 4x - 7/3 => m₂ = 4.
m₁ = m₂.
Answer: PARALLEL
b. x - 7y = 10 and 2x + 14y = 21
In standard form,
7y = x - 10 or y = (1/7)x - 10/7 => m₁ = 1/7
14y = - 2x + 21 or y = -1/7 + 3/2 => m₂ = -1/7
m₁ ≠ m₂ and m₁*m₂ ≠ -1.
Answer: NEITHER
c. 5x + 6y = 18 and 18x - 15y = 36
In standard form,
6y = -5x + 18 or y = -(5/6)x + 3 => m₁ = -5/6
15y = 18x - 36 or y = (6/5)x - 12/5 => m₂ = 6/5
m₁*m₂ = -1
Answer: PERPENDICULAR
d. x =1 and y = 1
x = 1 => m₁ is undefined
y = 1 => m₂ = 0
m₁ ≠ m₂ and m₁*m₂ ≠ -1
Answer: NEITHER
Answer:
Can you please include the complete question?
Step-by-step explanation:
it would take them 5 hours and 70 seconds
I believe the answer is 0.53