Answer:
Step-by-step explanation:
Firstly, note that -2i really is just z = 0 + (-2)i, so we see that Re(z) = 0 and Im(z) = -2.
When we're going from Cartesian to polar coordinates, we need to be aware of a few things! With Cartesian coordinates, we are dealing explicitly with x = blah and y = blah. With polar coordinates, we are looking at the same plane but with angle and magnitude in consideration.
Graphing z = -2i on the Argand diagram will look like a segment of the y axis. So we ask ourselves "What angle does this make with the positive x axis? One answer you could ask yourself is -90°! But at the same time, it's 270°! Why do you think this is the case?
What about the magnitude? How far is "-2i" stretched from the typical "i". And the answer is -2! Well... really it gets stretched by a factor of 2 but in the negative direction!
Putting all of this together gives us:
z = |mag|*(cos(angle) + isin(angle))
= 2*cos(270°) + isin(270°)).
To verify, let's consider what cos(270°) and sin(270°) are.
If you graph cos(x) and look at 270°, you get 0.
If you graph sin(x) and look at 270°, you get -1.
So 2*(cos(270°) + isin(270°)) = 2(0 + -1*i) = -2i as expected.
Let, length and breadth of rectangle is L and B respectively.
It is given that :
The length rectangle is 4 cm more than 3 times the width of the rectangle.
L = 3B + 4 ......1 )
Also, area of square = area of the rectangle + 66
L² = LB + 66
Putting value of L from
L² = ( 3B + 4 )( B ) + 66
L² = 3B² + 4B + 66
( 3B + 4 )² = 3B² + 4B + 66
9B² + 16 + 24B = 3B² + 4B + 66
6B² + 20B - 50 = 0
3B² + 10B - 25 = 0
3B² + 15B - 5B -25 = 0
3B( B + 5 ) -5( B + 5 ) = 0
B = 5/3 units
L = 3( 5/3 ) + 4
L = 5 + 4 = 9 units
Hence, this is the required solution.
Answer:
1 + i
Step-by-step explanation:
Given that A is a 3 * 3 singular matrix
one of its eigenvalue ( λ1 ) = 1 - i
Given that the determinant of a singular matrix is = 0
therefore the second eigen value ( λ2 ) = 1 + i
1 - i + 1 + i = 0
Answer:
B
Step-by-step explanation:
We know that it costs 37 cents to mail a letter that weighs 1 oz or less. This would mean that for x ≤ 1, P(x) should equal 37. Already, we can eliminate A and D.
We also know that it costs an additional 26 cents for at most another ounce added to the original 1 ounce. This means that for 1 < x ≤ 2, P(x) = 26 + 37 = 63. This is shown by B.
Thus, the answer is B.
<em>~ an aesthetics lover</em>
Y=mx+b, the b is your y-intercept so just rearrange your equation
y=(3/7)x+(2/7)
your y-intercept would be b) (2/7)
