Answer:
See explanations below
Step-by-step explanation:
Given the following complex numbers in polar form:
w = 2(cos(90°) + i sin (90°))
sin 90 = 1
cos 90 = 0
Substitute into the formula:
w = 2(0+i(1))
w = 2(0)+2i
w = 0+2i
Hence the value of w in rectangular form is 0+2i
For z:
z =√2(cos(225°) + i sin(225°))
z = √2(-1/√2+ i (-1/√2))
z = -√2/√2 - √2(-1/√2)i
z = -1+ 1i
Hence the value of z in rectangular coordinate is -1+ 1i
For w + z:
w + z = 0+2i + (-1+1i)
w+z = 0+2i-1+i
w+z = -1+3i
Write w+z in polar form
Get the modulus
|w+z| = √(-1)²+3²
|w+z| = √1+9
|w+z| = √10
Get the modulus
theta = tan^-1(-3)
theta = -71.56
theta = 180 - 71.56
theta = 108.43
The expression in polar form is z = √10(cos108.43+isin108.43)
The correct answer is option B which is {x | x ≤ 4.5}
<h3>What is a number line?</h3>
A number line is a representation of a graduated straight line used to represent real numbers in introductory mathematics.
Because the arrow is pointing to the left, the answer to the solution set needs to be less than the number the dot is on.
A solid dot on a number means that that number is included in the solution set.
In the picture the solid dot is on 4.5, so the solution set needs to be equal to or less than 4.5.
Therefore the correct answer is option B which is {x | x ≤ 4.5}
To know more about number lines follow
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Answer:
1) The total price, after tipping the driver 15% is 21.6
2) s = 0.75r
Step-by-step explanation:
Price of order = $24
She uses a coupon for 25% off.
Discount =
So, Cost after discount = 24-6=18
She wants to know the total price, after tipping the driver 15%.
So, Tip to driver = 15% of 24 = 3.6
So, Cost including tip = 18+3.6=21.6
Thus the total price, after tipping the driver 15% is 21.6
Now we are supposed to find equation to show the relationship between the sale price, s. and the regular price.
Let the regular price be r
Discount = 25%
So, Discounted price =
We are given that s denotes the sale price
So, s = 0.75r
Answer:
line AB is parallel to line CD
Step-by-step explanation:
Because they have the same gradient which is 2
Answer:
Quotient ( x² -4x +10)
Reminder -2
Step-by-step explanation:
We have to consider the polynomial function g(x) = x³ - 3x² + 6x + 8
Now, we have to divide g(x) by (x+1)
Let us arrange the terms of g(x) to get (x+1) as common.
x³ - 3x² + 6x + 8
= x³ +x² -4x² -4x +10x +10 -2
= x² (x +1) -4x (x +1) +10 (x +1) -2
= (x +1)( x² -4x +10) -2
Hence, if we divide g(x) by (x +1) then the quotient will be ( x² -4x +10) and the reminder will be -2. (Answer)