Answer:
Step-by-step explanation:
A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as <em>|z|).</em>
Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.
Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.
![\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bz%3D4%5B%5Ccos%20%28-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%20%2B%20i%5Csin%20%28-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5D%7D)
Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.
Hence, the complex number that has polar coordinate of (4,-45°) is
Answer:
Step-by-step explanation:
x+y = 6
y = (6-x)
7x +12y = 52
7x+12(6-x) = 52
7x +72 -12x = 52
-5x = -20
x= 4 4 days at $7 = $28
2 days at $12 = $24
28+24 = 52
Answer:
The manager can select a team in 61425 ways.
Step-by-step explanation:
The order in which the cashiers and the kitchen crews are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In how many ways can the manager select a team?
2 cashiers from a set of 10.
4 kitchen crews from a set of 15. So
The manager can select a team in 61425 ways.
Answer:
4, 6, 8, 10, 30
Step-by-step explanation:
Answer: 1350
Step-by-step explanation:
Here is the correct question.
Raquel can type an average of 63 words per minute. Rick can type 73 words per minute. how many more words can Rick type than Raquel in 135 minutes? Jared chose B as the correct answer. How did he get that answer? Jared said the answer is 4599. How did he get that answer?
Rick's word per minute= 73
Raquel's word per minute= 63
Ricks word in 135minute= 73×135 = 9855
Raquel's word in 135 minutes=63×135 = 8505
=9855 - 8505
= 1350
Rick can type 1350 more words than Raquel in 135 minutes.
Jared's answer is wrong. He got the answer by multiplying 63 by 73 which gives 4599.
