Use the formula z=a+bi=|z|(cosθ+isinθ), with |z|=√(a²+b²), and tanθ=b/a<span>
in this case, a=0, b=-3 so </span>|z|=√0²+(-3)²)=3
tanθ=
![\frac{-3}{0}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-3%7D%7B0%7D%20)
, notice the denominator is 0, undefined, so the value of θ=π/2
Substitute the values of <span>θ=π/2</span> and <span>|z|=3</span>. into the formula, you'll get <span>3(cos(</span>
![\frac{ \pi }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cpi%20%7D%7B2%7D%20)
)+isin(
![\frac{ \pi }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cpi%20%7D%7B2%7D%20)
))
To find the x-int., let y = 0 and solve for x: 13x = 6, so x = 6/13: (6/13, 0)
To find the y-int., let x =0 and read off the y-int: (0, -6)
The answer is 12 and 5
12+5=17
12X5=60
Hope that helps!
Answer:
50 and 80
Step-by-step explanation:
two numbers are in ratio 5;8 which is 5x + 8x
sum = 130
5x + 8x = 130
13x = 130 ( divide both sides by 13)
x = 10
to find the two numbers we multiply by x
5x = 5 x 10 = 50
8x = 8 x 10 = 80
'of' means multiply
1/4 of (1/4 times ) the opposite of (-) difference of 5 and a number (5-n) is lesss than 20 (<20)
1/4 times -(5-n)<20
multiply both sides by 1/4
-(5-n)<5
multiply both sides by -1 remember to flip sign
5-n>-5
add n
5>n-5
add 5
10>n
n<10
the number is any number less than 10