Answer:
Cartesian
z₁= 3 +4*j
z₂= 2 +3*j
Polar
z₁=5 * e^ (0.927*j)
z₁=√13 * e^ (0.982*j)
Step-by-step explanation:
for the complex numbers z the cartesian form of is
z= x + y*j
then
1) z₁= 3 +4*j (cartesian form)
2) z₂= 2 +3*j (cartesian form)
the polar form is
z= r* e^jθ
where
r= √(x²+y²) → r₁ = √(3²+4²) = 5 , r₂ = √(2²+3²) = √13
and
θ = tan⁻¹ (y/x) → θ₁ = tan⁻¹ (4/3)= 0.927 rad , θ₂ = tan⁻¹ (3/2)= 0.982 rad
then
z₁=5 * e^ (0.927*j)
z₁=√13 * e^ (0.982*j)
Answer:
The last option: 3 x (7 + 2) = (3 x 7) + (3 x 2)
Step-by-step explanation:
There is addition on the inside, and you are distributing the multiplication from the outside.
38 is the answer because 25+13=38
Use the z-score:
112 - 100
For 112, the z-score is --------------- = 12/15, or 0.8.
15
Next, find the AREA under the standard normal curve TO THE LEFT OF 0.8.
Use either a z-score table or a calculator for this purpose.
Using my calculator, I found that this area is 0.532. That places 112 in the 53rd percentile.
82 would be in a lower percentile: the 12th percentile.
Let me know if you have questions about how to use a calculator to do these calculations.
Answer:12, 84 and 84
Step-by-step explanation:
since we know 3 angles of a triangle = 180 degrees
1 angle = 12 degrees
12 + x + x = 180
12 + 2x = 180
2x= 180 - 12
2x = 168
x = 168/2
x = 84 degrees
Hope it helps! Mark it as Braniest
