It’s the first one plug it in
Answer:
{(-1,0),(-8, 9), (7,0), (1,3)}
Step-by-step explanation:
number 3 is the only one with no colliding outputs.
Answer: 12 minutes per mile
Step-by-step explanation: 20 miles) / (4 hours) = (20/4) (miles/hours) = 5 miles per hour
(4 hours) / (20 miles) = (4/20) (hours/miles) = 0.2 hours per mile
Using <span>De Moivre's formula
</span>
if z = a ( cos x + i sin x ) ⇒⇒⇒ ∴ z^n = a^n ( cos nx + i sin nx)
Part (1)
∴ [ 3 (cos 27° + i sin 27°) ]⁵ = (3⁵) ( cos 5*27° + i sin 5*27°)
= 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
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Part (2)
The angle 135° in the second quadrant ⇒ sin is (+) and cos is (-)
and its reference angle = 180° - 135° = 45°
sin 45° = cos 45°= 1/√2 = (√2)/2
∴ sin 135° = (√2)/2 and cos 135° = -(√2)/2
∴ 243 ( cos 135° + i sin 135°) = 243 [ -(√2)/2 + i (√2)/2 ]
= - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
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The correct answers are options (1) and (3)
option (1) ⇒⇒⇒ 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
option (3) ⇒⇒⇒ - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
So we have the formula:

where

is the distance in kilometers

is the petrol in liters

is the petrol consumption in kilometers per liter
We now for our problem that <span>David drove a distance of 187 km, so </span>

. We also know that he used 28 liters of petrol, so

. Lets replace those values in our formula to find the petrol consumption:



Now, remember that are some rules to determine the number of significant figures in a number:
1. Non-zero digits are always significant figures.
2. A zero between tow significant figures is always a significant figure.
Applying those tow rules we realize that

has 6 significant figures, whereas

has three significant figures and

only two. In mathematical operations with significant figures, the answer should be given with the same significant figures as the number with least significant figures involved in the operations. In our case, that number is

, and

has two significant figures, so our answer should have 2 significant figures. To give our answer with 2 significant figures, we are going to round it:


We can conclude that the patrol consumption of David's vehicle is
6.7 kilometers per liter.