Answer:
12.56 square units
Step-by-step explanation:
The formula for circumference is
C = 2πr
Our circumference is 12.56. Using 3.14 for π, we have
12.56 = 2(3.14)r
12.56 = 6.28r
Divide both sides by 6.28:
12.56/6.28 = 6.28r/6.28
2 = r
The area of a circle is given by the formula
A = πr²
Using 3.14 for π and our radius of 2, we have
A = 3.14(2²) = 3.14(4) = 12.56.
By using <span>Euler’s formula which state that:
e∧(iΘ) = cos Θ + i sin Θ
So, z₁ = 2 ( cos π/6 + i sin </span>π/6 ) = 2 e∧(i <span>π/6)
And </span><span>z₂ = 3 ( cos π/4 + i sin π/4 ) = 3 e∧(i <span>π/4)
Then </span></span>z₁ * z₂ = 2 e∧(i π/6) * <span>3 e∧(i π/4) = 6 </span><span>e∧[i (</span><span>π/6 + π/4)]
= </span><span>6 e∧(i 5<span>π/12)
= 6</span></span><span> ( cos 5π/12 + i sin 5π/12 )</span>
Answer:
Step-by-step explanation:
Slope intercept form of a line is expressed as
y=mx+b. (where m=slope and b=y intercept)
The only answer that is in this form is the top one
y=3x-2
Slope-intercept form is y=mx+b, where m is the slope, and b is the y-intercept.
So, to convert x+6y=-2, you have to isolate y. Your first step is to move the x to the other side. To do this, you subtract 1x from both sides:
6y=-x-2
Your final step is to divide both sides by 6:
y=-1/6x+1/3
Hope this helps :-)
The filling rate of the first tank is this:

The filling rate of the second tank is this:

Add them to get the combined rate:

Make a common denominator by multiplying the first fraction by 2/2:

Adding them together, we get:

So, now we know that the combined rate is 3 tanks per 2 hours... but we need to know how long it will take to fill only one tank. So, we need to find the unit value, which we do by doing this:

Then we can cross-multiply:

And divide both sides by 3 to get our final answer:

So, it takes 2/3 of an hour, or 40 minutes.
Hope I helped, let me know if you have any questions :)