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Answer: H. 33</h3>
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Work Shown:
Solve 5m^2 = 45 for m to get
5m^2 = 45
m^2 = 45/5
m^2 = 9
m = sqrt(9)
m = 3
I'm making m to be positive so that way the expression 12m is not negative. Otherwise, sqrt(12m) would not be a real number result.
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Plug m = 3 into the expression we want to evaluate
m^3 + sqrt(12m)
3^3 + sqrt(12*3)
27 + sqrt(36)
27 + 6
33
Sadly, 14% of US smokes that’s just adult
C, because the equation of the table is y=80x. The equation for the graph is y=45x. When x is 11, you have 880 and 495. The difference is 385.
It would be 190.8 square units.
Answer:
You will obtain a complex number rotated by an angle of 45 degrees (counterclockwise) with a modulus scaled by √2
Step-by-step explanation:
In order to see the effect of multiplying z by 1 + i, you can use the representation of complex numbers in the <em>Polar Form</em>. This representation gives you the angle formed by the complex number and the real axis and the distance from the origin to the point.
Let z=a+ib represent a complex number.<em> The Polar</em> Form is:
z = |z| (Cosα + iSinα)
Where |z| is the modulus of the complex number and α is the angle formed with the real axis.
|z| = √a²+b²
α= arctan (b/a)
The multiplication in<em> Polar Form</em> is:
Let Z0 and Z1 represent two complex numbers
Z0= |Z0| (Cosα + iSinα)
z1= |z1|(Cosβ + iSinβ)
The multiplication is:
Z0.Z1 = |Z0||Z1| [Cos(α+β) + i Sin(α+β)]
Notice that when you multiply complex numbers, you are adding angles and multiplying modulus. The addition of angles can be seen as a rotation of the complex number on the plane and the multiplication of modulus can be seen as changing the modulus of the complex number.
The given number 1+i in the Polar Form is:
z = |z| (Cosα + i Sinα)
|z| = √1²+1² = √2
α = arctan(1/1) = 45°
Therefore, you will obtain a complex number rotated by an angle of 45 degrees with a modulus scaled by √2
