Find the greatest common factor. 4x3a2 + 4x2a3

Mathematics

1 answer:

Ulleksa [173]2 years ago

6 0

Answer:

the greatest common factor for this equation is:

4x^2a^2(x + a)

Step-by-step explanation:

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The variable complex number z is given by z=1+cos 2θ+isin2θ,where θ takes all values in the interval −1/2π<θ<1/2π

FinnZ [79.3K]

The given complex number is
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π

Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ

Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)

Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN

Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]
$\frac{1}{z} = \frac{(1+cos2\theta - i\, sin2\theta)}{(1 + cos 2\theta + i\, sin 2\theta)(1+cos2\theta - i \,sin2\theta)}\\ = \frac{1+cos2\theta - i \,sin 2\theta}{(1+cos2\theta)^{2} + sin^{2}2\theta}$

The denominator is
$(1+cos2\theta)^{2}+sin^{2}2\theta \\ = 1+2cos2\theta+cos^{2}2\theta+sin^{2}2\theta \\ =2cos2\theta+2 \\ = 2(1+cos2\theta)$

Therefore
$\frac{1}{z} = \frac{1}{2} -i \frac{sin2\theta}{2(1+cos2\theta)}$

The real part of 1/ = 1/ (constant).

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2 years ago

On Monday, Amie rides her bike from home to school. After school, she bikes to work. After work, she bikes home. Based on the in

AfilCa [17]

To get a full answer we would need the diagram but to solve it I would find the distances between her house and school and add that to the distance from her school to her work then from her work home if Thier isn't information for her distance from work to her home I would double the amount that she already went

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2 years ago

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Solve y = 7x-3w for x

lorasvet [3.4K]

Y=7x-3w
y+3w=7x
y+3w/7=x

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2 years ago

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A recent study of 500 American males aged 18-21 found that 237 had 1 ticket in the past year, 112 had 2 tickets in the past year

Jobisdone [24]

Answer:

<em>The expected number of tickets is 1.273</em>

Step-by-step explanation:

<u>Expected Value of a Discrete Probability Distribution</u>

Given a discrete distribution with values

x={x1,x2,x3,...,xn}

And respective probabilities

p={p1,p2,p3,...pn}

The expected value EX of the entire distribution is

$EX=\sum_{i}x_i.p_i$

The recent study of American males provides an approximate distribution of probabilities based on the number of tickets they had past year, according to the following data:

237 had 1 ticket

112 had 2 tickets

17 had 3 tickets

5 had 4 tickets

1 had 5 tickets

The total number of tickets is 237+112+17+5+1=372

Taking the number of tickets as the independent variable, then

x={1,2,3,4,5}

Each probability can be found as the relative frequency of the number of tickets as follows:

$\displaystyle p_1=\frac{237}{372}=0.637$