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2 years ago

What is the solution to the equation -4(2x + 3) = 2x + 6 - (8x + 2)?

Mathematics

1 answer:

MrRa [10]2 years ago

4 0

Answer:

B. x = -8

Step-by-step explanation:

-4(2x + 3) = 2x + 6 - (8x + 2)

-8x -12 = 2x + 6 - 8x -2

(now, "-8" in both terms is cancelled):

-12 = 2x + 6 - 2

(leave 2x alone in second term):

-12 -6 +2 = 2x

-16 = 2x

-16/2 = x

-8 = x

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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

Enter the answer in the space provided.

Dennis_Churaev [7]

Answer:

Part 1: 1 mile.

Part 2: 1.32 mph.

Step-by-step explanation:

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2 years ago

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In developing an interval estimate for a population mean, a sample of 50 observations was used. the interval estimate was 19.76

alexandr402 [8]

The formula for interval estimate would be: μ = M ± Z(sM)

Where: μ is estimate

M is the mean

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(sM) is the standard error

μ = M ± Z(sM)

n = 200 rather than 50 (√200 = 2√50)

⇒ ME = (1/2) * 1.32 = .66

Using the formula above, plugging this in will give us: μ = 19.76 ± .66

= 19.76 ± .66 is the confidence interval or interval estimate

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2 years ago

Which polynomials are prime? Check all that apply. 2x2+ 7x + 1 5x2 – 10x + 5 3x2 + 8 4x2 – 25 x2 + 36

aleksley [76]

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Feliz [49]

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2 years ago

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