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soldi70 [24.7K]
2 years ago
15

Express the sum or difference as a product. sin 4x - sin 6x

Mathematics
2 answers:
max2010maxim [7]2 years ago
7 0

Answer:

sin 4x - sin 6x  = -2 cos 5x . sin x

Step-by-step explanation

We use the following result to solve this expression,

sin\,A-sin\,B=2\,cos\,(\frac{A+B}{2})\,sin\,(\frac{A-B}{2})

and sin(-x) = -sin x

Consider,

sin 4x - sin 6x

=2\,cos\,(\frac{4x+6x}{2})\,sin\,(\frac{4x-6x}{2})

=2\,cos\,(\frac{10x}{2})\,sin\,(\frac{-2x}{2})

=2\,cos\,5x\,sin\,(-x)

=2\,cos\,5x\,(-sin\,x)

=-2\,cos\,5x\,sin\,x

Therefore, sin 4x - sin 6x  = -2 cos 5x . sin x

allsm [11]2 years ago
5 0
Hello,

Since:
sin (a)- sin(b)=cos( \frac{a+b}{2}) sin( \frac{a-b}{2} )\\

sin(4x)-sin(6x)=-(sin(6x)-sin(4x))=-2 cos(5x) sin(x)\\


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katrin [286]

Answer:

The 95% confidence interval for the true proportion of all voters in the state who favor approval is (0.4384, 0.5050).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 865, \pi = \frac{408}{865} = 0.4717

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4717 - 1.96\sqrt{\frac{0.4717*0.5283}{865}} = 0.4384

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4717 + 1.96\sqrt{\frac{0.4717*0.5283}{865}} = 0.5050

The 95% confidence interval for the true proportion of all voters in the state who favor approval is (0.4384, 0.5050).

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3 years ago
Avery bought a washing machine originally priced at $864.72 but on sale for 30% off. After 4% sales tax, what was the total cost
atroni [7]

Answer: 629.51

Step-by-step explanation: 30% of 864.72 is 259.416

864.72 - 259.416 = 605.304      4% of 605.3 = 24.212     605.3 + 24.21 = 629.51

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