Giải phương trình: Sin^4 x - cos^4 x =1/2

Mathematics

2 answers:

tamaranim1 [39]2 years ago

5 0

Hello,

$cos^4(x)=(cos^2(x))^2=(1-sin^2(x))^2=1+sin^4(x)-2*sin^2(x)\\\\sin^4(x)-(1+sin^4(x)-2sin^2(x))=\dfrac{1}{2} \\\\1-2sin^2(x)=\dfrac{1}{2} \\\\\\sin^2(x)=\dfrac{1}{4} \\\\sin(x)=\dfrac{1}{2} \ or\ sin(x)=-\dfrac{1}{2} \\\\\\modulo\ 2\pi: \\\\x=\dfrac{\pi}{6}\ or\ x=\dfrac{5*\pi}{6}\ or\ x=-\dfrac{\pi}{6}\ or\ x=-\dfrac{5*\pi}{6}$

Sliva [168]2 years ago

4 0

Step-by-step explanation:

...........MaRk As BrAiNeSt

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Eduardwww [97]

Answer: 47.4 yds.

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A=40

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We gonna use the Pythagorean theorem to solve this problem

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2 years ago

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yKpoI14uk [10]

Answer:

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Step-by-step explanation:

the mean is given by:

$\overline{x} = \dfrac{\sum\limits_{i=1}^n x_i}{n} \quad\text{or}\quad \dfrac{\text{sum of all items}}{\text{number of items}}$

In our case this is:

$\overline{x} = \dfrac{19+15+6+11+24}{5} \Rightarrow \dfrac{75}{5}\\\\\overline{x} = 15\\\\$

side note: the main difference between sample mean and population mean is in the 'context'. However, the method to calculate them is the same.

By context I mean: if this the items are taken from some larger category for example: the ages of a few 'students' from a 'class'. Here 'students' are the sample from a larger set that is 'class'. The mean of the 'few students' will be called sample mean. In contrast, if we take the mean of the ages of the whole class then this is called population mean. (population mean == mean of the whole set)

In our case we aren't told exactly where these numbers come from, is this the whole set or a sample from it, the lack of context allows us to assume that the mean can either be population mean or sample mean. So we can safely use any symbol $\mu$ or $\overline{x}$ .