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3 years ago

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

Mathematics

2 answers:

tamaranim1 [39]3 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]3 years ago

4 0

Step-by-step explanation:

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

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What is the result of adding these two equations?

arsen [322]

Answer:

-2x-7y=-4

Step-by-step explanation:

5x+-7x=-2x

-9y+2y=-7y

1+-5=-4

So -2x-7y=-4

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3 years ago

The average of 8 scores is Q. If the average of 3 of the scores is Z, what is the average of the other 5 scores?

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$\dfrac{s_1+\cdots+s_8}{8}=Q\implies s_1+\cdots+s_8=8Q$
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Substituting into the first equation, this means

$s_4+\cdots+s_8=8Q-3Z$

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3 years ago

a family is 500 ft above the ground in the basket of a hot air balloon and ascending at the consistent rate shown. At that heigh

Ivan

We know that the balloon ascends at the same constant rate, that means that after the penny drop is:

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1 year ago

hey guys I really need this right now if my grade average is a 75 and I make a 36 on my 9 weeks test what my average be?

nlexa [21]

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Step-by-step explanation:

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3 years ago

The Highway Safety Department wants to study the driving habits of individuals. A sample of 37 cars traveling on a particular st

kodGreya [7K]

Answer:

90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

Step-by-step explanation:

We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.

Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average speed of cars = 70.7 miles per hour

s = sample standard deviation = 6.3 miles per hour

n = sample of cars = 37

$\mu$ = true mean speed

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the true mean, $\mu$ is ;

P(-1.688 < $t_3_6$ < 1.688) = 0.90 {As the critical value of t at 36 degree of

freedom are -1.688 & 1.688 with P = 5%}

P(-1.688 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.688) = 0.90

P( $-1.688 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.688 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.688 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.688 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.688 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.688 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }$ , $70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }$ ]

= [68.9517 miles per hour , 72.4483 miles per hour]

Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.

8 0

3 years ago