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Alexxandr [17]
2 years ago
15

Giải phương trình : 8cos 4 x – 4cos2x + sin4x – 4 = 0

Mathematics
1 answer:
alex41 [277]2 years ago
5 0

Answer:

Step-by-step explanation:

8(1+cos2x/2)^{2} -4c0s2x+sin4x-4=0\\2(1+2cos2x+cos^{2}2x )-4cos2x+sin4x-4=0\\2cos^{2} 2x+sin4x-2=0\\1+cos4x+sin4x-2=0\\cos4x+sin4x=1\\sin(4x+\pi /4)=sin\frac{\pi }{4} \\\left \{ {{4x+\frac{\pi }{4} =\frac{\pi }{4}+k2\pi  } \atop {4x+\frac{\pi }{4} =\frac{3\pi }{4} +k2\pi \\

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120 is the same as 394 fewer than Z
SpyIntel [72]

Answer:

z=514

Step-by-step explanation:

120=z-394

+394. +394

514=z

Hope this helps

8 0
3 years ago
What does the slope of graph show about the Hardware stores selling price for the rope?
SashulF [63]

Answer:

If the price is increasing or decreasing

Step-by-step explanation:

The slope is a visual representation of the cost over time.

3 0
2 years ago
Read 2 more answers
The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and
Firdavs [7]

Answer:

1a

  P(39 <  X < 48  ) = 0.8767

1b

    95% of all sample means will fall between 40.1  <  \mu < 49.9

1c

    \= x = 41. 795

2

   n =  25

Step-by-step explanation:

From the question we are told that

   The mean is n   =  45

   The population standard deviation is  \sigma =  10

   The sample size is n  =  16

Generally the standard error of the mean is mathematically represented as

       \sigma_{x} =  \frac{ \sigma}{\sqrt{n} }

=>    \sigma_{x} =  \frac{ 10 }{\sqrt{16 } }

=>    \sigma_{x} = 2.5

Generally the probability that the sample mean will be between 39 and 48 minutes is

    P(39 <  X < 48  ) =  P( \frac{ 39 - 45}{ 2.5} <  \frac{X - \mu }{\sigma } <  \frac{ 48 - 45}{ 2.5} )

=> P(39 <  X < 48  ) =  P(-2.4 < Z< 1.2 )

=> P(39 <  X < 48  ) =  P( Z< 1.2 ) - P(Z <  -2.4)

From the z table  the area under the normal curve to the left corresponding to  1.2  and  -2.4  is

=> P( Z< 1.2 ) = 0.88493

and  

    P( Z< - 2.4 ) = 0.0081975

So

   P(39 <  X < 48  ) = 0.88493 -0.0081975

=> P(39 <  X < 48  ) = 0.8767

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of   is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally the margin of error is mathematically represented as  

      E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

=>   E = 1.96 * 2.5  

=>   E =4.9  

Generally the  95% of all sample means will fall between

      \mu  -E <  and   \mu   +E

=>   45  -4.9\   and \  45  + 4.9

Generally the value which  90% of sample means is  greater than is mathematically represented

      P( \= X >  \= x  ) = 0.90

=>   P( \= X >  \= x  ) =  P( \frac{\= X  - \mu }{ \sigma_x} >  \frac{\= x  -45 }{ 2.5}  ) = 0.90

=>  P( \= X >  \= x  ) =  P( Z >  z  ) = 0.90

Generally from the z-table  the critical  value  of  0.90  is  

      z = -1.282

      \frac{\= x  -45 }{ 2.5}  = -1.282

=>   \= x = 41. 795

Considering question 2

 Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as

         s = \frac{1}{5} \sigma

  Generally the standard deviation of the sample mean is mathematically  represented as

          s = \frac{\sigma }{ \sqrt{n} }

=>       \frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }

=>       n =  5^2

=>       n =  25

5 0
3 years ago
A factory produces 60005/12
ycow [4]

Answer:

About\ 193 \frac{209}{372} \ tons\ of \ steel

Step-by-step explanation:

Given the amount of tons of steel produced monthly by a factory to be 6000 5/12 tons, to determine their daily production, we need to use the conversion;

Maximum of 31 days = 1 month

This means that the steel company produces 6000 5/12 tons of steel in 31 days.

6000 5/12 tons = 31 dsays

72,005/12 tons = 31 days

in a day, the company will therefore produce approx. (72,005/12)/31 tons of steel.

(72,005/12)/31  = 72,005/12 * 1/31

= 72,005/12*31

= 72,005/372

= 193  209/372 tons of steel.

Hence, the factory produces about 193 \frac{209}{372} tons of steel daily

6 0
3 years ago
Examples of how to reduce friction.
kkurt [141]

Answer:

the to objects go in the Same direction


Step-by-step explanation:


7 0
3 years ago
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