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sashaice [31]
2 years ago
10

1. find the exact value of cos2θ if sin 2θ=3/4 and θ is between 0° and 90°

Mathematics
1 answer:
musickatia [10]2 years ago
5 0

Answer:

<u>Identities used:</u>

  • sin²θ + cos²θ = 1
  • cos2θ = cos²θ - sin²θ

#1

  • sin2θ = 3/4, and θ in the first quadrant
  • cos²2θ = 1 - sin²2θ
  • cos2θ = √(1 - sin²2θ) = √(1 - 9/16) = √(7/16) = √7 / 4

#2

  • sinθ(cos²θ - cos2θ) =
  • sinθ(cos²θ - (cos²θ - sin²θ) =
  • sinθ(sin²θ) =
  • sin³θ

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Trava [24]
Area is multiplying the width and the length so
area= 3.2 × 1.5 = 4.8
and perimeter is adding all sides together so
perimeter= 3.2 + 3.2 + 1.5 + 1.5 = 9.4
3 0
3 years ago
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The speed of light is estimated at 186,000 miles per second rounded to the nearest thousand miles per second.
Sedbober [7]

It was rounding to the nearest THOUSAND.


We are looking at the thousands place, keep that in mind.


Remember: everything 5 and above is rounded up, everything below 5 is rounded down.


186,789 is above 500, it is rounded to 187,000


186,899 is above 500, it is rounded to 187,000


185,990 is above 500, it is rounded to 186,000


and 185,190 is below 500, it is rounded to 185,000


Only one matches the criteria of the question:


185,990 is above 500, it is rounded to 186,000


therefore the answer is 185,990 miles per second



Have a fantastic day!


Read more on Brainly.com - brainly.com/question/10945335#readmore

8 0
3 years ago
A large pool has a faucet to allow water to enter the pool and a drain to allow water to leave the pool.
Radda [10]

Answer:

it is 100 because it is bigger

Step-by-step explanation:

because it is bigger

4 0
3 years ago
A research study investigated differences between male and female students. Based on the study results, we can assume the popula
garri49 [273]

Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is of \mu = 3.5.
  • The standard deviation is of \sigma = 0.5.
  • Sample of 100, hence n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05

The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

-2 = \frac{X - 3.5}{0.05}

X - 3.5 = -0.1

X = 3.4

Z = 2:

Z = \frac{X - \mu}{s}

2 = \frac{X - 3.5}{0.05}

X - 3.5 = 0.1

X = 3.6

The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

7 0
2 years ago
there is a loss of 20% by selling a photocopy machine for rs 60000 at what price will the machine be sold to gain 12% find it
notsponge [240]

Answer:

Step-by-step explanation:

Loss is 20%

S.P=Rs60000

C.P=S.P*100/100-loss%

=60000*100/80=Rs75000

So he brought is at Rs75000

Now he wants 12% profit

So

S.P=(100+profit%)/100*C.P

=100+12/100*75000

=112/100*75000=Rs 84000

He will have to sell Rs14000 more to gain profit of 12%

6 0
3 years ago
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