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kifflom [539]
3 years ago
9

I know how to solve this normally, but not with a fraction. any help?

Mathematics
1 answer:
Setler79 [48]3 years ago
3 0

Answer:use g o o g l e search calculator and it will bring whatever you need and it helps me a lot

Step-by-step explanation:

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Sinx + siny=a<br> cosx + cosy=b<br> Find cos(x+y/2)
romanna [79]

Using the addition rule of the Sine function and the Cosine function, we obtain \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}.

<h3>What are the formulas for (sin x + sin y) and (cos x + cos y)?</h3>
  • The formula for the addition of two Sine functions (\sin x+\sin y) is \sin x + \sin y = 2\sin\frac{x+y}{2}\cos\frac{x-y}{2}.
  • The formula for the addition of two Cosine functions (\cos x+\cos y) is \cos x + \cos y = 2\cos\frac{x+y}{2}\cos\frac{x-y}{2}.

Given that

\sin x + \sin y = a\\\cos x + \cos y = b

Then using the above formulas, we get:

2\sin\frac{x+y}{2}\cos\frac{x-y}{2}=a       (1)

2\cos\frac{x+y}{2}\cos\frac{x-y}{2}=b       (2)

Dividing the equation (1) by (2), we get:

\dfrac{\sin\dfrac{x+y}{2}}{\cos\frac{x-y}{2}}=\dfrac{a}{b}\\\Longrightarrow \tan\dfrac{x+y}{2}=\dfrac{a}{b}             (3)

Now, we know that  \cos\theta=\dfrac{1}{\sqrt{1+\tan^2\theta}}.

Thus, using the above formula, we get from (3):

\cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\tan^2\dfrac{x+y}{2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\dfrac{a^2}{b^2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}

Therefore, using the addition rule of the Sine function and the Cosine function, we obtain \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}.

To know more about Sine and Cosine functions, refer: brainly.com/question/27728553

#SPJ9

3 0
2 years ago
The GMAC Insurance company reported that the mean score on the National Drivers Test was 70.5 with a standard deviation of 3.6 p
aliina [53]

In statistics, the 68–95–99.7 rule, also known as the three-sigma rule or empirical rule, states that nearly all values lie within three standard deviations of the mean in a normal distribution.

About 68.27% of the values lie within one standard deviation of the mean. Similarly, about 95.45% of the values lie within two standard deviations of the mean. Nearly all (99.73%) of the values lie within three standard deviations of the mean.

In mathematical notation, these facts can be expressed as follows, where x is an observation from a normally distributed random variable, μ is the mean of the distribution, and σ is its standard deviation:

P( μ – σ ≤ x ≤ μ + σ ) ≈ 0.6827

P( μ –2σ ≤ x ≤ μ + 2σ ) ≈ 0.9545

P( μ –3σ ≤ x ≤ μ + 3σ ) ≈ 0.9973

So here A = μ – σ = 78.7 – 3.5 = 75.2 (answer

7 0
4 years ago
Solve for x MUST SHOW ALL WORK IN ODER <br> (X-8)
makkiz [27]

x=1?  

Not to be rude sir but thats not enough information to solve the problem

8 0
3 years ago
Identify two ratios that are equivalent to 3:5
s344n2d4d5 [400]
The correct answer is 15:25
7 0
3 years ago
1 5/2 as a whole number
SVEN [57.7K]

Answer:

3 1/2

Step-by-step explanation:

7 0
3 years ago
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