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schepotkina [342]
3 years ago
14

Let P denote the set of primes and E the set of even integers. As always, Z and N denote the integers and natural numbers, respe

ctively. Find equivalent formulations of each of the following statements using the notation of set theory
a. √2 is a real number but not a rational number.
b. Every integer is a rational number.
c. 2 is an even prime number.
Mathematics
1 answer:
aniked [119]3 years ago
3 0

Answer:

sorry i dont know this answer

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grandymaker [24]

Answer with Step-by-step explanation:

We are given that

tan(\alpha+\beta)

\frac{sin(\alpha+\beta}{cos(\alpha+\beta)}

By using formulatan x=\frac{sin x}{cos x}

\frac{sin\alpha cos\beta+sin\beta cos\alpha}{cos\alpha cos\beta-sin\alpha sin\beta}

By using property:sin(x+y)=sin x cosy+cos x sin y

cos(x+y)=cos x cosy-sin x siny

Divide numerator and denominator by cos\alpha cos\beta

Then, we get

\frac{\frac{sin\alpha}{cos\alpha}+\frac{sin\beta}{cos\beta}}{1-\frac{sin\alpha sin\beta}{cos\alpha cos\beta}}

tan(\alpha+\beta)=\frac{tan\alpha+tan\beta}{1-tan\alpha tan\beta}

Hence, proved

Substitute \alpha=\beta

Then we get

tan 2\alpha=\frac{tan\alpha+tan\alpha}{1-tan^2\alpha}

tan(2\alpha)=\frac{2tan\alpha}{1-tan^2\alpha}

Hence, proved.

3 0
4 years ago
A bus is traveling at a constant speed. If the bus travels 15 1 2 15 1 2 miles in 1 3 1 3 of an hour, how many miles will the bu
fiasKO [112]

Answer:

46 1/2 miles

Step-by-step explanation:

Given that:

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Time taken for the travel = 1/3 of an hour

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Let number of miles traveled in 1 hour = n

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1/3 * n = 15 1/2 * 1

1/3n = 31/2

Divide both sides by 1/3

n = 31/2 ÷ 1/3

n = 31/2 * 3/ 1

n = 93/2

n = 46.5 miles = 46 1/2 miles

3 0
3 years ago
What is the answer to the question?
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I hope this helps you

8 0
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How do I find the circumference?
steposvetlana [31]

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Step-by-step explanation:

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