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PtichkaEL [24]
3 years ago
13

Is s the square root 6 rational

Mathematics
1 answer:
bogdanovich [222]3 years ago
7 0

Proof by contradiction.

Let assume \sqrt6 is rational. Therefore, it can be expressed as a fraction \dfrac{a}{b}, where \text{gcd}(a,b)=1

\sqrt6=\dfrac{a}{b}\\\\
6=\dfrac{a^2}{b^2}\\\\
a^2=6b^2

This means that a^2 must be even, and therefore also a must be even.

So, a=2k, k\in\mathbb{Z}

(2k)^2=6b^2\\\\
4k^2=6b^2\\\\
2k^2=3b^2

This means that 3b^2 must be even. The only way for this to be even is when b^2 is even and therefore also b is even.

But if a and b were even, then earlier assumption that \text{gcd}(a,b)=1 would be false. Therefore \sqrt6 is irrational.

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Find the sum of the first 20 terms of the arithmetic series 0.5 + 1.1
exis [7]

Answer:

0.5+1.1+1.7+2.3+2.9+3.5+4.1+4.7+5.3+5.9+6.5+7.1+7.7+8.3+8.9+9.5+10.1+10.7+11.3+11.9

Step-by-step explanation:

tell me if this isn't 20 terms

8 0
3 years ago
Read 2 more answers
Solve for x.<br> 13<br> =(5x+ 6)/8 + <br> (5x+4)/4
valkas [14]

Answer: x=6

Step-by-step explanation:

To solve for x, we want to isolate the variable.

\frac{5x+6}{8} +\frac{5x+4}{4} =13        [get common denominator]

\frac{5x+6}{8} +\frac{2(5x+4)}{8} =13     [add fractions]

\frac{5x+6+10x+8}{y} =13          [combine like terms]

\frac{15x+14}{8} =13                 [multiply both sides by 8]

15x+14=104            [subtract both sides by 14]

15x=90\\                      [divide both sides by 15]

x=6

Now, we know that x=6.

3 0
2 years ago
Please help me with this problem
Advocard [28]
Your answer would be C
7 0
3 years ago
Calculate sin to two decimal places.
mario62 [17]
Recall that sin(theta) = opposite / hypotenuse (soh cah toa!)

I will use x for theta.

Sin(x) = 7.78/23.9
x = sin^-1(7.78/23.9)
x = 18.99726...
x = 18.99

6 0
3 years ago
What dose h-1/2=11/4=
m_a_m_a [10]

Answer:

h=3.25

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, assuming you want to find h:

h-1/2=11/4

h=13/4

h=3.25

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

BTW, brainliest would be greatly appreciated, I only need one more before I advance, thanks!

8 0
3 years ago
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