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iren [92.7K]
3 years ago
10

I need help with all these questions

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
8 0

Answer:

Step-by-step explanation:

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Please solve with working out <br> simultaneous equations<br> 3x+2y=12<br> 2x+2y=10
Novay_Z [31]
Here, 3x + 2y = 12
2x + 2y = 10

Subtract 2nd from 1st equation, 
x = 2

Now, substitute in 2nd, 
2(2) + 2y = 10
2y = 10 - 4
y = 6/2
y = 3

In short, Your Answer would be: (2, 3)

Hope this helps!
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What are the potential solutions of In(x^2-25)=0?
Maslowich

Answer:

x =\pm \sqrt{26}

Step-by-step explanation:

<u>Given </u><u>:</u><u>-</u><u> </u>

  • ln ( x² - 25 ) = 0

And we need to find the potential solutions of it. The given equation is the logarithm of x² - 25 to the base e . e is Euler's Number here. So it can be written as ,

<u>Equation</u><u> </u><u>:</u><u>-</u><u> </u>

\implies log_e {(x^2-25)}= 0

<u>In </u><u>general</u><u> </u><u>:</u><u>-</u><u> </u>

  • If we have a logarithmic equation as ,

\implies log_a b = c

Then this can be written as ,

\implies a^c = b

In a similar way we can write the given equation as ,

\implies e^0 = x^2 - 25

  • Now also we know that a^0 = 1 Therefore , the equation becomes ,

\implies 1 = x^2 - 25 \\\\\implies x^2 = 25 + 1 \\\\\implies x^2 = 26 \\\\\implies x =\sqrt{26} \\\\\implies x = \pm \sqrt{ 26}

<u>Hence</u><u> the</u><u> </u><u>Solution</u><u> </u><u>of </u><u>the</u><u> given</u><u> equation</u><u> is</u><u> </u><u>±</u><u>√</u><u>2</u><u>6</u><u>.</u>

6 0
2 years ago
Using De-Moivre's theorem, prove that i^2= -1.​
Novosadov [1.4K]

Write i in trigonometric form. Since |i| = 1 and arg(i) = π/2, we have

i = exp(i π/2) = cos(π/2) + i sin(π/2)

By DeMoivre's theorem,

i² = exp(i π/2)² = exp(i π) = cos(π) + i sin(π)

and it follows that i² = -1 since cos(π) = -1 and sin(π) = 0.

3 0
2 years ago
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