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2 years ago

3

Mathematics

1 answer:

Ronch [10]2 years ago

5 0

Answer:

2 x + y = − 2 , x + 2 y = 2 , 6 x 2 + 3 y 2 = 12 , x + y = 2

x − y = 9 , x + y = 6, 2 x + y = − 2 , x + 2 y = 2 6 x 2+ 3 y 2 = 12 , x + y = 2 x − y= 9 , x + y = 6

Step-by-step explanation:

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Use series to verify that<br><br> <img src="https://tex.z-dn.net/?f=y%3De%5E%7Bx%7D" id="TexFormula1" title="y=e^{x}" alt="y=e^{

SVETLANKA909090 [29]

$y = e^x\\\\\displaystyle y = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y= 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \frac{d}{dx}\left( 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+\ldots\right)\\\\$

$\displaystyle y' = \frac{d}{dx}\left(1\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{2!}\right) + \frac{d}{dx}\left(\frac{x^3}{3!}\right) + \frac{d}{dx}\left(\frac{x^4}{4!}\right)+\ldots\\\\\displaystyle y' = 0+1+\frac{2x^1}{2*1} + \frac{3x^2}{3*2!} + \frac{4x^3}{4*3!}+\ldots\\\\\displaystyle y' = 1 + x + \frac{x^2}{2!}+ \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y' = e^{x}\\\\$

This shows that $y' = y$ is true when $y = e^x$

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Note 1: A more general solution is $y = Ce^x$ for some constant C.
Note 2: It might be tempting to say the general solution is $y = e^x+C$ , but that is not the case because $y = e^x+C \to y' = e^x+0 = e^x$ and we can see that $y' = y$ would only be true for C = 0, so that is why $y = e^x+C$ does not work.

6 0

3 years ago

Is there a answer to this

hodyreva [135]

Answer:

mean=71

Step-by-step explanation:

Mean x¯¯¯x¯

Median x˜x~

Mode

64, 83, 79, 38, 81, 90, 59, 93, 70, 73, 71, 51

Range

Minimum

Maximum

Count n

Sum

852

Quartiles

Quartiles:

Q1 --> 61.5

Q2 --> 72

Q3 --> 82

Interquartile

Range IQR

20.5

Outliers

none

5 0

2 years ago

What is the solution?

exis [7]

Answer:

no solution

Step-by-step explanation:

The lines do not cross at any point; therefore, there is no solution.

3 0

3 years ago

what is the slope of the line that passes through the points (3,6) and (1,2)? write your answer i’m simplest form.

Nikitich [7]

Answer:

Slope (m) = 2

Step-by-step explanation:

Here's the full equation⤵⤵⤵

$y = 2x$

Picture of graph (labeled) is above⤴⤴⤴

Hope this helped :)

6 0

3 years ago

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Dima020 [189]

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2 years ago