Determine this systems of equations no solution, one solution, infinitely many solutions

Mathematics

1 answer:

zlopas [31]3 years ago

6 0

Answer:

one solution

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

At a amusement ,park 360 visitors rode the roller coaster in 3 hours.Write and solve a proportion to find the number of visitors

Pachacha [2.7K]

First you need to find out about how many people went on the roller coaster in one hour by doing 360 divided by 3 and you would get 120. So then you would try to find out how many people went on the coaster in 7 hours by doing 360 times 2 because 3 hours multiplied by 2 is 6 and you would do that to find out how many people went on the coaster in 6 hours, and you would get 720. Next, you have 1 more round of people, so you need to do 720 + 120 which is 840. So about 840 people rode the coaster in 7 hours. Hope this helped.

6 0

3 years ago

This one is number 6

iren2701 [21]

I’m not entirely sure, but i do think it could be B.

5 0

2 years ago

Read 2 more answers

Convert 77 centimeters into feet. Hint: 1 in = 2.54 cm; 1 ft = 12 in

Over [174]

Answer:

77 centimeters = 2.52625 feet