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3 years ago

What is the gcf of 54 and 90

Mathematics

2 answers:

Viktor [21]3 years ago

8 0

The greatest common factor of 54 and 90 is 18

ikadub [295]3 years ago

5 0

The prime factorization of 54 is 2 * $3^{3}$
The prime factorization of 90 is 2 * $3^{2}$ * 5
What do they have in common? 2 * 3², which is 18.

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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.

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3 years ago

Taylor wants to read 2 books. One book has 232 pages and the other has 184 pages. She needs to return the books to the library i

dalvyx [7]

i think you add 232 and 184 then divide by 13.

Hope this helps!

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3 years ago

Which best describes the angles of some rhombuses?

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3 years ago

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

kramer

Given:

The sequence is:

$16,80,400,...$

To find:

The 6th term of the given sequence.

Solution:

We have,

$16,80,400,...$

Here, the first term is:

$a=16$

The ratio between consecutive terms are:

$\dfrac{80}{16}=5$

$\dfrac{400}{80}=5$

The given sequence has a common ratio 5. So, the given sequence is a geometric sequence.

The nth term of a geometric sequence is:

$a_n=a(r)^{n-1}$

Where, a is the first term and r is the common ratio.

Substitute $a=16,r=5,n=6$ to get the 6th term.

$a_6=16(5)^{6-1}$

$a_6=16(5)^{5}$

$a_6=16(3125)$

$a_6=50000$

Therefore, the 6th term of the given sequence is 50000.

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3 years ago

Charmaine's penny bank is

dlinn [17]

We shall take X as the total amount of cash her piggy bank can hold
therefore 1x/10+400=1x/2
400=1x/2-1x/10
we should make the denominator's the same
400=5x/10-1x/10
400=4x/10
400*10=4x
4000=4x
4000/4=X
1000=X
hope u found this useful

4 0

3 years ago