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Ivenika [448]
3 years ago
14

What equals 60 36 and 48

Mathematics
2 answers:
Deffense [45]3 years ago
7 0
60. 1 times 60 equals 60 2 times 30 equals 60 3 times 20 equals 60 4 times 15 equals 60 5 times 12 equals 60 6 times 10 equals 60 10 times 6 equals 60 12 times 5 equals 60 15 times 4 equals 60 20 times 3 equals 60 30 times 2 equals 60 60 times 1 equals 60                                                                                                                                                                                                     1 times 36 equals 36 2 times 18 equals 36 3 times 12 equals 36 4 times 9 equals 36 6 times 6 equals 36 9 times 4 equals 36 12 times 3 equals 36 18 times 2 equals 36 36 times 1 equals 36

1 times 48 equals 48 2 times 24 equals 48 3 times 16 equals 48 4 times 12 equals 48 6 times 8 equals 48 8 times 6 equals 48 12 times 4 equals 48 16 times 3 equals 48 24 times 2 equals 48 48 times 1 equals 48
WINSTONCH [101]3 years ago
4 0
If you mean the greatest common divisor of the three numbers, then the answer is 12
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How do you solve this limit of a function math problem? ​
hram777 [196]

If you know that

e=\displaystyle\lim_{x\to\pm\infty}\left(1+\frac1x\right)^x

then it's possible to rewrite the given limit so that it resembles the one above. Then the limit itself would be some expression involving e.

For starters, we have

\dfrac{3x-1}{3x+3}=\dfrac{3x+3-4}{3x+3}=1-\dfrac4{3x+3}=1-\dfrac1{\frac34(x+1)}

Let y=\dfrac34(x+1). Then as x\to\infty, we also have y\to\infty, and

2x-1=2\left(\dfrac43y-1\right)=\dfrac83y-2

So in terms of y, the limit is equivalent to

\displaystyle\lim_{y\to\infty}\left(1-\frac1y\right)^{\frac83y-2}

Now use some of the properties of limits: the above is the same as

\displaystyle\left(\lim_{y\to\infty}\left(1-\frac1y\right)^{-2}\right)\left(\lim_{y\to\infty}\left(1-\frac1y\right)^y\right)^{8/3}

The first limit is trivial; \dfrac1y\to0, so its value is 1. The second limit comes out to

\displaystyle\lim_{y\to\infty}\left(1-\frac1y\right)^y=e^{-1}

To see why this is the case, replace y=-z, so that z\to-\infty as y\to\infty, and

\displaystyle\lim_{z\to-\infty}\left(1+\frac1z\right)^{-z}=\frac1{\lim\limits_{z\to-\infty}\left(1+\frac1z\right)^z}=\frac1e

Then the limit we're talking about has a value of

\left(e^{-1}\right)^{8/3}=\boxed{e^{-8/3}}

# # #

Another way to do this without knowing the definition of e as given above is to take apply exponentials and logarithms, but you need to know about L'Hopital's rule. In particular, write

\left(\dfrac{3x-1}{3x+3}\right)^{2x-1}=\exp\left(\ln\left(\frac{3x-1}{3x+3}\right)^{2x-1}\right)=\exp\left((2x-1)\ln\frac{3x-1}{3x+3}\right)

(where the notation means \exp(x)=e^x, just to get everything on one line).

Recall that

\displaystyle\lim_{x\to c}f(g(x))=f\left(\lim_{x\to c}g(x)\right)

if f is continuous at x=c. \exp(x) is continuous everywhere, so we have

\displaystyle\lim_{x\to\infty}\left(\frac{3x-1}{3x+3}\right)^{2x-1}=\exp\left(\lim_{x\to\infty}(2x-1)\ln\frac{3x-1}{3x+3}\right)

For the remaining limit, write

\displaystyle\lim_{x\to\infty}(2x-1)\ln\frac{3x-1}{3x+3}=\lim_{x\to\infty}\frac{\ln\frac{3x-1}{3x+3}}{\frac1{2x-1}}

Now as x\to\infty, both the numerator and denominator approach 0, so we can try L'Hopital's rule. If the limit exists, it's equal to

\displaystyle\lim_{x\to\infty}\frac{\frac{\mathrm d}{\mathrm dx}\left[\ln\frac{3x-1}{3x+3}\right]}{\frac{\mathrm d}{\mathrm dx}\left[\frac1{2x-1}\right]}=\lim_{x\to\infty}\frac{\frac4{(x+1)(3x-1)}}{-\frac2{(2x-1)^2}}=-2\lim_{x\to\infty}\frac{(2x-1)^2}{(x+1)(3x-1)}=-\frac83

and our original limit comes out to the same value as before, \exp\left(-\frac83\right)=\boxed{e^{-8/3}}.

3 0
3 years ago
What is the value of x? <br> A:12 <br><br> B:15<br><br> C: 6<br><br> D: 30
mel-nik [20]

Answer: C

Step-by-step explanation: If this is drawn to scale, 12 15 and 30 make absolutely no sense, because if you multiply any of those numbers by 5 your gonna get a number bigger than 60.

Therefore, 6 is the answer

5 0
3 years ago
I need to know the answer to this problem. <br><img src="https://tex.z-dn.net/?f=2%20-%202%20%5Ctimes%203%20%2B%203%20%3D%20%20"
algol13
2 - 2 x 3 + 3 

= 2 - 6 + 3

= -4 + 3

= - 1
6 0
3 years ago
You are converting 8 centimeters to meters
morpeh [17]

Answer:

8cm = 0.08m

Step-by-step explanation:

8×10^-2 Because we convert

from cm to m.

8 0
3 years ago
Read 2 more answers
Is the differenu<br> of 6 and 2?
frozen [14]

Answer:

4

Step-by-step explanation:

4

5 0
2 years ago
Read 2 more answers
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