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Gnesinka [82]
3 years ago
13

Find the least common denominator of x-2/x^2-x and 3/x^2-1

Mathematics
1 answer:
laila [671]3 years ago
7 0
The least Common Denominator is 24 x x^{3}y^{2}
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Y= 3/5x - 15/5
This should be your answer
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Put the numbers in order from least to greatest.
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None of the answers are correct because it would be 4, 10, 12, 17, then 41
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0.5771 divided by 0.528
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Use mathematical induction to show that 4^n ≡ 3n+1 (mod 9) for all n equal to or greater than 0
cestrela7 [59]
When n=0, you have

4^0=1\equiv3(0)+1=1\mod9

Now assume this is true for n=k, i.e.

4^k\equiv3k+1\mod9

and under this hypothesis show that it's also true for n=k+1. You have

4^k\equiv3k+1\mod9
4\equiv4\mod9
\implies 4\times4^k\equiv4(3k+1)\mod9
\implies 4^{k+1}\equiv12k+4\mod9

In other words, there exists M such that

4^{k+1}=9M+12k+4

Rewriting, you have

4^{k+1}=9M+9k+3k+4
4^{k+1}=9(M+k)+3k+3+1
4^{k+1}=9(M+k)+3(k+1)+1

and this is equivalent to 3(k+1)+1 modulo 9, as desired.

3 0
3 years ago
A cardboard box without a top is to have volume 62500 cubic cm. find the dimensions which minimize the amount of material used.
bezimeni [28]

Answer: A cardboard box without a lid is to have a volume of 32,000 cubic cm. Find the dimensions that minimize the amount of cardboard used

. ans: base 40 x 40, height = 20  

Solution:  

The typical box might look like the one below  

where . In addition we have xyz = 32000 ,so we need to minimize .  

We have,  

 

From the geometry of the problem  so y = x. So  or x = 40.  

Finally, y = x = 40 and z = 32000/(xy)=20.

8 0
3 years ago
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