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katrin [286]
2 years ago
6

What’s the least common multiple of 12 and 2

Mathematics
1 answer:
NNADVOKAT [17]2 years ago
7 0

For example, for LCM (12,30) we find:

Using the set of prime numbers from each set with the highest exponent value we take 22 * 31 * 51 = 60. Therefore LCM (12,30) = 60.

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Explain why a balance of less than -$10 represents a debt greater than $10?
SIZIF [17.4K]

Answer:

Because -$10 is basically nothing because it is negative you don't have ten dollar, but a debt of $10 means you have it which is why it is greater than -$10

5 0
2 years ago
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Which is the graph of r = 6 cos?
Alex777 [14]

Answer:

Using the formula

r

=a

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(

θ

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or

r

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(

θ

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r

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6

cos

(

θ

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Step-by-step explanation:

4 0
3 years ago
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Help Please! △ABC is given with line m drawn through A parallel to BC¯¯¯¯¯¯¯¯. In the course of proving that the interior angle
Viefleur [7K]

not sure but i thibj the second one

8 0
2 years ago
Find the number to which the sequence {(3n+1)/(2n-1)} converges and prove that your answer is correct using the epsilon-N defini
Nat2105 [25]
By inspection, it's clear that the sequence must converge to \dfrac32 because

\dfrac{3n+1}{2n-1}=\dfrac{3+\frac1n}{2-\frac1n}\approx\dfrac32

when n is arbitrarily large.

Now, for the limit as n\to\infty to be equal to \dfrac32 is to say that for any \varepsilon>0, there exists some N such that whenever n>N, it follows that

\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|

From this inequality, we get

\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|=\left|\dfrac{(6n+2)-(6n-3)}{2(2n-1)}\right|=\dfrac52\dfrac1{|2n-1|}
\implies|2n-1|>\dfrac5{2\varepsilon}
\implies2n-1\dfrac5{2\varepsilon}
\implies n\dfrac12+\dfrac5{4\varepsilon}

As we're considering n\to\infty, we can omit the first inequality.

We can then see that choosing N=\left\lceil\dfrac12+\dfrac5{4\varepsilon}\right\rceil will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that N\in\mathbb N.
6 0
3 years ago
The contrapositive of a conditional statement is "If an item is not worth five dimes, then it is not worth two quarters.”
balandron [24]
Example of use of terms:
Statement:  If it is far, we take a bus.
Inverse:       If it is not far, we do not take a bus.
Converse:   If we take a bus, it is far.
Contrapositive:  If we do not take a bus, it is not far.

We also know that
1. The inverse of the inverse is the statement itself, and similarly for converse and contrapositive.
2. Only the contrapositive is logically equivalent to the original statement.
This means that the converse and inverse are logically different from the original statement.

Now back to the given statement.
To find the original statement, we find the contrapositive of the contrapositive.
We then find the converse from the original statement, as in the example above.

Original statement
(note that in English, if it is not worth X dollars, means if it is not worth AT LEAST X dollars")
contrapositive of 
<span>
"If an item is not worth five dimes, then it is not worth two quarters.”
is the negation of the converse, which become
"If an item is worth two quarters, then it is worth (at least) five dimes."


The converse of the previous statement is therefore
"If an item is worth (at least) five dimes then it is worth two quarters"

In this particular case, we can also take advantage of the fact that the contrapositive is the negation of the converse.  So all we have to do is the provide the negation of each component of the contrapositive to get the converse:
"If an item is worth (at least) five dimes, then it is worth two quarters".
as before.

Note that the converse does NOT logically mean the same as the original statement.

</span>
6 0
2 years ago
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