Mathematics: Problem 4. let m and n be two integers. show that m^3- n^3 is even if and only if m n is even.

A)if 39.99 is the 100%, what is 10 in percentage? wellsolve for x .b)now, with the discount, the amount is 29.99, thus if 29.99 is the 100%, what is 1.95 from it in percentage?solve for x .c)the original price is 39.99, the markup on that is 60%, how much is that?well now, after the discount, the price is 29.99, how much is 23.994 in percentage of 29.99?well solve for x ....

Problem 4. let m and n be two integers. show that

Ответ:

ari9425

12.03.2022

Mathematics

The expression m^3-n^3 is even if both variables (m and n) are even or both are odd

Step-by-step explanation:

Let's remember the logical operations with even and odd numbers

odd*odd=odd

even*even=even

odd*even=even

odd-odd=even

even-even=even

even-odd=odd

Now, the original expression is:

m^3-n^3 which can be expressed as:

(m*(m*m))-(n*(n*n))

If m and n are both odd, then:

(m*(m*m))=odd*(odd*odd)=odd*(odd)=odd

(n*(n*n))=odd*(odd*odd)=odd*(odd)=odd

Then, (m*(m*m))-(n*(n*n))=odd-odd=even

If m and n are both even, then:

(m*(m*m))=even*(even*even)=odd*(even)=even

Then, (m*(m*m))-(n*(n*n))=even-even=even

Finally if one of them is even, for example m, and the other is odd, for example n, then:

(m*(m*m))=even*(even*even)=odd*(even)=even

(n*(n*n))=odd*(odd*odd)=odd*(odd)=odd

Then, (m*(m*m))-(n*(n*n))=even-odd=odd

In conclusion, the expression m^3-n^3 is even if both variables (m and n) are even or both are odd. If one of them is even and the other one is odd, then the expression is odd.

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Ответ:

dontcareanyonemo

25.09.2020

Mathematics

A)

if 39.99 is the 100%, what is 10 in percentage? well

$\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
39.99&100\\
10&x
\end{array}\implies \cfrac{39.99}{10}=\cfrac{100}{x}$

solve for "x".

b)

now, with the discount, the amount is 29.99, thus if 29.99 is the 100%, what is 1.95 from it in percentage?

$\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
29.99&100\\
1.95&x
\end{array}\implies \cfrac{29.99}{1.95}=\cfrac{100}{x}$

solve for "x".

c)

the original price is 39.99, the markup on that is 60%, how much is that?
well

$\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
39.99&100\\
x&60
\end{array}\implies \cfrac{39.99}{x}=\cfrac{100}{60}\implies 39.99\cdot 60=100x
\\\\\\
\cfrac{39.99\cdot 60}{100}=x\implies 23.994=x$

now, after the discount, the price is 29.99, how much is 23.994 in percentage of 29.99?

well $\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
29.99&100\\
23.994&x
\end{array}\implies \cfrac{29.99}{23.994}=\cfrac{100}{x}$

solve for "x".

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Problem 4. let m and n be two integers. show that m^3- n^3 is even if and only if m n is even.

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