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marusya05 [52]
3 years ago
9

Prove that the sum of two odd functions is odd.

Mathematics
1 answer:
katrin [286]3 years ago
7 0
Odd function: f(-x) = -f(x)

Let two odd functions be f(x) and g(x)

Let k(x) = f(x) + g(x)

Then k(-x) = f(-x) + g(-x) = -(f(x) + g(x)) = -k(x)

So k(x) is odd too.
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Answer: divide both numbers

Step-by-step explanation:

20.95

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3 years ago
Suppose we write the numbers $1,2,3,4,5,6$, and then color each number red or blue. The coloring is called factorific if there i
Oxana [17]

Answer:

The probability that his coloring is factorific is 0.28125

Step-by-step explanation:

For calculate the probability is necessary to identify the total number of ways to color the six number. This can be calculate with the rule of multiplication as:

2*2*2*2*2*2=64

Because we have 2 options to color every number.

For know the number of ways in which the coloring is factorific, first we need to identify the divisors of each number:

1: the divisor is 1

2: The divisors are 2 and 1

3: The divisors are 3 and 1

4: The divisors are 4, 2 and 1

5: The divisors are 5 and 1

6: The divisors are 6, 3 and 1

From these information we analyse that for made a factorific coloring, is necessary that the number 1 is color blue. Additionally if the number 4 is color blue, the number 2 needs to be color blue and if the number 6 is blue, the number 3 needs to be blue.

So, the number of ways in which we can create a factorfic number is determined by the following cases:

  • The number 2 is blue and the number 3 is blue: In this case we have 1 option for number 1, one for number 2 and 1 for number 3. Taking into account that the number 2 and 3 are blue, if the number 4 and 6 are blue or red doesn't change the fact that the coloring is going to be factorific. So, we have two options for number 3 and 2 options for number 6. Finally the color of the number 5 is independent of the colors of number 2 and 3, so we also have 2 options for coloring number 5 and the coloring is going to be factorific. Then the number of ways for this situation is calculate as:

<u>   1           </u>*<u>        1          </u>*  <u>   1           </u> * <u>          2   </u>  *<u>         2    </u>* <u>    2          </u>=   8

number 1    number 2    number 3   number 4  number 5  number 6

At the same way we can calculate the following cases:

  • The number 2 is blue and the number 3 is red:  If the number 3 is red, the coloring is only going to be factorific is number 6 is red. Then the number of ways for this situation is calculate as:

<u>   1           </u>*<u>        1          </u>*  <u>   1           </u> * <u>          2   </u>  *<u>         2    </u>* <u>    1          </u>=  4

number 1    number 2    number 3   number 4  number 5  number 6

  • The number 2 is red and the number 3 is red:  If the number 2 and 3  are red, the coloring is only going to be factorific is number 4 and 6 are red. Then the number of ways for this situation is calculate as:

<u>   1           </u>*<u>        1          </u>*  <u>   1           </u> * <u>           1   </u>  *<u>         2    </u>* <u>    1          </u>=  2

number 1    number 2    number 3   number 4  number 5  number 6

  • The number 2 is red and the number 3 is blue:  If the number 2 is red, the coloring is only going to be factorific is number 4 is red. Then the number of ways for this situation is calculate as:

<u>   1           </u>*<u>        1          </u>*  <u>   1           </u> * <u>          1   </u>  *<u>         2    </u>* <u>    2          </u>=  4

number 1    number 2    number 3   number 4  number 5  number 6

If we sum all the cases, we obtain 18 ways to make a factorific coloring. So the probability can be calculated as:

P= \frac{18}{64} =  0.28125

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3 years ago
Sketch plane M intersecting plane N. Then sketch plane 0 so that it instersects plane N, but not plane M.
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It can be a transversal kind of intersecting.....

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a square has a perimeter of 48cm.the square is cut in half . the two halves are put together to make this shape . what is the pe
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Answer:

The length of each side is 12cm.

Explanation:

The perimeter of a square is calculated by the formula:

P=4a, where P=perimeter, and a=length of any side, all sides being equal in a square.

From the given data we write:

48=4a

Divide both sides by 4.

12=a

The length of each side is 12cm.

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3 years ago
If a area of a rectangle is 24,396 centimeters and if width is 38 centimeters what is length?
Arisa [49]
Divide 24,396 by the width which is 38. It ends up being 642 cm. that is the length
4 0
3 years ago
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