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Usimov [2.4K]
3 years ago
9

Find the product. (-5a ^2)^3 · a^5

Mathematics
1 answer:
GrogVix [38]3 years ago
4 0

Answer:

<u><em>−125a^(11)</em></u>

Step-by-step explanation:

<u><em>(−5a^(2)3a^(5) Then you solve</em></u>

<u><em>=−125a^(11)</em></u>

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Prove algebraically if the following functions are even, odd, or neither. (12 points)
alukav5142 [94]

Answer:

  a. even

  b. odd

  c. odd

  d. even

Step-by-step explanation:

We suppose that "prove algebraically" means that you are to substitute -x for x in each equation and show that f(x) = -f(-x) for an odd function, and that f(x) = f(-x) for an even function.

It is easier to do this generically, so that you can make use of the rule that ...

  • if a polynomial function consists only of even-degree terms, it is an even function
  • if a polynomial function consists only of odd-degree terms, it is an odd function

__

So, for even-degree, we can assume that the polynomial is of the form ...

  f(x) = ax^2 + b

Then we have ...

  f(-x) = a(-x)^2 +b = (-1)^2·ax^2 +b = ax^2 +b

or ...

  f(-x) = f(x) . . . . regardless of the values of "a" and "b"

__

For an odd-degree function, we can assume that the polynomial is of the form ...

  g(x) = x·f(x) . . . . where f(x) is of even degree

Then ...

  g(-x) = -x·f(-x) = -x·f(x) . . . . since f(x) = f(-x) as shown above

or

  g(-x) = -g(x) . . . . . . . . regardless of the coefficients in f(x)

__

a. f(x) matches the form of our even-degree f(x) above, so is even.

b. g(x) matches the form of our odd-degree g(x) above (with a=0), so is odd.

c. h(x) = x(5x^2 -1) matches the form of our odd-degree g(x), so is odd.

d. f(x) matches the form of our even-degree f(x) above, so is even.

_____

<em>Comment on the problem</em>

For part (b), we have assumed that "x +1x" means 2x. If it is supposed to be something else, it needs to be properly written. (x+1/x is an odd function, because -x+1/(-x) = -(x +1/x).)

8 0
3 years ago
Degrees to radians no decimals
irga5000 [103]

Answer

To convert degrees to radians you multiply your degree by π, then divide by 180. Hope that helps :)

6 0
3 years ago
The length of a rectangle Is 6.5 inches and the width is 3.5
Tamiku [17]

Answer:

13:7

Step-by-step explanation:

If you divide each number (6.5 and 3.5) by .5

6.5/.5=13

3.5/.5=7

7 0
3 years ago
Decide whether the integral is improper. <br> [infinity]<br> â« ln(x3) dx <br> 0
marusya05 [52]

Answer:

Yes, It is improper.

Step-by-step explanation:

<em>Your answer is correct. The limits of integration are finite. The integrand is not continuous on [1, ∞). At least one of the limits of integration is not finite. The integrand is continuous on [1, ∞).</em>

8 0
3 years ago
Find the equation of the line that contains the point (21,27) and is parallel to the x-axis.
Stells [14]

Answer:

y - 27 = 0 (x - 21) or y = 27

Step-by-step explanation:

8 0
3 years ago
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