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o-na [289]
2 years ago
15

Determine the intervals on which f(x) is x>0 and on which f(x) is x<0.

Mathematics
1 answer:
Simora [160]2 years ago
7 0

Answer:

  • f(x) > 0 for (-2.203, -1) U (2.203, ∞)
  • f(x) < 0 for (-∞, -2.203) U (-1, 2.203)

Step-by-step explanation:

A graph shows real zeros at ±2.203 and -1. The value of f(x) changes sign at each of these.

The positive leading coefficient indicates the graph trends generally upward, so the function will be positive in intervals with an even number of zeros to the right.

<h3>f(x) positive</h3>

There are an even number of zeros to the right of x = 2.203 and the interval (-2.203, -1).

  f(x) is positive in the intervals (-2.203, -1) or (2.203, ∞).

<h3>f(x) negative</h3>

The function will be negative where it is not positive (except at the zeros)

  f(x) is negative in the intervals (-∞, -2.203) or (-1, 2.203).

_____

<em>Additional comment</em>

The graph shows the only rational real root of the function is x=-1. Using synthetic division to reduce the polynomial, we find ...

  f(x) = (x +1)(x^4 -3x^2 -9)

The remaining factor is a quadratic in x^2, which has roots ...

  x = ±√(1.5 ±√11.25)

The real roots are approximately ±2.20320266118. The value 2.203 used above is a stand-in for the exact value √(1.5 +√11.25)).

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3 years ago
Any help on this please ?
dlinn [17]

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(0,-5), I believe.

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the length of the apothem of a regular hexagon with 10-cm sides?
vodka [1.7K]

Answer:

The length of apothem of given hexagon is 8.66 cm

Step-by-step explanation:

Apothem of a polygon is given by:

apothem = \frac{s}{2\ tan\ (\frac{180}{n})}

Here

s is length of side

tan is trigonometric function

and n denotes number of sides

Given that the polygon is a hexagon

s = 10cm\\n = 6

Putting the values in the formula

apothem = \frac{10}{2\ tan\ (\frac{180}{6})}\\= \frac{10}{2\ tan\ 30}\\=\frac{10}{2 * 0.5773}\\=\frac{10}{1.1546}\\=8.6610\\Rounding\ off\ to\ nearest\ hundredth\\= 8.66\ cm

Hence,

The length of apothem of given hexagon is 8.66 cm

6 0
3 years ago
What is the product of (5× + 1)(5x - 1)?
padilas [110]

we are given

(5x + 1)(5x - 1)

we can distribute it

5x*5x-1*5x+1*5x-1*1

25x^2-5x+5x-1

now, we can simplify it

25x^2-1...............Answer

6 0
3 years ago
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
topjm [15]

Answer:  B. neither

<u>Step-by-step explanation:</u>

A function is even when f(x) = f(-x).

A function is odd when f(-x) = -f(x).


f(x) = 2x³ - x²

f(-x) = 2(-x)³ - (-x)²

      = -2x³ - x²

f(x) = 2x³ - x²     ≠    f(-x) = -2x³ - x²     so it is NOT EVEN


-f(x) = -(2x³ - x²)

      = -2x³ + x²

f(-x) = -2x³ - x²     ≠    -f(x)= -2x³ + x²     so it is NOT ODD  


Therefore, it is NEITHER even nor odd.

5 0
3 years ago
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