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aivan3 [116]
3 years ago
5

Find the zeros of the polynomial function: f(x) = 9x^3 - 27x^2 - 4x + 12.

Mathematics
1 answer:
hichkok12 [17]3 years ago
3 0

Answer:

  {-2/3, 2/3, 3}

Step-by-step explanation:

The equation can be factored by grouping.

  f(x) = (9x^3 -27x^2) +(-4x +12)

  f(x) = 9x^2(x -3) -4(x -3)

  f(x) = (9x^2 -4)(x -3)

We recognize the first factor as the difference of squares, so know it can be further factored to give ...

  f(x) = (3x -2)(3x +2)(x -3)

The zeros are the values of x that make these factors be zero:

  3x -2 = 0   ⇒   x = 2/3

  3x +2 = 0   ⇒   x = -2/3

  x -3 = 0   ⇒   x = 3

The zeros of the polynomial are x = -2/3, 2/3, 3.

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Swimming speed of salmon. The graph is showed below shows the influence of the temperature T on the maximum sustainable swimming
Doss [256]

Answer:

Here we have the relation between the speed of the salmon and the temperature.

a) the relation dS/dT tell us how the speed of the salmon changes as the temperature changes, and the units should be (if speed is m/s and temperature is in °C )

[dS/dT ] = [m/s*°C ].

b) I can not do a draw of the figure, but i can give a aproximation.

For T = 18°C, we can see that we are around the maximum of the curve, this means that around this point we will find the zero in the first derivate.

then S'(18) ≈ 0 m/s*°C

this means that around this point the changes are small.

for T = 10°C

Around this region, we can see almost a linear behavior.

so we can take a range of +-2°C

S(12°C) = 25m/s

S(8°C) = 20m/s

then the slope can be obtained using the relation:

S = (Y2 - Y1)/(X2 - X1) where this is the slope for the line that goes trough the pairs. (X1, Y1) and (X2, Y2)

S = (25 - 20)/(12 - 8) = 5/4

then we have that S´(10°C) ≈ 5/4 m/s*°C

Those two results are approximations, you may find better approximations by doing this with a ruler and drawing the tangents.

5 0
3 years ago
solve, showing all work. state if there is one solution, no solution, or infinite solutions 2(2b-4)+5=7+2b help asap i need the
WINSTONCH [101]

Answer:

one solution

Step-by-step explanation:

2(2b-4)+5=7+2b

4b - 8 + 5 = 7 + 2b

4b -3 = 7 + 2b

4b - 2b = 7 + 3

2b = 10

b = 10/2

b = 5.

it can have only 5 as solution that will be only one solution if we change the value of 5 to other number then the answer will be wrong

4 0
2 years ago
Explain in words how to convert 2/5 to a decimal. What is 2/5 as a decimal.
Alja [10]
You can simply divide 2 by 5 and you will get 0.4
6 0
3 years ago
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Greatest common factor of 23x to the power of 2 and 6x
nirvana33 [79]
First, list all the prime factors of both terms:
23x²: 1, 23, x, and x
6x: 1, 2, 3, and x
The two numbers share the prime factors 1 and x, so the GCF of 23x² and 6x is 1x, or x.
6 0
3 years ago
A bag contains eight blue marbles six Green marbles 12 yellow marbles and 10 orange marbles a marble is drawn at random from the
Marta_Voda [28]
28/36=7/9
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hope that helped
3 0
3 years ago
Read 2 more answers
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