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Anika [276]
3 years ago
15

9x4 + 24x3 - 27x2 + 12x

Mathematics
1 answer:
serg [7]3 years ago
5 0

Answer:

3x(3x³ + 8x² – 9x + 4)

Step-by-step explanation:

9x4 + 24x3 - 27x2 + 12x =

9x⁴ + 24x³ – 27x² + 12x =

3(3x⁴ + 24x³ – 27x² + 12x) =

3x(3x³ + 24x² – 27x + 12).

3x³ + 24x² – 27x + 12 cannot be factored

[rational numbers].

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Answer:

The rocket will reach its maximum height after 6.13 seconds

Step-by-step explanation:

To find the time of the maximum height of the rocket differentiate the equation of the height with respect to the time and then equate the differentiation by 0 to find the time of the maximum height

∵ y is the height of the rocket after launch, x seconds

∵ y = -16x² + 196x + 126

- Differentiate y with respect to x

∴ y' = -16(2)x + 196

∴ y' = -32x + 196

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- Add 32x to both sides

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- Round it to the nearest hundredth

∴ x = 6.13 seconds

∴ The rocket will reach its maximum height after 6.13 seconds

There is another solution you can find the vertex point (h , k) of the graph of the quadratic equation y = ax² + bx + c, where h = -\frac{b}{2a} and k is the value of y at x = h and k is the maximum/minimum value

∵ a = -16 , b = 196

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∴ h = 6.125

∵ h is the value of x at the maximum height

∴ x = 6.125 seconds

- Round it to the nearest hundredth

∴ x = 6.13 seconds

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