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Trava [24]
2 years ago
9

Help! Everyone keeps trolling me!

Mathematics
1 answer:
zhenek [66]2 years ago
5 0

9514 1404 393

Answer:

  1. 0 < x < 4
  2. (- ∞ < x < 0) ∪ (4 < x < ∞)
  3. x ∈ {0, 4}

Step-by-step explanation:

1. The solution is the set of x-values for which the graph is above the x-axis, where y = 0. Those x-values are in the interval (0, 4).

__

2. The solution is the set of x-values for which the graph is below the x-axis. Those x-values are in either of the two intervals (-∞, 0) or (4, ∞).

__

3. The x-intercepts of the graph are x=0 or x=4.

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Evaluate the definite integral. <br> 1 x4(1 + 2x5)5 dx.
Nata [24]

Answer:

Step-by-step explanation:

Given the definite integral \int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx, we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

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= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} }  \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du }  \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}]  \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\

= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C

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= \dfrac{1}{40(1-2x^5)^4} +C

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So it will take 80 cubes of side length 1/2 to have a volume equal to 10u^3

6 0
3 years ago
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