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serg [7]
3 years ago
8

(X^3)^1/3 What is the simplest form of this expression?

Mathematics
1 answer:
Norma-Jean [14]3 years ago
7 0
The simplest form would be x

The rule for power to a power is 'keep the base and multiply the powers'.
3 * (1/3) = 1
So it would be x^1 or just x
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consider the function and then use calculus to answer the questions that follow 1 1/x 5/x^2 1/x^3 (a) Find the interval(s) where
boyakko [2]

Answer:

a)X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)

b)Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0  )

Step-by-step explanation:

From the question we are told that

The Function

f(x)=1+\frac{1}{x}  +\frac{5}{x^2} +\frac{1}{x^3}

Generally the differentiation of function f(x) is mathematically solved as

f(x)=1+\frac{1}{x}  +\frac{5}{x^2} +\frac{1}{x^3}

f(x)=\frac{x^3+x^2+5x+1}{x^2}

Therefore

f'(x)=\frac{x^2+10x+3}{x^4}

Generally critical point is given as

f'(x)=0

\frac{x^2+10x+3}{x^4}=0

x=-5 \pm\sqrt{22}

Generally the maximum and minimum x value for critical point is mathematically solved as

f'(-5 \pm\sqrt{22})

Where

Maximum value of x

f'(-5 +\sqrt{22})

Minimum value of x

f'(-5 +\sqrt{22})

Therefore interval of increase is mathematically given by

f'(-5 -\sqrt{22}),f'(-5 +\sqrt{22})

f(x)

Therefore interval of decrease is mathematically given by

(-\infty,-5 -\sqrt{22}),f'(-5 +\sqrt{22},0),(0,\infty)

Generally the second differentiation of function f(x) is mathematically solved as

f''(x)=\frac{2(x^2+15x+6)}{x^5}

Generally the point of inflection is mathematically solved as

f''(x)=0

x^2+15x+6=0

Therefore inflection points is given as

x=\frac{1}{2} (-15 \pm \sqrt{201}

f''(x)>0,\frac{1}{2}(-15-\sqrt{201})

a)Generally the concave upward interval X is mathematically given as

X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)

f''(x)

b)Generally the concave downward interval Y is mathematically given as

Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0  )

5 0
3 years ago
You have just started a colony on Mars. One of the biggest concerns for the colony is government. What is your colony going to d
777dan777 [17]

Answer:

we will use democracy so that everyone gets a say in what happens to the colony, second the government will make the decisions and the people will provide options and different ideas, and i believe its the best type because everyone has a say in what happens and the government isn't too powerful and has as much power as the people do.

Step-by-step explanation:

3 0
2 years ago
W6+58=-138!! what is x PLEASE
mote1985 [20]

Answer:

the answer is -196 im sorry if i got it wrong

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
If xy is rational, must x and y each be rational?
balu736 [363]
<span>Your answer is is simply,no x and y could have a common irrational factor. </span>
3 0
3 years ago
Someone sells a product for 10 cents and he sells 1000 products, how much money did he earn
zheka24 [161]

Answer:

$100

Step-by-step explanation:

  1. 10¢ × 1,000 = 10,000¢
  2. To convert to dollars: Cents ÷ cents in 1 dollar
  3. To convert to dollars: 10,000¢ ÷ 100¢ = $100

I hope this helps!

3 0
3 years ago
Read 2 more answers
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