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3 years ago

(8x^2)^3 multiplying monomials

1 answer:

8 0

Simplify the following:
(8 x^2)^3
Multiply each exponent in 8 x^2 by 3:
8^3 x^(3×2)
3×2 = 6:
8^3 x^6
8^3 = 8×8^2:
8×8^2 x^6
8^2 = 64:
8×64 x^6
8×64 = 512:
Answer: 512 x^6

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Consider the function f ( x ) = − 2 x 3 + 27 x 2 − 108 x + 9 . For this function there are three important open intervals: ( − [

Darya [45]

Answer:

Step-by-step explanation:

<u>Increasing and Decreasing Intervals of Functions</u>

Given f(x) as a real function and f'(x) its first derivative.

If f'(a)>0 the function is increasing in x=a

If f'(a)<0 the function is decreasing in x=a

If f'(a)=0 the function has a critical point in x=a

As we can see, the critical points may define open intervals where the function has different behaviors.

We have

$f ( x ) = - 2 x^3 + 27 x^2 - 108 x + 9$

Computing the first derivative:

$f' ( x ) = - 6 x^3 + 54 x - 108$

We find the critical points equating f'(x) to zero

$- 6 x^3 + 54 x - 108=0$

Simplifying by -6

$x^2 -9 x +18=0$

We get the critical points

$x=3,\ x=6$

They define the following intervals

$(-\infty,3),\ (3,6),\ (6,+\infty)$

Thus A=3 and B=6

3 0

3 years ago

A cube has a base area (B) of 49 in?. what is the volume?

timofeeve [1]

Answer:

$Base Area , B = 49\\side,a = \sqrt{49 } = 7\\Volume, V = B* a = 49 * 7 = 343$

5 0

3 years ago

Is the following correspondence a function

GenaCL600 [577]

No, because element b has 2 correspondents.

7 0

4 years ago

Read 2 more answers

5x^(2)+2 in verbal form

USPshnik [31]

Answer:

Five x squared plus two

Step-by-step explanation:

An exponent of two is always pronounced as "squared"

8 0

3 years ago

A rectangular prism has a length of 1/1/4 yards, a width of 2/1/2 yards, and a height of 4 yards. Enter the volume of the prism

dmitriy555 [2]

Prism volume = lbh

= 10*8*12

= 960cm^3

Note: I'm assuming the hole was cut right through it...

Hole volume = lbh

= 2*3*12

= 72cm^3

Final volume = 960 - 72 = 888cm^3

7 0

3 years ago