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liq [111]
3 years ago
11

Which of these numbers are irrational

Mathematics
1 answer:
Alinara [238K]3 years ago
4 0

Be sure that the answer is c)

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

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Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (E
xxTIMURxx [149]

Answer:

(-∞,-3) and (3,∞)  

Step-by-step explanation:

f(x) = x³ − 27x + 3

1. Find the critical points

(a) Calculate the first derivative of the function.

f'(x) = 3x² -27  

(b) Factor the first derivative

f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)

(c) Find the zeros

3(x + 3) (x - 3) = 0

x + 3 = 0      x - 3 = 0

     x = -3          x = 3

The critical points are at <em>x = -3</em> and x = 3.

2. Find the local extrema

(a) x = -3

f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57

(b) x = 3

f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51

The local extrema are at (-3,57) and (3,-51).

3, Identify the local extrema as maxima or minima

Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)

f'(-4) = 3x² -27 = 3(4)² - 27  = 21

f'(0) = 3(0)² -27 = -27

f'(4) = 3(4)² - 27 = 51

The function is increasing on the intervals (-∞,-3) and (3,∞).

The graph below shows the critical points of your function.

6 0
3 years ago
Find the volume of the rectangular prism.
gavmur [86]

Answer:

The answer is C, 281.25 cubic feet.

Step-by-step explanation:

First, you need to multiply all three sides of the rectangular prism.

10x4.5=45

45x6.25=281.25

So the answer is 281.25

Hope this helps!

5 0
3 years ago
How much would $600 invested at 8% interest compounded continuously be worth after 3 years? Round your answer to the nearest cen
eduard

Answer:

yes

Step-by-step explanation:

You just do it

5 0
2 years ago
-1/5y+7=7<br> What is the value of y?
liq [111]
The answer is y=0

See the attached photo for details

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

8 0
2 years ago
Ms. Velez will use both x gray bricks and y red bricks to build a wall around her garden. Gray bricks cost $0.45 each and red br
Alekssandra [29.7K]

It is given in the question that

Ms. Velez will use both x gray bricks and y red bricks to build a wall around her garden. Gray bricks cost $0.45 each and red bricks cost $0.58 each. She can spend up to $200 on her project, and wants the number of red bricks to be less than half the number of gray bricks.

Maximum she can spend is $200. That is

0.45x + 0.58y \leq 200&#10;\\  y< \frac{1}{2} x

And

x\geq 0 , y \geq 0

And that's the required inequalities .

7 0
3 years ago
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