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Tresset [83]
3 years ago
5

Plz help will mark brainliest if correct ​

Mathematics
2 answers:
slamgirl [31]3 years ago
6 0

Answer:

In order by appearance

1. rational

2. irrational

3. rational

4. rational

5. irritatinal

6. rational

7. irritational

Step-by-step explanation:

1) 99/264

2) 8√5

3) 7.12

4) 6

5) pi is not a rational number

6) fractions are rational

7) 1/2·(√6-1)  

Rational numbers are numbers that can be shown as a ratio or a fraction and irrational numbers are the opposite of that

vlabodo [156]3 years ago
5 0
3rd one goes in the first one,
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Consider the equation below. (If you need to use -[infinity] or [infinity], enter -INFINITY or INFINITY.)f(x) = 2x3 + 3x2 − 180x
soldier1979 [14.2K]

Answer:

(a) The function is increasing \left(-\infty, -6\right) \cup \left(5, \infty\right) and decreasing \left(-6, 5\right)

(b) The local minimum is x = 5 and the maximum is x = -6

(c) The inflection point is x = -\frac{1}{2}

(d) The function is concave upward on \left(- \frac{1}{2}, \infty\right) and concave downward on \left(-\infty, - \frac{1}{2}\right)

Step-by-step explanation:

(a) To find the intervals where f(x) = 2x^3 + 3x^2 -180x is increasing or decreasing you must:

1. Differentiate the function

\frac{d}{dx}f(x) =\frac{d}{dx}(2x^3 + 3x^2 -180x) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\f'(x)=\frac{d}{dx}\left(2x^3\right)+\frac{d}{dx}\left(3x^2\right)-\frac{d}{dx}\left(180x\right)\\\\f'(x) =6x^2+6x-180

2. Now we want to find the intervals where f'(x) is positive or negative. This is done using critical points, which are the points where f'(x) is either 0 or undefined.

f'(x) =6x^2+6x-180 =0\\\\6x^2+6x-180 = 6\left(x-5\right)\left(x+6\right)=0\\\\x=5,\:x=-6

These points divide the number line into three intervals:

(-\infty,-6), (-6,5), and (5, \infty)

Evaluate f'(x) at each interval to see if it's positive or negative on that interval.

\left\begin{array}{cccc}Interval&x-value&f'(x)&Verdict\\(-\infty,-6)&-7&72&Increasing\\(-6,5)&0&-180&Decreasing\\(5, \infty)&6&72&Increasing\end{array}\right

Therefore f(x) is increasing \left(-\infty, -6\right) \cup \left(5, \infty\right) and decreasing \left(-6, 5\right)

(b) Now that we know the intervals where f(x) increases or decreases, we can find its extremum points. An extremum point would be a point where f(x) is defined and f'(x) changes signs.

We know that:

  • f(x) increases before x = -6, decreases after it, and is defined at x = -6. So f(x) has a relative maximum point at x = -6.
  • f(x) decreases before x = 5, increases after it, and is defined at x = 5. So f(x) has a relative minimum point at x = 5.

(c)-(d) An Inflection Point is where a curve changes from Concave upward to Concave downward (or vice versa).

Concave upward is when the slope increases and concave downward is when the slope decreases.

To find the inflection points of f(x), we need to use the f''(x)

f''(x)=\frac{d}{dx}\left(6x^2+6x-180\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\f''(x)=\frac{d}{dx}\left(6x^2\right)+\frac{d}{dx}\left(6x\right)-\frac{d}{dx}\left(180\right)\\\\f''(x) =12x+6

We set f''(x) = 0

f''(x) =12x+6 =0\\\\x=-\frac{1}{2}

Analyzing concavity, we get

\left\begin{array}{cccc}Interval&x-value&f''(x)\\(-\infty,-1/2)&-2&-18\\(-1/2,\infty)&0&6\\\end{array}\right

The function is concave upward on (-1/2,\infty) because the f''(x) > 0 and concave downward on (-\infty,-1/2) because the f''(x) < 0.

f(x) is concave down before x = -\frac{1}{2}, concave up after it. So f(x) has an inflection point at x = -\frac{1}{2}.

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Ray picked 30 apples and put them equally into 3 baskets. Then he ate two of the apples in a basket
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Now he has 28 apples left. 
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Crank

Answer:

7.625

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Three​ roads, A,​ B, and​ C, all run south to north. They each meet a highway that runs west to east. Road B is4.5 of Road A. Ro
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Answer: The moon was 20 farms away from earth so If I ate a couch then went to my treadmill outside of my cow, I could add the letter Grammar to my checklist.

Explanation: You see, If there was a man who had no arms or legs he would be walking with his feet right? SO If I added chickens to my head and ate the Eifel tower am I 50% a chocolate bar. Hope this helps

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2 years ago
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The blue dot is at what value on the number line?<br> PLEASE HELP FAST
Elodia [21]

Answer:

-22

Step-by-step explanation:

The blue dot on the number line is 4 units below -10. The number -16 is also labeled, but it is instead just 2 units below -10. If -16 is 2 units below -10, then 2 units is equal to a distance of 6, which means 1 unit is equal to a distance of 3. Because the blue dot is 4 units below -10, the blue dot is 12 less than -10, meaning that the blue dot is at -22.

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