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boyakko [2]
3 years ago
5

HELP PLEASE (i need the answer and maybe an explanation but all i really want is an answer please)

Mathematics
1 answer:
Alina [70]3 years ago
3 0
C. 2x
This is because 2(2) is 4 and 2(4) is 8. You basically find the pattern between x and y. For these numbers you take x and multiply it by 2.
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Which of the following is equal to π
Kruka [31]

Answer:

Step-by-step explanation:

C = πd.  An equivalent formula is C = 2πr.

Solving the first equation for π, we get π = C/d.  Solving the second equation for r, we get π = C / (2r)

4 0
3 years ago
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}.

7 0
3 years ago
Luis is a professional musician.He needs to
Deffense [45]

Step-by-step explanation:

The following prices for the same make  and model used guitar for his work are :

$699.20,$700.30,$680.50,$700.30, and  $800.25.

Mean of ungrouped data = sum of observations/total no of observations

\text{Mean}=\dfrac{699.20+700.30+680.50+700.30+800.25}{5}\\\\\text{Mean}=\$716.11

For median, arrange the given data in ascending order.

$680.50, $699.20, $700.30, $700.30, $800.25

Median = middle value

Median = $700.30

The value that comes most often is called mode.

$700.30 comes two times. So, mode is $700.30

Hence, Mean = $716.11, median = $700.30 and mode = $700.30

5 0
3 years ago
Slope is 2, and (3,8) is on the line.<br> Please help :(
MaRussiya [10]
Are you trying to write an equation?

y-8=2(x-3)
y=2x-6+8

y=2x+2
5 0
3 years ago
"Ten subtracted from the quotient of a number and<br>7 is less than -6.​
RideAnS [48]
Written out, this would be (x / 7) - 10 < -6

solved, it would be x < 28
5 0
3 years ago
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