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MissTica
2 years ago
11

Which object would weigh closest to 5 pounds A.Bee B. Flour C.Hat D.Football​

Mathematics
1 answer:
kodGreya [7K]2 years ago
5 0

I believe the answer is football.

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a contractor was hired to remodel a kitchen. she can complete 3/8 of the kitchen remodeling project in one day. how much of the
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She would have 5/8 days left
8 0
3 years ago
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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}.

7 0
3 years ago
The histogram shows the prices for six-packs of adult socks and six-packs of kid socks at a store. What is true about the variab
Agata [3.3K]

Answer:

a. There is more variability in the prices of kid socks because they have a greater range.

Step-by-step explanation:

A measure of variability is a summary statistic that represents the amount of dispersion in a dataset. Common examples are range, interquartile range (IQR), variance, and standard deviation.

From the histogram

Highest Number of Packs of Adult Socks = 7

Lowest Number of Packs of Adult Socks = 5

Range = 7 - 5 =2

Highest Number of Packs of Kid Socks = 7

Lowest Number of Packs of Kid Socks = 4

Range = 7-4 = 3

We conclude that there is more variability in the prices of kid socks because they have a greater range.

The correct option is A.

8 0
3 years ago
Cw 11.1 11.4 round to the tenths
wariber [46]

Answer:

1. A = 21,924.0

2. A = 1,584.0

3. A = 104.0

4. A = 126.0

5. A = 81.0

6. A = 217.0

7. A = 67.5

8. x = 6.0

9. x = 20.0

Step-by-step explanation:

Kindly find the attached for the step by step explanation

3 0
3 years ago
Read 2 more answers
X Cube - 5x Square - 2 x + 24​
Otrada [13]

Answer:

(x+2)(x-4)(x-3)

(x²-4x+2x-2)(x-3)

(x²-2x-2)(x-3)

=x³-5x²-2x+24

So the answer true

8 0
3 years ago
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