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AlexFokin [52]
3 years ago
10

A community swimming pool has a deep end and a shallow end. The volume of water

Mathematics
1 answer:
marysya [2.9K]3 years ago
6 0

Bc

Answer:

24

Step-by-step explanation:

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A trader buys pens at $44 a dozen and sells them at $20 each. Find his profit if he sells 60 pens.
Stels [109]
60 pens/ A dozen pens= 5 packs of a dozen pens
$44*5= $220 total spent
$20*60=$1200 total money a trader gets
$1200-$220=$980 in profits.

Hope I didn't mess up for your sake.
4 0
3 years ago
Dion has a pizza with a diameter of 10 1/3 inch is the square box shown big enough to fit the pizza inside justify your answer
I am Lyosha [343]

Given :

Diameter of pizza , D=10\dfrac{1}{3}=\dfrac{31}{3} .

To Find :

Is square box of size equal to diameter big enough to fit pizza inside it .

Solution :

Area of pizza :

A_p=\pi(\dfrac{D}{2})^2\\\\A_p=\pi\times (\dfrac{31}{3\times 2})^2\\\\A_p=83.86\ inch^2

Area of square with side equal to diameter :

A_s=D^2\\\\A_s=(\dfrac{31}{3})^2\\\\A_s=106.78\ inch^2

Since , the area of square is more than area of pizza .

Therefore , pizza can easily be fitted .

Hence , this is the required solution .

8 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
HELP ME PLS ANYONE THIS IS HARD
amm1812

Answer: C(14, -5)

Step-by-step explanation:

7 0
3 years ago
Refer to the figure. Barton Road and Olive Tree Lane
Fantom [35]

Angles at right-angle add up to 90 degrees

The measure of acute angle Tryon Street forms with Barton Road is <em>33 degrees</em>

The angle is given as:

\mathbf{A = 57^o} ---- <em>Angle formed by Tryon Street with Olive Tree Lane. </em>

The measure of the acute angle formed by Tryon Street with Barton Road (B) is calculated using:

\mathbf{A + B = 90} ---- angle at right-angle

Make B the subject

\mathbf{B = 90 - A}

Substitute 57 for A

\mathbf{B = 90 - 57}

\mathbf{B = 33}

Hence, the measure of acute angle is 33 degrees

Read more about acute angles at:

brainly.com/question/10334248

3 0
2 years ago
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