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The radius and the height of the dimension that will minimize the amount of material used in the construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.

The dimension that minimizes the surface area of a cylinder can be determined by:

Given that:

The area of the cylinder = (2 πr)h + 2(πr²)

The volume of the cylinder

Let's identify the constraint equation and Optimization equation:

To minimize the surface area of the can, we have:

The constraint equation is the equation that limits us:

So, Let's solve for h in our volume equation, we have:

3000 = πr² h

h = 3000/πr²

Now, from the Area equation

[tex]\mathbf{A = 2 \pi r(\dfrac{3000}{\pi r^2}) + 2\pi r^2}[/tex]

Taking the derivate and setting it to zero, we have;

Derivative:

[tex]\mathbf{A = \dfrac{6000}{ r}+ 2\pi r^2}[/tex]

[tex]\mathbf{A = 6000 r^{-1} + 2\pi r^2}[/tex]

[tex]\mathbf{A' = -6000 r^{-2} + 4\pi r}[/tex]

[tex]\mathbf{A' = 4\pi r-\dfrac{6000}{ r^{2} }}[/tex]

Setting it to zero, we  have:

[tex]\mathbf{0=\dfrac{ 4 \pi r^3 - 6000}{r^2}}[/tex]

Factor out 4

0 = 4(πr³ - 1500)

1500 = πr³

r³ = 1500/π

[tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex]

The above is the radius that minimizes the surface area of the cylinder;

From [tex]\mathbf{h = \dfrac{3000}{\pi r^2}}[/tex]

[tex]\mathbf{h = \dfrac{3000}{\pi ( \sqrt[3]{\dfrac{1500}{\pi}} )^2}}[/tex]

[tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex]

Thus, the radius and height that minimize the amount of material to be used in its construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.

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Answer:

A) 5

Explanation:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 - (y_2 - y_1)^2}[/tex]

Here given points:

Distance:

[tex]\rightarrow \sf \sqrt{(6 - 3)^2 - (8 - 4)^2}[/tex]

[tex]\rightarrow \sf \sqrt{9 +16}[/tex]

[tex]\rightarrow \sf \sqrt{25}[/tex]

[tex]\rightarrow \sf 5[/tex]

The mean of the data set is 22.1

The sample proportion of numbers less than the mean is %53

To find the mean,

We would sum the numbers and then divide them by the number of data.

25.5 + 26 + 18.2 + 15.3 + 28.5 + 27 + 20.7 + 20.2 + 26.1 + 18.2 + 21.4 + 17.9 + 24.3 + 22.6 + 19.6

= 331.5

331.5/15= 22.10.

To find the proportion of numbers, we would order them:

15.3

17.9

18.2

18.2

19.6

20.2

20.7

21.4

---------

22.6

24.3

25.5

26

26.1

27

28.5

The discontinuous line shows the split of the data that are less than the mean.

Those data are 8 in number and their proportion is:

8 / 15

= 0.53

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Answer: Second statement is false

Step-by-step explanation: You cannot subtract 89 from 500 and get 500. You get 411.

Answer:

f(x) = -1/2x + 8

or

The first one

Step-by-step explanation:

hope this helps

have a good day

Answer:

∠N = 21

Step-by-step explanation:

Sum of all angles of triangle = 180°

   4x - 13 + 2x - 13 + 5x + 19 = 180

    4x + 2x + 5x  -13 - 13 + 19 = 180

Combine like terms

                       11x  - 7  = 180

                               11x = 180 + 7

                                11x = 187

                                  x = 187/11

x = 17

m∠N = 2x - 13

           = 2*17 - 13

           = 34 - 13

          = 21

Answer:

=170/3 or (decimal 56.67)

Step-by-step explanation:

Steps

∫⁵ x²+3dx

⁰

Apply the Sum Rule: ∫fx) + gx) dx = ∫f(x)dx +-∫ g(x)

dx

∫⁵ x² dx +∫⁵ 3dx

⁰ ⁰

∫⁵ x² dx=125/3

⁰

∫⁵ 3dx=15

⁰

125/3+15

=170/3

The area of the reflective material is:  284 square yards.

A rectangle is a quadrilateral with four sides and four right-angles.

it has two lines of symmetry.

Analysis:

To find the area of the reflecting material we find the area of the following shapes: trapezium + rectangle + triangle

bigger base of trapezium = 2 + 6 + 2 = 10 yard

smaller base of trapezium = 6

length of rectangle = 18 yard

width of rectangle : 2+6+2 = 10 yard

base of triangle is =  10 yard

Area of reflective material = 1/2(6+10) + 18x10 + 1/2(10)(8) = 284 square yards

In conclusion, the area of reflective material is : 284 square yards.

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[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{9}{3}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{4}) \\\\\\ y-1=3x-12\implies y=3x-11[/tex]

Answer:

The answer is 76.

Step-by-step explanation:

The median would be the middle number in a box and whisker plot.

Answer:

D

Step-by-step explanation:

the number of days for 80 - 82 is 7 and the number of days for 82-84 is 9. Those are the only temperatures below 84 degrees, so you add them and get 16 :)

Answer:

28 m

Step-by-step explanation:

full roll length: r

Ryan bought: r/4

He trimmed 2 m: r/4 - 2

Length left: 5

r/4 - 2 = 5

r/4 = 7

r = 28

Answer: 28 m

Answer:

5ft

Step-by-step explanation:

8/10=0.8

4/0.8=5

in an exponential expression, the rate of change is usually the parenthesized expression, namely on y = a(b)ˣ, the rate will be "b", so in this case the rate is just ∛24

[tex]\sqrt[3]{24} ~~ \begin{cases} 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^3\cdot 3 \end{cases}\implies \sqrt[3]{2^3 \cdot 3}\implies 2\sqrt[3]{3}[/tex]

hmmm well, don't be so  hmmm off due to it, the wording in the exercise sux0rs bad, is very poorly worded and laid out.

if X and Y are numbers, hmmm say let's give them hmmm ohhh X = 7 and Y = 13.

And X and Y are also complete cubes, well, let's make them so, X = 7³ and Y = 13³.

which of those expressions are complete cubes, or namely, something that we can write as a number with a "3" in the exponent, let's check each one.

[tex]\begin{array}{ll|l|l|lllll} 8X&\implies 8\cdot 7^3& 2^3\cdot 7^3& (2\cdot 7)^3& 14^3 ~~ \checkmark\\&&&&\\ X,Y&\implies 7^3,13^3 ~~ \checkmark&&\\&&&&\\ -X&\implies -7^3~~ \checkmark&&\\&&&&\\ 27XY&\implies 27\cdot 7^3\cdot 13^3& 3^3\cdot 7^3\cdot 13^3& (3\cdot 7\cdot 13)^3& 273^3~~ \checkmark\\&&&&\\ XY+27&\implies 7^3\cdot 13^3+27&(7\cdot 13)^3 + 3^3&&91^3+3^3 ~~ \bigotimes \end{array}[/tex]

what's wrong with the last one?  well, if we were to add 91³ + 3³ = 753598.  Now, is 753598 a complete cube? well, only if we could write it as a whole number with a "3" above, can we? nope.

we can simply check that by getting the 3rd root of that value,

[tex]\sqrt[3]{753598}\approx 91.00108681228277\impliedby \textit{not a complete cube}[/tex]

Based on the calculation below, the amount that can be withdrawn each month for 10 years is a. $769.27.

First, we calculate the future value (FV) of the amount after 20 years using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = A * (((1 + r)^n – 1) / r) ................................. (1)

Where,

FV = Future value of the amount after 20 years =?

A = Monthly deposit = $235.15

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 20 * 12 = 240

Substituting the values into equation (1), we have:

FV = $235.15 * (((1 + 0.00266666666666667)^240 – 1) / 0.00266666666666667) = $78,910.41

The amount planned to be withdrawn on monthly basis can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:

P = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

P = Monthly withdrawal or payment = ?

PV = Present value = FV calculated above = $78,910.41

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 10 * 12 = 120

Substitute the values into equation (2), we have:

P = $78,910.41PV / ((1 - (1 / (1 + 0.00266666666666667))^120) / 0.00266666666666667) = $769.27

Therefore, the amount that can be withdrawn each month for 10 years is $769.27.

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The answer is A: $769.27

-----------------------------------------------------------------

Have a great day and God bless! :D

Answer:

5 / 16

Step-by-step explanation:

For a question such as this, we most often simply use a calculator. However, I suppose that to do this by hand you would do as follows:

0.025 / 0.080

= 0.005  / 0.016

= 100 * (0.005 / 0.016)

= 5 / 16

The first step is a simplification. Both the numerator and denominator are divisible by 0.005.  In the next step, we can multiply the numerator and denominator both by 100 to get whole numbers. Because we multiply each by the same number, we have not changed the value of the original fraction. This leaves us with 5 / 16.

Done

Answer:

  800 ft²

Step-by-step explanation:

The total surface area of a square-base pyramid is given by the formula ...

  A = s(s +2h) . . . . . . where s is the side length, h is the face slant height

In this problem, we need to find the slant height of a face in order to use this formula.

__

The distance from the middle of one edge of the base to the peak of the pyramid is the slant height of a face of the pyramid. It is the hypotenuse of a right triangle whose legs are the pyramid height, and half the width of the base. For this pyramid, that is a right triangle with legs 15 and 8.

The Pythagorean theorem is used to find the hypotenuse of that triangle:

  c² = a² +b² . . . . square of hypotenuse = sum of squares of legs

  c² = 15² +8² = 225 +64 = 289

  c = √289 = 17

The slant height of a face of the pyramid is 17 ft.

The area formula tells us the total surface area is ...

  A = s(s +2h)

  A = (16 ft)(16 ft + 2×17 ft) = (16 ft)(50 ft)

  A = 800 ft²

The total surface area is 800 square feet.

Answer:

[tex]y=\sqrt{\frac{x^{2}}{2} +34}[/tex]

Step-by-step explanation:

[tex]2y\left( x\right) y^{\prime }\left( x\right) =x[/tex]

[tex]\Longrightarrow \int 2y\left( x\right) y^{\prime }\left( x\right) dx=\int x\ dx[/tex]

[tex]\Longrightarrow y^{2}\left( x\right) =\frac{x^{2}}{2} +c\ \text{(c is a constant)}[/tex]

[tex]y\left( 2\right) =6\Longleftrightarrow y^{2}\left( 2\right) =36[/tex]

[tex]y^{2}\left( 2\right) =36\Longleftrightarrow \frac{\left( 2\right)^{2} }{2} +c=36\ \Longleftrightarrow c=34[/tex]

[tex]\Longrightarrow y\left( x\right) =\pm\sqrt{\frac{x^{2}}{2} +34}[/tex]

Answer:

Step-by-step explanation:

-u-5+10u-25=9u-30

it was easy.

Answer:

Could you possible line the numbers up a little bit, it'd be better to understand that way.

Answer:

[tex]l(\widehat {ST})=6\pi [/tex]

Step-by-step explanation:

The required length of an arc ST is 6π units which is subtended by an angle.

The arc is a portion of the circumference of a circle.

The formula for calculating the arc states that:

Arc length = 2πr (θ/360)

Where r = the radius of the circle,

θ = the angle (in degrees) subtended by an arc at the center of the circle.

As per the question, we have:

θ = 90° and r = 12 units

Substitute the given values in the formula,

Arc length = 2π(12) (90/360)

Arc length = 6π

Therefore, the required length of an arc ST is 6π units.

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Using an exponential function, it is found that the population of Clay County will be of $13,482.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, the current population is 10,300 people, with a growth rate of 3%, hence A(0) = 10,300 and r = 0.03.

The equation is given by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 10300(1 + 0.03)^t[/tex]

[tex]A(t) = 10300(1.03)^t[/tex]

Hence, in 10 years, the population will be given by:

[tex]A(10) = 10300(1.03)^{10} = 13842[/tex]

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Answer: 7,595

Step-by-step explanation:

ixl

Answer:

Since there isn't any of the following attached, I made my wn attached below

Step-by-step explanation:

Population size: 12

Median: 28.5

Minimum: 23

Maximum: 37

First quartile: 25.5

Third quartile: 30.75

Interquartile Range: 5.25

Outliers: none

Hope this helps you a little more for your last day of finishing hmw :)

Let me know if you need anymore help !

OR have questions

Answer:

[tex] |x|1 | \: 2 | \: 3 | \: 4 | \: 5 | \\ |y| 5| \: 4 \: | 3 \: | 2 | 1| [/tex]

Step-by-step explaination:

We were told that:

[tex] x + y = 6 [/tex]

therefore to see if it is correct you can just input the values for x and y and see if they add up to 6 (add the vertical values). For example;when x = 1, y = 5 or when x = 2, y = 4

Answer:

Option 4

Step-by-step explanation:

Equating given length and width to the area :

Finding the dimensions :

Answer:

Yes, 1.010010001 is rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Answer:

Step-by-step explanation:

A rational number has the form p q, where p and q are integers, q* 0 otherwise it is an irrational number.

The solution range of the given inequality is  (-∞, -4.121) and (0.121,∞)

Here we want to solve:

[tex]2x - 1/(x + 4) \geq 0[/tex]

To solve this, we multiply both sides by (x + 4) so we get:

[tex]2x*(x + 4) - 1 \geq 0\\\\2x^2 + 8x - 1 \geq 0[/tex]

Now we can solve it graphically, below we have:

There we can see that the solution range is (-∞, -4.121) and (0.121,∞), the regions where the graph is equal or above the horizontal axis.

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Answer:

8x4-2x2+7

Step-by-step explanation:

it's 100 percent right trust me