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3 years ago

Can someone pls help

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

7 0

Answer:

Step-by-step explanation:

I honestly dont know the step by step process but im pretty sure its A

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A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

Factor completely and then place the factors in the proper location on the grid. 4y 2 + 25y + 6

astraxan [27]

(4y + 1)(y + 6)
I don't know what you mean by proper location
It shouldn't matter what order the factors are in.

8 0

3 years ago

2X-1/4y=1 solve for Y

Schach [20]

Answer:

Y=8x-4

Step-by-step explanation:

2x -1/4y= 1

2x -1 = 1/4 y

4(2x -1) =y

8x -4 = y

5 0

3 years ago

Write an equation of a line passing

Makovka662 [10]

Answer:

slope of line pass throught jk is 0.5 slope

since line perpendicular to jk then x × 0.5= -1 so slope of line perpendicular is -2

then eq of line is y= -2x -15

6 0

3 years ago

Does the sides 14, 3, 9 make a triangle?

lakkis [162]

Answer: No

Step-by-step explanation: The way that you know is you put the #s from least to greatest 3,9,14 then add the 2 smallest #s and if it is greater than the biggest #it does make a triangle so it would be 12<14 and that is false .

3 0

3 years ago