All categories

2 years ago

What shape is created by the rotation and what is the

Mathematics

1 answer:

zlopas [31]2 years ago

4 0

Answer:

Option D: A cylinder with a circumference of about 50 units

Step-by-step explanation:

The rest of the question is the attached figure.

The square shown has a perimeter of 32 units. The square is rotated about line k. What shape is created by the rotation and what is the approximate circumference of the base? Circumference of a circle: C = 2πr

===================================================

Given: the perimeter of the square = 32

perimeter of a square is four times the length of its side

So, the side length of square = 32/4 = 8 units

The square is rotated about line k.

So, it will form a cylinder with radius 8 units.

Circumference of a circle = 2 π r

Where, r is the radius of the circle.

Circumference of the base is C = 2 π * 8

∴ C = 16π = 16 * 3.14

∴ C = 50.26548 ≈ 50

The shape is created by the rotation is a cylinder with a circumference of about 50 units.

So, the answer option is D.

You might be interested in

a prayng mantis is an interesting insect that can rotate its head 180 degrees.Suppose the praying mantis at the right is 10.5 ce

cricket20 [7]

The fact that it can turn its head 180 degrees is just extra information. They tell us that it is 10.5 cm long. What they're asking for is the length in a mixed number, so 10.5 as a mixed number.

7 0

2 years ago

Read 2 more answers

What is the slope 5x+2y=-2

SpyIntel [72]

The slope is -2.5 because you subtract 2y from both sides, then add two to both sides, then divide both sides by 2 to isolate y

6 0

2 years ago

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. The area of printed material on the po

grin007 [14]

Answer:

Dimensions of printed poster are

length is 32 cm

width is 48 cm

Step-by-step explanation:

Let's assume

length of printed poster is x cm

width of printed poster is y cm

now, we can find area of printed poster

so, area of printed poster is

$=xy$

we are given that area as 1536

so, we can set it to 1536

$xy=1536$

now, we can solve for y

$y=\frac{1536}{x}$

now, we are given

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm

so, total area of poster is

$A=(8+x+8)\times (12+y+12)$

$A=(x+16)\times (y+24)$

now, we can plug back y

$A=(x+16)\times (\frac{1536}{x}+24)$

now, we have to minimize A

so, we will find derivative

$A'=\frac{d}{dx}\left(\left(x+16\right)\left(\frac{1536}{x}+24\right)\right)$

we can use product rule

$A'=\frac{d}{dx}\left(x+16\right)\left(\frac{1536}{x}+24\right)+\frac{d}{dx}\left(\frac{1536}{x}+24\right)\left(x+16\right)$

$=\frac{d}{dx}\left(x+16\right)\left(\frac{1536}{x}+24\right)+\frac{d}{dx}\left(\frac{1536}{x}+24\right)\left(x+16\right)$

now, we can simplify it

$A'=-\frac{24576}{x^2}+24$

now, we can set it to 0

and then we can solve for x

$A'=-\frac{24576}{x^2}+24=0$

$-\frac{24576}{x^2}x^2+24x^2=0\cdot \:x^2$

$-24576+24x^2=0$

$x=32,\:x=-32$

Since, x is dimension

and dimension can never be negative

so, we will only consider positive value

$x=32$

now, we can solve for y

$y=\frac{1536}{32}$

$y=48$

so, dimensions of printed poster are

length is 32 cm

width is 48 cm

5 0

2 years ago

Tim 2/3 of 1 3/4 cups of flower with sugar and butter what fraction of the flower did he use

ivann1987 [24]

2/3 of 1¾ is simply their product, let's firstly convert the mixed fraction to improper fraction.

$\bf \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\\\ \cfrac{2}{3}\cdot \cfrac{7}{4}\implies \cfrac{2}{4}\cdot \cfrac{7}{3}\implies \cfrac{1}{2}\cdot \cfrac{7}{3}\implies \cfrac{7}{6}\implies 1\frac{1}{6}$

8 0

3 years ago

What is 3/5 written as a percent? A 3.5% B 30% C 35% D 60%

goldfiish [28.3K]

D is the correct answer.

6 0

2 years ago

Read 2 more answers