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Art [367]
2 years ago
15

1. Name the two-dimensional shapes that when rotated around the vertical axis form the following three-dimensional solids?

Mathematics
2 answers:
Vedmedyk [2.9K]2 years ago
7 0

Problem 1

Answers:

  • Cone: Triangle
  • Cylinder: Rectangle
  • Sphere: Circle

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

Explanation:

Imagine a fan blade rotating. As it rotates really quickly, it occupies a 3D space. Or perhaps imagining rotating eggbeaters is a better thing to have in mind. Those blades spin really fast to form a 3D shape. So that's what's going on with this problem. If you spin a triangle around an axis, a cone will form. The base of the triangle forms the base of the cone. Half the base of the triangle is the radius of the cone. The height of the triangle is the height of the cone.

Similarly, a rectangle rotated around its center axis forms a cylinder. Think of a revolving door. That's often a classic example. Finally, a circle spun around any of its diameters will form a sphere.

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

Problem 2

Answers:

  • Object 1: Cup = Cylinder
  • Object 2: Ball = Sphere
  • Object 3: Funnel = Cone
  • Object 4: Paper towel roll = Cylinder

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

Explanation:

Pick objects around your house that are fairly simple in design and resemble either a cylinder, sphere, or cone. A cup resembles a cylinder just it doesn't have a top to it. A ball is a 3D sphere that has an interior to it, unless the ball is filled with air. A funnel resembles a cone due to its triangular shape of sorts. A paper towel roll (the card board piece or the cardboard plus the actual paper towels) resemble a cylinder as well. You can pick any four other objects you have around your house such as a cylindrical speaker, batteries (shaped as a cylinder), soup cans (also cylinders), and so on.

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

Problem 3

Answers:

  • a) volume of cylinder = pi*r^2*h
  • b) volume of sphere = (4/3)*pi*r^3
  • c) volume of pyramid = (1/3)*L*W*H
  • d) volume of cone = (1/3)*pi*r^2*h

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

Explanation:

These formulas are what you should memorize or have handy on a flashcard. It is possible to derive them, but it would require calculus to do so. Also, such a process is quite length. So memorization or flashcards are the better way to go.

For the cylinder and cone, r is the radius and h is the height. Note how the formulas are nearly identical except the cone has the (1/3) term. This shows that the cone's volume is 1/3 that of the cylinder's volume where they both have the same radius r and height h.

The sphere also deals with the radius r, but we don't have to worry about the height of the sphere (it's really just 2r).

For the pyramid, L,W,H represent the length width and height respectively. The length and width form the base of the pyramid. Recall that L*W*H is the volume of a rectangular block. The volume of a pyramid is 1/3 of that rectangular block's volume.

Molodets [167]2 years ago
4 0

Answer:

3. State the volume formulas for a cylinder, sphere, pyramid, and cone.

a. Volume formula for a cylinder:

b. Volume formula for a sphere:

c. Volume formula for a pyramid:

d. Volume formula for a cone:

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Ahh help plss!! thank u
AnnZ [28]
Basically you’re multiplying them both
(x^3 + 2x - 1)(x^4 - x^3 + 3)

so you need to make sure you multiply each one, if you do it right, you should end up with
x^7 - x^6 + 3x^3 + 2x^5 - 2x^4 + 6x -x^4 +x^3 -3

simplify by adding like terms
x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3

your answer would be the third option
4 0
2 years ago
The geometric sequence a i a i ​ a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 ​ =8a, start subscr
frozen [14]

Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0
3 years ago
How can you put 32.3 as a mixed number in the simplest form
ludmilkaskok [199]

32.3 is a decimal number in which 3 is the digit at the tenth place.

Mixed number contains a whole number and a fraction part.

32.3 expressed as mixed fraction is 32\frac{3}{10} , here 32 is the whole number  and \frac{3}{10} is the fraction part.

\frac{3}{10} is the fraction in the simplest form.

For this reason, 32.3 expressed as a mixed number in the simplest form is 32\frac{3}{10}.

7 0
3 years ago
Paula tiene una cartulina de 50x65 cm. Quiere hacer 5 rectángulos de 210x297 mm. ¿Tendrá suficiente con una cartulina?
brilliants [131]

Answer:

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3 0
2 years ago
Solve the equation 15p2 + 7p − 4 = 0 by completing the square.
natulia [17]

Answer:

p=0 or p=-7/15

Step-by-step explanation:

15p2+7p=0

p(15p+7)=0

p=0 or 15p+7=0

4 0
1 year ago
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