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Alona [7]
3 years ago
14

helpppp plsss What shape is created by the rotation around the given axis "a"? Prism Cone Pyramid Sphere

Mathematics
1 answer:
coldgirl [10]3 years ago
3 0

Answer:

Option (2)

Step-by-step explanation:

From the picture attached,

When the given shape is rotated about the axis 'a',

Triangle ABC forms a 3-D figure of a cone.

Segment AB is the diameter of the circular base and CD is the height of the cone.

Therefore, Option (2) CONE will be the answer.

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Let x,y \epsilon R. Use mathmatical induction to prove the identity.
mariarad [96]

Step-by-step explanation:

We will prove by mathematical induction that, for every natural n,  

(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=x^{n+1}-y^{n+1}

We will prove our base case (when n=1) to be true:

Base case:

(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=(x-y)(x^{1}+y^{1})=x^2-y^2=x^{1+1}-y^{1+1}

Inductive hypothesis:  

Given a natural n,  

x^{n+1}-y^{n+1}=(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})

Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

Observe that, for y=0 the conclusion is clear. Then we will assume that y\neq 0.

(x-y)(x^{n+1}+x^{n}y+...+xy^{n}+y^{n+1})=(x-y)y(\frac{x^{n+1}}{y}+x^{n}+...+xy^{n-1}+y^{n})=(x-y)y(\frac{x^{n+1}}{y})+(x-y)y(x^{n}+...+xy^{n-1}+y^{n})=(x-y)y(\frac{x^{n+1}}{y})+y(x^{n+1}-y^{n+1})=(x-y)x^{n+1}+y(x^{n+1}-y^{n+1})=x^{n+2}-yx^{n+1}+yx^{n+1}-y^{n+2}=x^{n+2}-y^{n+2}\\

With this we have proved our statement to be true for n+1.    

In conlusion, for every natural n,

(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=x^{n+1}-y^{n+1}

8 0
3 years ago
Can someone plz help with this, this is one question, the choices for the first option are; coin, quartered spinner, number cube
ICE Princess25 [194]

Answer:

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5 0
3 years ago
4) y=-4x-1<br> Finding slope
Lisa [10]

Answer:

4/1

Step-by-step explanation:

this is because it is 4x

6 0
3 years ago
Read 2 more answers
What is theoretical vs practical domain in an exponential equation. Plz provide an example too
olya-2409 [2.1K]

Answer:

The theoretical probability of an event occurring is an "expected" probability based upon knowledge of the situation. It is the number of favorable outcomes to the number of possible outcomes. Example: ... There are 6 possible outcomes when rolling a die: 1, 2, 3, 4, 5, and 6. The only favorable outcome is rolling a 6.Practical domains and ranges narrow the solution sets to be realistic within defined parameters.The possible values of "x" is called the domain. The possible values of "y" is called the range.

Step-by-step explanation:

7 0
3 years ago
Pine Bluff Middle School is having its annual Spring Fling dance, which will cost \$400$400dollar sign, 400. The student treasur
nikklg [1K]

The <em><u>correct answers</u></em> are:

The inequality is 75+4t ≥ 400, and they must sell at least 82 tickets.

Explanation:

t is the number of tickets sold. They start out with $75, so that is where our inequality begins. Each ticket is $4; this gives us the expression 4t. Together with the $75 carry over, we have 75+4t.

They must make at least $400 to pay for the dance. This means it must be more than or equal to 400; this gives us 75+4t ≥ 400.

To solve this, first subtract 75 from each side:

75+4t-75 ≥ 400-75

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Divide both sides by 4:

4t/4 ≥ 325/4

t ≥ 81.25

We cannot sell a portion of a ticket, so we round. While mathematically this number would "round down," if they only sell 81 tickets, they will not have enough money. Therefore we round up to 82.

7 0
3 years ago
Read 2 more answers
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