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____ [38]
3 years ago
14

An inflatable beach ball has a circumference of 141.3 centimeters what is the volume of the beach ball when fully inflated

Mathematics
1 answer:
Naddik [55]3 years ago
4 0

The volume of fully inflated ball is 47688.75 cubic centimeter

Step-by-step explanation:

Step 1 :

The circumference of the given beach ball = 141.3 centimeters

We need to find volume of the inflated ball

Step 2 :

Circumference  = 2 \pi r = 141.3 [r is the radius]

=> r =  22.5 [ This is obtained by dividing 141.3 by 2  \pi]

The volume of the fully inflated ball is the volume of a sphere with the radius 22.5

Therefore volume = (4/3)  \pi r³ =  (4/3)  \pi (22.5)³ = 47688.75 cubic centimeter

Step 3 :

Answer :

The volume of fully inflated ball is 47688.75 cubic centimeter

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If 18√8 - 8 √18 = √n, what is n?
Yuliya22 [10]

Answer:

n=288

Step-by-step explanation:

Rewrite the equation as  

√

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√

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n

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(

18

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18

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2

Cancel the common factor of  2  

Cancel the common factor.

n

1

2

⋅

2

=

(

18

√

8

−

8

√

18

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2

Rewrite the expression.

n

1

=

(

18

√

8

−

8

√

18

)

2

Simplify.

n

=

(

18

√

8

−

8

√

18

)

2

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(

18

√

8

−

8

√

18

)

2

Simplify each term.

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2

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(

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(

2

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2

Rewrite  

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2

Pull terms out from under the radical.

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(

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−

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2

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−

8

√

9

(

2

)

)

2

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9

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3

2

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n

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(

36

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−

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√

3

2

⋅

2

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2

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36

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2

−

8

(

3

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2

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2

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2

2

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x

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2

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(

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n

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n

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=

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2

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2

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2

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144

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2

2

2

Cancel the common factor of  

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2

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2

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5 0
3 years ago
According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x^5
nata0808 [166]

Answer:

The correct option is A.

Step-by-step explanation:

The question is:

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?

A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12

B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x

C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3

D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48

Solution:

The function given to us is:

3x5 – 2x4 + 9x3 – x2 + 12

Find the factors of 12 and consider it as 'p'

The factors of 12 are:

p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6

Now find the factors of 3 and consider it as 'q'

The factors of 3 are:

q = +/- 1 , +/- 3

We know that we write rational terms in p/q form.

Therefore the Rational roots are given by p/q

+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3

Now we will solve the first function given in part A.

f(x) = 3x^5 – 2x^4 - 9x^3 + x^2 - 12

Again find the factors of 12 and consider it as 'p'

The factors are:

p = +/- 1 , +/-2 , +/-3 , +/- 4 , +/-6

Now find the factors of 3 and consider it as 'q' .

q = +/- 1 , +/- 3

Rational root are given by p/q

+/- 1 , +/-2 , +/-3 , +/- 4 , +/-6 , +/- 1/3 , +/- 2/3 , +/- 4/3

Therefore the rational roots of the given function matches the rational roots of the given equation.

Hence the correct option is A

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