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4 years ago

A sphere and a cone have the same volume each figure has a radius of 3 inches what is the height of the cone

1 answer:

4 0

Volume of the sphere = 4/3πr³
Volume of the sphere = 4/3 (π) (3)³
Volume of the sphere = 36π

Volume of the sphere = Volume of the cone

36π = 1/3π(3)²h
36π = 3πh
h = 36π ÷ 3π
h = 12

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Answer: The height is 12 inches.
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Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)

Svetlanka [38]

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial $p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17$ . The polynomial is in standards when has the form $p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}$ , where $n$ is the order of the polynomial. The example has the following information:

$n = 3$ , $a_{0} = 17$ , $a_{1} = -6$ , $a_{2} = 2$ , $a_{3} = 5$ .

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials $p_{1}$ and $p_{2}$ such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$ and $p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}$ , where $m \geq n$

$p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}$

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be $p_{1}$ a polynomial such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$

And $\alpha$ an scalar. If the polynomial is multiplied by the scalar number, then:

$\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}$

Lastly, the following expression is constructed by distributive property:

$\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}$

Hence, polynomials are closed with respect to multiplication.

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3 years ago

The sum of three times a number and six is twelve.

Kaylis [27]

For this case we must raise the equation according to the given statement.

Let the variable "x" be the unknown number.

So, three times the number is: $3x$

If to that term is added "6" we have:

$3x+6$

The sum of both terms is "12", then:

$3x+6 = 12$

Thus, the equation is: $3x+6 = 12$

Answer:

$3x+6 = 12$

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3 years ago

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Yuri [45]

Answer:

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Step-by-step explanation:

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3 years ago

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AnnyKZ [126]

Answer:

h=$65/13

Step-by-step explanation:

So he has $85

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