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3 years ago

A company makes two sizes of cylindrical shaped boxes. The ratio of the heights is 5:7.

Mathematics

1 answer:

Dmitrij [34]3 years ago

8 0

Answer:

The volume ratio is also 5 : 7

Step-by-step explanation:

The volume of a cylinder is given by the following formula:

volume = pi*r²*h

Since we have two cylinders and their height varies at a ratio of 5:7 we can say that the smaller one has a height of "h" while the bigger has height of "(7/5)*h". Thefore their volume is:

volume smaller = pi*r²*h

volume bigger = pi*r²*(7/5)*h

volume bigger = (7/5)*pi*r²*h

The ratio of their volume is given by the division of the smaller volume by the bigger one:

volume ratio = volume smaller / volume bigger

volume ratio = (pi*r²*h) / [(7/5)*pi*r²*h] = 1/(7/5)

volume ratio = 5/7

The volume ratio is also 5 : 7.

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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.

4 0

3 years ago

Triangle ABC is graphed on the coordinate plane below. What is the approximate length of segment AB in units.

Citrus2011 [14]

Answer:

5 units

Step-by-step explanation:

Count from point A to point B on the x-axis.

8 0

3 years ago

68% of the tickets sold at a water park were child tickets. If the park sold 50 tickets in all, how many child tickets did it se

Mnenie [13.5K]

Answer:

$\boxed{\bf\: The \: park \: sold \boxed{ 34{}} \: child \: tickets.}$

Step-by-step explanation:

Given:

Percentage of Tickets sold at a water park - 68%

The Number of Tickets if the park sold in all - 50

To Find:

The Number of child tickets the park sold.

Solution:

We know that 68% equals to 68/100.

Step 1: Multiply 68/100 by 50 which is the number of tickets the park sold :-

$\sf \: = \: \cfrac{68}{100} \times 50$

Note:The Simplified form of 68/100 * 50 would be the answer to this question.

Step 2: Cancel One zero of 50 and one zero of 100,That is:-

$\sf = \cfrac{68}{ 10\cancel0} \times 5 \cancel0$

Results to,

$\sf = \cfrac{68}{10} \times 5$

Step 3: Cancel 5 and 10, That is:-

$\sf = \cfrac{68}{ \cancel{10 }} \times \cancel5$

Results to,

$\sf =\: \cfrac{68}{2} \times 1$

$\sf = \cfrac{68}{2}$

Step 4: Cancel 68 and 2, That is:-

$\sf =\: \cfrac{ \cancel{68}}{ \cancel2}$

Results to,

$\sf = \cfrac{34}{1}$

$\sf = 34$

34 is the result.

Hence,

$\underline{ \rm \: The \: park \: sold \: \bold{ 34 } \: child \: tickets.}$

________________________________

I hope this helps!

Let me know if you have any questions.I am joyous to help!

6 0

3 years ago

Please help!!! For extra credit.

qaws [65]

Answer:

x=24

Step-by-step explanation:

8x-13 = 7x+11; (because it's a rectangle)

8x - 7x = 11 + 13; (moving xs to one side, the rest to the other)

x = 24

7 0

3 years ago

CAN SOMEONE HELP MEEEEE

Lorico [155]

Answer:

Ok 1 is 54 yards 2 is 225 KM 3 64 Ft

please give braineist I never got 1 thank you maybe we can be friends !!! :) :D

6 0

3 years ago

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