The volume of a cylinder can be determined using the formula V=πr2h, where r and h represent the radius and height of the cylinder, respectively. A volume of paint expressed as (8x3 + 31x2 + 32x)π and a volume of paint expressed as (10x3 + 17x2)π are poured into a paint can in the shape of a cylinder. Determine possible expressions for the radius of the can and the depth of the paint in the can.

Answers

Answer 1

Answer:

Possible expressions for the radius of the can and the depth of the paint in the can are [tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex] and [tex]h = 2\cdot x[/tex], respectively.

Step-by-step explanation:

Let be the initial volumes of the initial cans represented by these expressions:

[tex]V_{1} = (8\cdot x^{3}+31\cdot x^{2}+32\cdot x)\cdot \pi[/tex] (1)

[tex]V_{2} = (10\cdot x^{3}+17\cdot x^{2})\cdot \pi[/tex] (2)

The resulting volume of the paint can is the sum of the two functions:

[tex]V_{3} = (18\cdot x^{3}+48\cdot x^{2}+32\cdot x)\cdot \pi[/tex] (3)

Then, we proceed to factor the polynomial:

[tex]V_{3} = 2\cdot (9\cdot x^{2}+24\cdot x +16)\cdot x \cdot \pi[/tex]

[tex]V_{3} = \pi\cdot (9\cdot x^{2}+24\cdot x + 16)\cdot (2\cdot x)[/tex] (3b)

By direct comparison with the volume formula for the cylinder we have the following expressions:

[tex]r^{2} = 9\cdot x^{2}+24\cdot x + 16[/tex]

[tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex]

[tex]h = 2\cdot x[/tex]

Possible expressions for the radius of the can and the depth of the paint in the can are [tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex] and [tex]h = 2\cdot x[/tex], respectively.


Related Questions

here is my question.

Answers

Answer:

the answer is 18

Step-by-step explanation:

9X6=54

54/3=18

Answer:

18

Step-by-step explanation:

PLEASE HELP WILL MARK BRAINLY

.In the zombie apocalypse, the ratio of children to adults was 3 to 4. The ratio
of adults to zombies was 4 to 5. If there were 200 zombies, then how many
children were there?

2. (4^5)(4^−7) = 4^?

3. . What is the circumference and area of the circle? Use 22/7
for π. Radius=42cm

Answers

Step-by-step explanation:

diameter is 84 thereare 2 time 42 .84.

follow me nice study bye .

please help me with this one!!

Answers

Answer:

V = 960 cm^3

Step-by-step explanation:

Volume of a rectangular prism = L * W * H

V = 12 * 8 * 10

V = 960 cm^3

Answer:

d. 960 cm^3

Step-by-step explanation:

The formula for volume is length x width x height. To solve you have to multiply 12 by 8 by 10 to get 960

Clarence has $90 in a savings account that earns 10% annually. The interest is not
compounded. How much will he have in 5 years?

Answers

Answer:

132 dollars I think

Step-by-step explanation:

Take a factor out of the square root:
a) √6x^2, where x≥0
b)√9a^3
d)√50b^4
plz help 30 points will give brainliest

Answers

Answer:

Question A)

[tex]=\sqrt{6}x[/tex]

Question B)

[tex]=3a\sqrt{a}[/tex]

Question C)

[tex]=5\sqrt{2}b^2[/tex]

Step-by-step explanation:

A)

We are given:

[tex]\sqrt{6x^2}\, \text{ where } x\geq 0[/tex]

We can rewrite the expression:

[tex]=\sqrt{6}\cdot \sqrt{x^2}[/tex]

The square root and square will cancel each other out. Thus:

[tex]=\sqrt{6}x[/tex]

B)

We are given:

[tex]\sqrt{9a^3}[/tex]

Rewrite:

[tex]=\sqrt{9}\cdot \sqrt{a^3}[/tex]

Note that the square root of 9 is simply 3. We can also factor the second part:

[tex]=3\cdot \sqrt{a^2\cdot a}[/tex]

Rewriting:

[tex]=3\cdot\sqrt{a^2}\cdot\sqrt{a}[/tex]

Simplify:

[tex]=3a\sqrt{a}[/tex]

C)

We are given:

[tex]\sqrt{50b^4}[/tex]

Rewrite. Note that 50 = 25(2):

[tex]=\sqrt{25}\cdot \sqrt{2}\cdot \sqrt{b^4}[/tex]

Simplify. We can rewrite the factor as:

[tex]=5\cdot \sqrt{2}\cdot \sqrt{(b^2)^2}[/tex]

The square and square root will cancel out. Thus:

[tex]=5\sqrt{2}b^2[/tex]

jesse has never used the sliding board at his daycare because he is afraid. His teacher has encouraged him, but he refuses to slide down. one day his mother stands at the bottom And say's Jesse let's go and slides into his mother's arms Laughing The situation is a example of....

A Resiliency
B Adaptability
C Conditioning
D Social referencing

Answers

D is the answer i believe

jesse has never used the sliding board at his daycare because he is afraid. His teacher has encouraged him, but he refuses to slide down. one day his mother stands at the bottom And say's Jesse let's go and slides into his mother's arms Laughing The situation is a example of Social referencing. Option (d) is correct.

What do you mean by Situation?

Situation refers to a group of conditions or a current state of events.

Social reference is the method through which newborns control their behavior toward surrounding items, people, and circumstances by observing the emotive displays of an adult.

For adaptive social functioning to occur, one must recognize and make use of the emotional communication of others. The ability to negotiate complicated and frequently ambiguous settings is known as social referencing in the developmental literature and social appraisal in adult studies.

Therefore, Option (d) is correct. The situation is a example of Social referencing.

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PLEASE HELP
WILL GIVE BRAINLIEST

Identify the situation that each graph could represent.

A ray is graphed in the first quadrant. The horizontal axis is labeled Time. The ray starts at the bottom left and continues to the upper right.



A. the length of a necklace that you make at a rate of 10 cm per hour without taking a break
B. the height of a balloon as it rises, gets caught in a tree for a few minutes, and then continues to rise
C. the total distance you are from home if you ride your bicycle three miles per hour for one hour, and then stop and take a rest
D. The volume of water in a bath tub as it is draining.

Answers

Answer:

The answer your looking for is, C.

The answer that you are looking for is c

What is an equation of the line that passes through the point (6,-2) and is perpendicular to the line 6x+y=2

Answers

Here it is!
I hope it is useful.

True or False: All horizontal lines have a y-intercept.

Answers

Answer:

If you are looking at a graph then yes it will have a y-axis

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

A horizontal line goes on infinitely on both ends will eventually cross the y-axis, making a y-intercept.

find the mean median mode, round to the neaerest tenth. 60,70,75,78,80,80,83,85,87,90.90,90,90,93,95,95,98,100.

Answers

Answer:

Mean: 84.6

median:85

mode:90,80

range:40

minimum:60

maximum:100

Step-by-step explanation:

Answer:

mean = 85.5

median = 88.5

mode = 90

Step-by-step explanation:

Okay, so the mean is the sum of the terms divided by the total number of term so basically:

60 + 70 + 75 + 78 + 80 + 80 + 83 + 85 + 87 + 90 + 90 + 90 + 90 + 93 + 95 + 95 + 98 + 100 = 1,539

1,539 ÷ 17 = 85.5

Now, the median is just the number in the middle so we already have our numbers in order so the middle numbers are 87 and 90, so we just have to add them together and then divide by 2:

87 + 90 ÷ 2 = 88.5

and the mode is just the number that's repeated most, and that number is 90

hope this helps:)

A cylinder has a volume of 2,309.07 cubic cm and a height of 15 cm. What is the
radius of the cylinder? Use 3.14 for st in your calculations and round to the
nearest whole number.
cm

Answers

Answer:

7

Step-by-step explanation:

the answer I got was 7 hope this helped

Can anyone help find x?

Answers

Answer:

119

Step-by-step explanation:

Answer:

x= 61

Step-by-step explanation:

i think

what are the answers to a, b, c, d?

Answers

Answer:

Step-by-step explanation:

Find the length of the third side. If necessary, round to the nearest tenth.
15
25

Answers

Answer:

20.

Step-by-step explanation:

x^2 = 25^2 - 15^2

x^2 = 400

x = 20

P(x) = x2 + x +1
How many terms does this polynomial have?

Answers

Answer:

3

Step-by-step explanation:

According to the Chronicles of Contrived Statistics (March, 2016), the probability that Elon Musk will offer you a free trip into space in the next month is 41%. The probability that scientists from Area 51 will start selling pet aliens next month is 27%. Finally, the probability that either Elon Musk will offer you a free trip to space or that scientists will begin sales of pet aliens next month is 24%. What is the probability that both Elon Musk will offer you a free trip into space and scientists from Area 51 will start selling pet aliens in the next month?

Answers

Answer:

[tex]P(A\ and\ B) = 44\%[/tex]

Step-by-step explanation:

Given

Represents the event as follows:

A = [tex]Elon\ Musk[/tex] will offer you a [tex]free\ trip[/tex] into space in the next month\

B = Scientists from [tex]Area\ 51[/tex] will [tex]start\ selling[/tex] pet aliens next month

So, we have:

[tex]P(A) = 41\%[/tex]

[tex]P(B) = 27\%[/tex]

[tex]P(A\ or\ B) = 24\%[/tex]

Required

Determine [tex]P(A\ and\ B)[/tex]

This is calculated as:

[tex]P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)[/tex]

So, we have:

[tex]P(A\ and\ B) = 41\% + 27\% - 24\%[/tex]

[tex]P(A\ and\ B) = 44\%[/tex]

If function g is a quadratic function that contains the points (-3,5) and (0,14), which statement is true over the interval [-3,0]?

Answers

Your answer for this question is B

The average rate of change of f(x) is less than average rate of change of g(x). Then the correct option is C.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) is given in the table, then the rate of change of the function f(x) will be

Rate of change of f(x) = (-2 + 4.5) / (-2 + 3)

Rate of change of f(x) = 2.5

If function g is a quadratic function that contains the points (-3,5) and (0,14).

Then the rate of change of the function g(x) will be

Rate of change of g(x) = (14 - 5) / (0 + 3)

Rate of change of g(x) = 9/3

Rate of change of g(x) = 3

Thus, the average rate of change of f(x) is less than average rate of change of g(x).

Then the correct option is C.

More about the function link is given below.

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Which graph represents an equation with the values shown in the table?

Answers

Answer:

4

Step-by-step explanation:

Answer:


4
That’s should be the answer

Surface areas 98 Find the shaded area. Round to the nearest tenth if necessary. 22 mm 18 mm 9 mm​

Answers

Answer:

297 sq mm

Step-by-step explanation:

Area of Rectangle: 22 x 18 = 396

Area of Triangle:  (1/2)(22)(9) = 99

Area of Rectangle - Area of Triangle = Area of Shaded area

396 - 99 = 297

martin has read ​20% of a book. He has 8 more pages to finish. How many pages are there in the​ book?

Answers

Answer:

10 pages are in the page if im correct

(PLZ I NEED HELP QUICLY) Angela lives in a remote area serviced by only two cell phone towers. Tower 1 is located 5 miles west and 2 miles south of her home and transmits a signal for 12 miles. Tower 2 is located 8 miles east and 7 miles north of her home and transmits a signal for 10 miles. Consider the location of Angela’s house to be (0, 0) on a coordinate grid. The system of inequalities represents this scenario.
Angela travels to a friend’s house, which is 4 miles east and 8 miles north of her house. Will Angela have cell phone service at her friend’s house?

A. Angela will not have any cell phone service.
B. Angela will have cell phone service from tower 1 only.
C. Angela will have cell phone service from tower 2 only.
D. will have cell phone service from both towers.

Answers

Angela will have cell phone service from tower 2 only , Option C is the answer.

What is an Inequality ?

An inequality is an algebraic expression connected to another algebraic expression with an inequality operator.

The two inequalities given are

(x+5)² + (y+2)² ≤ 144

(x-8)² +(y-7)²  ≤100

The inequalities are plotted on the graph

and the location of Angels's Friends ( 4 , 8) is also plotted

If this lies in the area of the Inequalities she will have signal.

At Angela's friends house she will have the signal of Tower 2 only.

Therefore Option C is the answer.

To know more about Inequalities

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48 - 5 + 7 · 3² ÷ (7-10)²

Answers

Answer:

the answer is 50

Answer:

50

Step-by-step explanation:

BODMAS/BIDMAS

48 - 5 + 7 x [tex]3^{2}[/tex] ÷ (7-10)²

= 48 - 5 + 7 x [tex]3^{2}[/tex] ÷ (-3)²

= 48 - 5 + 7 x [tex]3^{2}[/tex] ÷ 9

= 48 - 5 + 7 x 9 ÷ 9

= 48 - 5 + 63 ÷ 9

= 48 - 5 + 7

= 43 + 7

= 50

You are making a fence for your garden. The length is five less than two times
the width

a. Write a polynomial that represents the perimeter of the garden.

b. Write a polynomial that represents the area of the garden

c. Find the perimeter and area of the garden when the width is 8 feet.

Answers

Answer:Answer: (a) = P = 2(x + 2x-5) = 2(3x-5) = 6x - 10.

Step-by-step explanation:

Part a : Polynomial represents the perimeter of the garden is 6W-10

Part b : Polynomial represents the area of the garden is [tex]2w^{2}-5w[/tex]

Part c : Perimeter = 38 feet and area = 88 feet square

What is polynomial?

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables

What is perimeter?

A perimeter is a closed path that encompasses, surrounds

What is area?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface

Given,

Length is five less than two times the width

Consider

L is the length and W is the width

Then,

L=2W-5

Part a

Perimeter = 2(L+W)

Substitute the value of L

P=2(L+W)

P=2((2W-5)+W)

P=2(2W-5+W)

P=2(3W-5)

Perimeter= 6W-10

Part b

Area of the garden = L×W

Area = (2W-5)W

Area = [tex]2w^{2}-5w[/tex]

Part c

Given width W = 8 feet

Perimeter = 6W-10

P=6×8-10

Perimeter =38 feet

Area = [tex]2w^{2}-5w[/tex]

Area=[tex]2(8^{2})-5(8)[/tex]

Area = 88 feet square

Hence,

Part a : Polynomial represents the perimeter of the garden is 6W-10

Part b : Polynomial represents the area of the garden is [tex]2w^{2}-5w[/tex]

Part c : Perimeter = 38 feet and area = 88 feet square

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what is the positive solution to the equation 4x^{2}+12x=135

Answers

Answer:

9/2 = 4 1/2

Step-by-step explanation:

Which quadrant of a coordinate plane contains the point (-2,8) ?
A) Quadrant I
B) Quadrant II
C) Quadrant III
D) Quadrant IV

Answers

Answer:

Step-by-step explanation:

i think its C

Which table represents a quadratic function? No downloadable links or files, I will mark brainliest.

It is not the 3rd option.

Answers

Answer:

where is the table lol

guys can you help me answer this?​

Answers

I can’t see nothing it to white don’t let me Click

2.
It cost Enica $9 75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was
Erica's total profit?

Answers

It would probably be 20.25$

Answer:

$8.75

Step-by-step explanation:

Cost price= $9.75

Selling price= $1.00

profit= C.P-.SP

= 9.75-1.00

= $8.75

Find the area of this kite.
3 m
5 m
6 m
5 m

Answers

Answer:

450m

Step-by-step explanation:

40
in.
in?
What is the area of this trapezoid?
b2 = 5 in.
h = 4 in.
2 in.
3 in.
b = 10 in.

Answers

The area of the trapezoid is 30

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