Mathematics High School

The volume of a can (right circular cylinder) is 10 cubic feet. the curved surface area is the area of the side. write the curved surface area s as a function of the radius r. s =

Answers

Answer 1

The volume formula of a cylinder is given as:

V = π r^2 h

So plugging in the value of the volume:

10 ft^3 = π r^2 h

h = 10 / (π r^2) ---> eqtn 1

The formula for the surface area of cylinder is:

s = 2 π r h + 2 π r^2

plugging in eqtn 1:

s = 2 π r [10 / (π r^2)] + 2 π r^2

s = (20 / r) + 2 π r^2 (ANSWER)

Related Questions

Which of the following inequalities is shown in the graph

Answers

D.) y ≤ (5/2)x + 5

Check It
0≤(5/2)0+5
0≤0+5
0≤5

The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.

What is an inequality?

In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

From the graph the inequality intersect lines at (-2, 0) and (0, 5).

The graph is shaded below the line.

So, inequality y ≤ [tex]\frac{5}{2}[/tex] x+5.

The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.

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Evaluate the expression 3(7 + 4)2 − 14 ÷ 7. (5 points)

50

361

363

586

Do not just give me the answer, walk me through it. I am literally so shallow minded when it comes to Algebra and I am trying really hard to understand it.

Answers

3(7 + 4)2 − 14 ÷ 7

First do the parenthesis

7 + 4 = 11

so the question looks like: 3(11)2 - 14/7

Then multiply 3, 11, and 2 together

3 x 11 x 2 = 66

66 - 14/7

14/7 equals to 2

66 - 2

Then just simplify

66 - 2 = 64

64 is your answer

hope this helps

I am assuming that (7 + 4)2 means (7 + 4)^2. The 2 is an exponent.

You must follow the correct order of operations.
PEMDAS
P - parentheses first
E - then Exponents
MD - then Multiplications and Divisions in the order they appear from left to right
AS - then Additions and Subtractions in the order they appear from left to right

3(7 + 4)^2 − 14 ÷ 7

Parentheses first:
3(11)^2 - 14 ÷ 7

Now the exponent:
3(121) - 14 ÷ 7

Now multiplications and division from left to right:
363 - 2

Finally additions and subtractions from left to right:
361

If 20 pounds of flour were needed to make 31 pounds of bread, how many pounds of other ingredients would be needed to produce 60 pounds of bread?

Answers

you have some growth ratio r:

20 pounds flour make 31 pounds bread
20*r=31
r=31/20

x pounds flour make 60 pounds bread
x*r=60
x=60/r
x=60/(31/20)
x=20*60/31

or about 38.7 pounds of flour

Other ingredients:

11 pounds "other" for 31 pounds of bread
-> 11/31 per pound
-> 60*11/31 pounds of "other" for 60 pounds breads
=660/31
=21+(9/31)

Is this true 1/2 >0.25

Answers

Yes, 1/2 is 0.50. So it is greater than 0.25.

Yes It’s always true because 0.25 is smaller than 0.5 which would be 1/2

What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit? a.13.4 units b.17.9 units c.26.8 units d.40.0 units

Answers

To calculate the perimeter, consider each side separately. Since this is a rectangle, you have 2 pairs of sides of equal length, so you just have to calculate the length of one of each pair of sides and then double each and add them to find the perimeter.

Top side: If you look carefully, this side is really the hypotenuse of a triangle that is 4 units tall and 8 units long. Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be 8^2 + 4^2 = c^2 --> c = 8.9

Left side: Just like the top side, this side is the hypotenuse of a triangle that is 4 units tall and 2 units long. Pythagoras again: 4^2 + 2^2 = c^2 --> c = 4.5

Since you have two of each side that are the same length, double each and add for the final perimeter: 8.9*2 + 4.5*2 = 26.8

A coordinate plane is a graphical image that shows two number lines. These number lines have a y-axis and x-axis. The y-axis is the vertical number line and the x-axis is the horizontal number line.

The perimeter of the rectangle is 26.8 units

We would be applying Pythagoras Theorem to find the length and breadth of the rectangle.

Pythagoras Theorem states that:

c² = a² + b²

Note that c = The length or breadth of the rectangle

Step 1 : Looking at upper part, and dividing the rectangle into a triangle,

We have 4 units and 8 units.

a = 4 units

b = 8 units

Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be

c² = 4² + 8²

c² = 80

c = √ 80

c = 8.9 units

Applying this to the lower part,

We have 4 units and 2 units.

a = 2 units

b = 4 units

Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be

c² = 2² + 4²

c² = 20

c = √20

c = 4.5 units

Step 2: We find the Perimeter of a rectangle

Formula = 2L + 2B

Where

L = Length = 8.9 units

B = Breadth = 4.5 units

Hence:

8.9 x 2 + 4.5 x2 = 26.8 units

Therefore, the perimeter of the rectangle is 26.8 units

Option C is the correct answer

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Which expression is equivalent to 1/5(15 + 10x-5)?

A. 2 + 2x

B. 2 - 2x

C. -2 + 2x

D. -2 - 2x

Answers

Expand the equation;

1/5(15-5+10x)
1/5(10+10x)
2+2x

Therefore A

Hope I helped :)

What is x if rs= 6, st=9, tu=7, uv=15,vr=14

Answers

When I leave home to walk to school2And what I think I've seen3Now, what can I say4And I've kept careful track5Just a broken down wagon6When Isay that i saw it on Mulberry St7The story would really be better to hear8A reindeer is better; he's fast and he's fleet9To pull a thing that runs on wheels10Jack or Fred of Joe or NAT-11Say! That makes a story that no one can beat12But he'd look simply grand13If a man sits and listens while hitched on behind14But now what worries me is this...15To guide them through where's traffic's thick-16And he raises his hat as they dash by the stand.17With a roar of its motor an airplane appears18A big magician doing tricks..19For I had a story that NO ONE could beat!20There was so much to tell, I JUST COULDN'T BEGIN!21"Nothing," I said, growing red as a beet

If two pyramids are similar and the ratio between the lengths of their edges is 3:11, what is the ratio of their volumes?

Answers

The Answer is 27:1331

Answer: The ratio of the volumes of two pyramids is 27 : 1331.

Step-by-step explanation: Given that two two pyramids are similar and the ratio between the length of their edges is 3 : 11.

We are to find the ratio of the volumes of two pyramids.

Let a units and b units be the lengths of the edges of the two pyramids.

The, according to the given information, we have

[tex]a:b=3:11.[/tex]

We know that the ratio of the volumes of two similar pyramids is equal to the ratio of the cubes of the lengths of edges of the two pyramids.

Therefore, the ratio of the volumes of two pyramids will be

[tex]V:V'=\dfrac{V}{V'}=\dfrac{a^3}{b^3}=\left(\dfrac{a}{b}\right)^3=\left(\dfrac{3}{11}\right)^3=\dfrac{27}{1331}=27:1331\\\\\\\Rightarrow V:V'=27:1331.[/tex]

Thus, the ratio of the volumes of two pyramids is 27 : 1331.

2(4x-3)-8=4+2x solving equations plz help ASAP show work and ill give brainliest

Answers

8x - 6 - 8 = 4 + 2x
8x - 14 = 4 + 2x
8x = 4 + 2x + 14
8x = 2x + 18
8x - 2x = 18
6x = 18
x = 18/6
x = 3

*Answer is x = 3 because 18/6 is 3 since 3 * 6 = 18.

First you will distribute
8x - 6 - 8 = 4 + 2x
Then combine like terms
8x - 14 = 4 + 2x
6x = 18
Divide
x = 3

how do i sketch the graph of each function?

Answers

check the picture below.

notice the hole in the line going to the right-side, because x > -3, meaning "x is greater, BUT not -3".

Suppose three candidates are running in the texas democratic primary for governor. what happens if candidate x wins 45% of the vote, candidate y receives 30% of the vote, and candidate z wins 25% of the vote?

Answers

winners in primary elections in TX are determined by majority vote. If no candidate receives 50% of the vote, then the top 2 candidates proceed to a run-off election.

So in the above problem, since nobody received the majority vote of 50%, the candidate X and candidate Y are going to proceed to a run-off election to determine the democratic candidate for governor

Final answer:

Since no candidate won an absolute majority in the Texas Democratic Primary for governor, a runoff election is necessitated between Candidate X and Candidate Y, the top two vote-getters, to ensure the nominee is chosen by a majority.

Explanation:

In the scenario where Candidate X wins 45% of the vote, Candidate Y receives 30%, and Candidate Z wins 25% in the Texas Democratic Primary for governor, no candidate has achieved an absolute majority, as required by Texas law to win the primary outright. An absolute majority means that a candidate must have more than 50% of the votes, specifically fifty percent plus one vote. Since this did not happen, a runoff election is triggered.

The runoff will take place between the two candidates who received the most votes, which in this case, would be Candidate X and Candidate Y. This runoff ensures that the final nominee for governor from the Democratic Party will have the support of a majority of its voters, reflecting a more democratic outcome. The system prevents a candidate from winning the primary nomination with only a plurality of the vote, which could be less representative of the party's voters as a whole.

"the sum of the squares of two consecutive odd integers is 2594. find the two integers."

Answers

Final answer:

To find two consecutive odd integers whose squares sum to 2594, a quadratic equation is set up and solved, revealing that the integers are 35 and 37.

Explanation:

To solve for two consecutive odd integers whose squares sum to 2594, we can set up equations based on the characteristics of odd integers. Let the smaller integer be n, then the next consecutive odd integer would be n + 2.

The equation based on the sum of the squares of the two numbers is then:

n2 + (n + 2)2 = 2594

Solving this equation:

n2 + n2 + 4n + 4 = 25942n2 + 4n - 2590 = 0n2 + 2n - 1295 = 0

Solving the quadratic equation we find that n = 35 and n + 2 = 37. Hence, the two consecutive odd integers are 35 and 37.

What's the answer of the photo I just sent you

Answers

The answer is 86 degrees.
You would just add 26 and 69.

m∠KLB+m∠BLM=26°+60°=86°

The sum of three consecutive integers is -255. what are they?

Answers

-84-85-86=-255 is your answer

The hood of Christina's car is the shape of a trapezoid. The base bordering the windshield measures 30 inches and the base at the front of the car measures 24 inches. What is the width of the median of the hood?

The width of the median of the hood is
_______inches.

Answers

30-24 = 6

6/2 = 3

24 + 3 = 27

median width = 27

Here is your answer:

First you have to subtract 30 and 24

30-24 = 6

Then divide six by two:

6÷2 = 3

Then add 24 and 3

24 + 3 = 27

Your answer is...

= 27

What is the value of x?

Answers

GDH=180 because it is a supp. So 62+(x+2)=180
Subtract 62 from both sides
(X+2)=118
Den subtract 2
Which is 116
Hope this helps good luck

Determine whether the following pair of lines is parallel, perpendicular or neither 2x+3y=3: 2y=3x-4

Answers

First, you have to simplfy your equations, 2x+3y=3. Subtract 2x from both sides, get 3y=-2x+3. Divide each side by 3, get y=-2/3x+1.
Simplify your other equation, 2y=3x-4. Divide each side by 2, get y=3/2x-2.
Now you have your 2 equations, y=-2/3x+1, and y=3/2x-2. These lines are perpendicular if you make a graph and plot the lines.

A box containing 4 identical books weighs 5kg. if the weight of the box is 600g, what is the weight of each book? answer key

Answers

5kg=5000g
5000g-600g=4400g
4400g/4=1100g

So your answer is 1,100 grams.

Answer:

1100 grams

Step-by-step explanation:

Point A is located at –24 and point C is located at 36 on the number line below. Which value would represent point B, halfway between point A and point C?

Answers

To find the midway point of 2 numbers, we find their sum and divide that by 2. For this, we add -24 and 36 ( which amounts to 12) and divide that by 2, meaning that midpoint B is 12/2=6

Answer:

Point B will be 6

Step-by-step explanation:

We have point A= -24 and point B = 36, we want to know point B which is halfway between points A and C.

To find the middle between two points we have to add the two numbers and divide them by 2:

We would have:

(A+C)/2

We substitute the values of A and C:

B = (-24+36)/2

B = 12/2

B = 6.

We can also write this on a number line and get point B by counting how many numbers there are in between point A and C, and this result divides it by 2. This is in the attachment.

the tour boats at the Laguna can carry 8 passengers. jacob watched 6 floats by. one of the board has 2 empty seats. the other were full. how many passengers were on the 6 boats?

Answers

46 passengers is the answer to your problem

(42 pts) What is the value of g(−3) when g(x)=2x−2 ? Enter your answer in the box.

Answers

-8 is the answer to the equation. Plug -3 into the equation then solve

equation = g(x) = 2x-2

when g(-3) replace x with -3

so you get g(-3) = 2(-3)-2

2*-3 = -6-2 = -8

g(-3) = -8

If 3cot^2x - 5cotx = -2, then cotx = _____.
A. -2, -1/3
B. -1, -2/3
C. 1, 2/3
D. 2, 1/3

Answers

3cot²x - 5cotx = -2

Lets pretend cotx = t

3t² - 5t = -2
3t² - 5t + 2 = 0

factor polynomial
(3t-2)(t-1) = 0

3t-2 = 0
t-1 = 0

then "t" which is also cotx is equal to 1 or 2/3

a. Write an expression that represents the following expression using the variable b: "Billy's age in 8 years." b. Write an equation using the expression above if in 8 years Billy will be 21 years old. c. How old is Billy now? d. Write and solve a word problem that matches the equation: a - 6 = 10.

Answers

a. b+8
b. b+8=21
c. b=21-8=13 Billy is 13 now
d. Ann was ten years old six years ago. How old is she now? a-6=10, a=16. Ann is 16 now.

Answer:

"Billy's age in 8 years", this refers to a future age, which implies adding 8 years to the present age. The expression would be:

[tex]B+8[/tex]

"In 8 years Billy will be 21 years", this expression, using the first one too, would be:

[tex]B+8=21[/tex]

How old is Billy now?

The answer to this question is the solution of the second equation:

[tex]B+8=21\\B=21-8=13[/tex]

Billy is 13 years old now.

A problem for the expression [tex]A-6=10[/tex] could be:

Six years ago Adam was 10 years old.

The six years in the past refers subtracting, and the age back then is the result of that difference.

Writing are the equations m + 3 = -5 and m = -2 equivalent? explain

Answers

m + 3 = -5
m = -5 - 3
m = - 8

and m = -2

no, they are not equivalent because they do not equal.

Which number(s) below belong to the solution set of the inequality? Check all that apply.x + 16 < 51.

A. 80
B. 35
C. 38
D. 32
E. 34
F. 16
please help me

Answers

If you subtract 16 on both sides... x will be alone. Therefore 51-16=35
x=35 (B)

That would be 32, 16 and 34.

Triangle PQR has vertices at the following coordinates : P(0,1) Q(3,2) R(5,-4) . Determine wether or not triangle PQR is a right triangle . Show all calculations for full credit .

Answers

Here is my answer. Hope this help.

The sum of the squares of two sides is not equal to the square of the third side, the triangle PQR is not a right triangle.

What is Pythagoras Theorem?

According to Pythagoras Theorem, in a right angled triangle the square of the side opposite to the right angle is equal to the sum of squares of the other two sides.

Height² + Base² = Hypotenuse²

If a triangle is a right angle, then its sides should satisfy Pythagoras theorem.

The distance formula will be used to determine the length of the sides.

PQ² = ( 3 - 0)² + (2-1)²

PQ² = 10

PQ = √10

RQ² = ( 5 - 3)² + (-4-2)²

RQ² = 40

RQ = √40

RP² = ( 5 - 0)² + (-4-1)²

RQ² = 25 + 36

RQ² = 61

Applying the Pythagoras's Theorem,

61 ≠ 40 + 10

Therefore, it is not a right angled triangle.

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miss. Nikkel want to divide her class of 23 students into 4 equal teams.is this reasonable?why or why not

Answers

No, because if you divide 23 / 4, you get 5.75. You can't get 0.75th of a kid. So it is not reasonable, because it is a decimal, and not a whole number.

Hope this helped! ☺♥

It's impossible to get good quantity of command with the total quantity of 23.
So possible numbers of commands are 3 commands, 4 commands, 5 commands.
3 commands: There are 7 students inside each and 2 students out of commands.
4 commands: There are 6 students inside each and there is no one students inside one command.
5: commands: There are 5 students inside each and there is no two students inside one command.
So 4 commands will be reasonable for the 23 students. But one command still without 1 student.

which equation is an identity?

a. 11- (2v + 3) = -2v - 8
b. 5w + 8 - w = 6w - 2( w - 4)
c. 7m - 2 = 8m + 4 - m
d. 8y + 9 = 8y - 3

Answers

5w + 8 - w = 6w - 2(w - 4)

Hope this helps :)

Answer:

Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]

Step-by-step explanation:

To find : Which equation is an identity?

Solution :

Option a - [tex]11- (2v + 3) = -2v - 8[/tex]

If we open the parenthesis,

[tex]11- 2v -3 = -2v - 8[/tex]

[tex]-2v+8\neq -2v - 8[/tex]

No identity applied.

Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]

If we apply distributive property, [tex]a(b+c)=ab+ac[/tex]

[tex]5w + 8 - w = 6w - 2w+8[/tex]

[tex]4w+8= 4w+8[/tex]

Distributive identity is applied.

Option c - [tex]7m - 2 = 8m + 4 - m[/tex]

Solve by subtracting in RHS

[tex]7m - 2 \neq 7m + 4[/tex]

No identity applied.

Option d- [tex]8y + 9 = 8y - 3[/tex]

This is not possible as [tex]8y + 9 \neq 8y - 3[/tex]

No identity applied.

Therefore, Option b is correct.

Archie is putting 24 books on 2 shelves. Each shelf holds 16 books.

How many more books can Archie put on the shelves?

Answers

Since each shelf can hold 16 books and there are 2 shelves, both shelves can hold a total of 32 books. Since he is already adding 24 books, he can add 32- 24 = 8 more books.

Archie can put 9 more books on the shelf

Which expression is equivalent to the expression −2\3 (3- 1\2) (-1)?

Question 3 options:

-2 + 1\3 + 2\3

2 - 1\3

-2 +1\3-1

2 + 1\3

Answers

The Answer Is B.2-1/3

Hope It Helps Mark Me The Brainlyest

Final answer:

The expression −2/3(3-1/2)(-1) is equivalent to -5/3.

Explanation:

To simplify the expression −2/3(3-1/2)(-1), we can start by simplifying the expressions within the parentheses.

3-1/2 = 6/2 - 1/2 = 5/2

Next, we can multiply the expression −2/3(5/2)(-1).

−2/3(5/2)(-1) = -2/3 * 5/2 * -1 = -10/6 = -5/3

Therefore, the expression is equivalent to -5/3.

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