the buoy is made from two homogeneous cones each having a radius of 1.5 ft. if h=1.2 ft, find the distance z¯ to the buoy’s center of gravity g.

Answers

Answer 1

The distance to the center of gravity of the buoy is equal to the distance from the center of the base to the midpoint of the axis of symmetry, which is approximately 0.8 ft.

To find the distance to the center of gravity of the buoy, we first need to determine the volumes of the two cones.

Since the cones are identical, we can find the volume of one cone and double it.

The formula for the volume of a cone is V = (1/3)πr²h,

where V is the volume, r is the radius, and h is the height.

Substituting r = 1.5 ft and h = 0.6 ft (half of the total height), we get:

V = (1/3)π(1.5 ft)²(0.6 ft) ≈ 0.85 ft³

The total volume of the two cones is therefore approximately 1.7 ft³.

The center of gravity of the buoy is located at a point on the axis of symmetry of the two cones.

Since the cones are identical, this point is located at the midpoint of the axis of symmetry.

The distance from the center of the base of the cones to the midpoint of the axis of symmetry can be found using similar triangles.

The ratio of the height of the smaller cone (0.6 ft) to the distance from the center of the base to the midpoint is equal to the ratio of the height of the larger cone (0.6 + h = 1.8 ft) to the total height of the buoy (2.4 ft).

Solving for the distance from the center of the base to the midpoint, we get:

d = (0.6 ft) × (2.4 ft) / (1.8 ft) = 0.8 ft

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Answer 2

To find the distance z¯ to the buoy's center of gravity, we can use the principle of moments.The principle of moments states that the sum of the moments of all the forces acting on a body is equal to zero.

First, we need to find the volume and the weight of the buoy. Since the buoy is made from two identical cones, we can find the volume of one cone and then multiply it by 2.

The volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height. For the buoy, r = 1.5 ft and h = 1.2 ft, so the volume of one cone is:V = (1/3)π(1.5 ft)²(1.2 ft) ≈ 2.827 ft³

Therefore, the volume of the buoy is approximately 2 x 2.827 ft³ = 5.654 ft³.

To find the weight of the buoy, we need to know the density of the material it's made from. Let's assume the density is ρ = 62.4 lb/ft³, which is the density of water.

The weight of the buoy is then: W = ρV = (62.4 lb/ft³)(5.654 ft³) ≈ 352.12 lb

Next, we need to find the center of gravity of the buoy. Since the buoy is symmetric, its center of gravity is located at the midpoint of the height, which is h/2 = 0.6 ft from the base.

Finally, we can use the principle of moments to find the distance z¯ to the buoy's center of gravity. We can consider the weight of the buoy acting downwards at its center of gravity, and a force F acting upwards at a distance z¯ from the center of gravity. For the buoy to be in equilibrium, the sum of the moments of these forces must be equal to zero.

The moment of the weight about the center of gravity is W(h/2) = (352.12 lb)(0.6 ft) = 211.27 lb·ft. The moment of the force F about the center of gravity is F(z¯ - 0.6 ft).

Setting the sum of these moments to zero, we have:

W(h/2) = F(z¯ - 0.6 ft)

Substituting the values we found earlier, we get:

211.27 lb·ft = F(z¯ - 0.6 ft)

Solving for z¯, we get:

z¯ = (211.27 lb·ft) / F + 0.6 ft

Since we don't know the value of F, we can't find an exact numerical answer for z¯. However, we can see that the distance z¯ is inversely proportional to the force F, which makes intuitive sense: the stronger the force pushing up on the buoy, the closer its center of gravity will be to the waterline.

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Related Questions

please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!will give brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

vertical angles

Step-by-step explanation:

They don't share a common side, so they are not adjacent!

Hope that helps!

Test Scores. You are taking a math test in which items in part A are worth 10 points and items in part B are worth 15 points. It takes 3 min. to complete each item of part A and 6 min. to complete each item in part B. The total time allowed is 60 min. and you do exactly 16 questions. How many questions of each part did you complete? Assuming that all your answers were correct, after all you had a GREAT Math Teacher, what was your score?

Answers

Answer:

465 is the total points he got and he solved 14 in part A and 2 in part B

hope it helps you

mark me as brainlist

thank you

Please help me I will give brainlyiest or how ever u spell it

Answers

Answer:

2

Step-by-step explanation:

the answer is 2

If there was a point R(-2, 4) and it was dilated to R'(-8, 16), what was the scale factor? *

Answers

Answer:

4

Step-by-step explanation:

HELP ASAP!!!!!!!!

Find the cite of each variabile

Answers

tan = opp/adj

x = 13(tan 45)

x = 13

//

a² + b² = c²

13² + 13² = 338²

square root of 338 is not a rational number so turn into mixed radical.

//

[tex]x \: = 13[/tex]

[tex]y = 13 \sqrt{2} [/tex]

Please I need this TOMORROW ​

Answers

Answer:

here u go !! <3

Part 1:

1. 18 - [(15 - 9 + 4] - 2 = 6

2. 6² - [3² + (3 + 12)] = 12

3. 21 - [(2 × 4) + 2 + 5] = 6

4. [(17 - 10) + 4] + 5² = 36

5. 36 ÷ 6 + [(5 × 3) + (13 - 6) + 10] = 38

Part 2:

6. 15 ÷ 3 × 5 - 16 = c. 9

7. 2 [5 + (30 ÷ 6)²] = d. 60

8. [3² × 4] - [6 + 4²] = b. 14

9. 8 [6² - 3 × (2 + 5) - 8 + 3] = e. 80

10. 15 - {27 - 2 × [33 - 4 × (5 + 1)]} = a. 6

Answer:

(1 )14

(2) 45

(3) 20

(4) 36

(5)121

(6) 6

(7)9

(8) 14

(9)80

(10)60

Justin wants to place one of his 4 signed hockey sticks on his shelf. The length of the shelf is exactly 1.05 meters. His 4 hockey sticks and their lengths are shown below.

Answers

Answer:

Stick 2

Step-by-step explanation:

Given

[tex]L = 1.05m[/tex] --- Shelf length

Missing information from the question are:

[tex]Stick\ 1 = 1.4m[/tex]

[tex]Stick\ 2 = 1.041m[/tex]

[tex]Stick\ 3 = 1.14m[/tex]

[tex]Stick\ 4 = 1.104m[/tex]

See attachment

Required

Which stick best fits the shelf?

The following observations are to be noted:

The length of stick 1 of 1.4m is greater than the length of the shelfThe length of stick 3 of 1.14m is greater than the length of the shelfThe length of stick 4 of 1.104m is greater than the length of the shelf

Only stick 2 (of length 1.041m) has a smaller length when compared to the length of the shelf.

Hence, Justin should choose stick 2


What is the measure of arc FG?
PLEASE HELP , i’ll make BRAINLIEST

Answers

The measure of arc FG could be 108
The correct answer is 103 degrees (180-77) Since there is a line exactly in the half of the circle and we know that one portion is 77° so the remaining portion must be the difference of a half circle which is 180° minus the 77°.

The temperature outside changed from 64°F to 43°F over a period of seven days. If the temperature changed by the same amount each day, what was the daily temperature change?

Answers

Answer: -3°F

Step-by-step explanation:

From the question, we are informed that the temperature outside changed from 64°F to 43°F over a period of seven days. The total change will be:

= 43°F - 64°F

= -21°F

If the temperature changed by the same amount each day, the daily temperature change will now be:

= -21°F / 7

= -3°F

The temperature decreased by 3°F daily

PLEASE HEEEEELP IS URGENTT​

Answers

Answer:

75.

Step-by-step explanation:

17−14−8(8−17)

=75

Part A: find the value for x:
Part B: what is the value of angle A?

Answers

Answer:

part A:

If ABC is a triangle then,

2x+4+2x-9+x=180degree

or, 5x-5=180degree

or, 5x=(180+5)degree

or, 5x= 185degree

or, x=185÷5 = 37degree ans.

PartB

now put the value of x in angle A

i.e angle A = 2x-9

or, angle A= (2×37) - 9

or, angle A= 74 - 9

therefore, angle A= 65degree ans.

A seabird is 28 meters above the surface of the ocean. What is its elevation?

Answers

Answer:

The elevation is 28 meters.

Step-by-step explanation:

This is pretty obvious because it says that the bird is above the ocean, not below. So, it is positive.

Hope this helps! :)

I am in need of help

Answers

Answer:

The answer is Step 2: m<w + m<z = 180 degrees (suppplmentary angles).

Step-by-step explanation:

First, Step 2 says m<w - m<z = 90 degrees. That's false because the m<w - m<z  would equal an acute angle, not a right angle. Secondly, the m<w + m<z = 180 degrees. Supplementary angles equal 180 degrees.

GIVING BRAINLIEST IF CORRECT! Megan drew a scale drawing of a house and its lot. She used the scale 1 centimeter : 7 meters. The actual length of the back patio is 28 meters. How long is the patio in the drawing?

Answers

Answer:

What I believe it may be is 4 centimeters.

Step-by-step explanation:

One centimeter = 7 meters.

7 x 4 equals 28.

Comment:

I hope this helped you.

If this is the wrong answer, I am sorry.

   

if you answer correctly I will give you 5 stars a thank you AND brainliest

Answers

Answer:

the answer is an acute triangle

Step-by-step explanation:

it is an acute triangle because all angles are less than 90° but all the angles added together are equal to 180°

Answer:

It is a scalene triangle.

Please answer I need it asap!!!

Answers

Answer:

Use ratios of corresponding sides:

EH/FH = FH/GHFH² = EH*GH  

4.

FH² = 6*3 ⇒ FH = √18 = 3√2

5.

GH = FH²/EH = 6²/12 = 3

6.

FH = √(19-15)*15 = √60 = 2√15

Find the slope of the line between the following points:
(27, 11) and (11, 3)
Record your answer in simplest form.

Answers

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (27, 11) and (x₂, y₂ ) = (11, 3)

m = [tex]\frac{3-11}{11-27}[/tex] = [tex]\frac{-8}{-16}[/tex] = [tex]\frac{1}{2}[/tex]

the slope equals 1/2.

3) If the slope of PQ is 4 and the slope of OR is – 1/2 , find the slope of SR so that PQRS is a parallelogram.​

Answers

Answer:

Step-by-step explanation:

the anwser is 1/3

0.25 (771-20q) simplified expression

Answers

Answer:

191.5

Step-by-step explanation:

Answer:

191.5

Step-by-step explanation:

Find the value of x in the triangle, pls help I need this so bad, if you want points you can tell me in the COMMENTS and I'll make a thing just for u!! But pls don't answer if u don't know♥️ thanks love u!!

Answers

Answer:

67 degrees, the 4th choice.

Step-by-step explanation:

As you may know, sum of angles in a triangle is 180 degrees. The best thing about this question here, is that 2 of the angles are already given. Now, all you need to do is add the two angles and subtract the result from 180.

You can also use the process of elimination to start.

First off, you can eliminate the second answer, sum of angles in triangle is 180, and 293 is way to much.

7 degrees is way too little, and it can be found by common sense, and knowing that 7+60+53 is already gonna be less than 180. (Didnt mean to be rude though. lol)

The only options left are 113 degrees and 67 degrees. now, lets use the actual formula of sum of angles in triangle.

60+53=113

180-113=67.

So, its 67 degrees! Process of elimination can help, but if you need proof for your answer, do not do that work in front of your teachers, only show the actual proof.

Hope you learned and liked my explanation! If so, please leave a rating and thanks (and hopefully brainliest!!) Have a great day!

3.3 - 3.7n - 2n + 8 nnnnnnnnnnnnnnnnnn

Answers

Answer:

-5.7n + 11.3

Step-by-step explanation:

3.3 - 3.7n - 2n + 8 = -3.7n - 2n + 3.3 + 8 = -5.7n + 11.3

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Amelia bought 40 plain black T-shirts for $4 each.She painted designs on them and then sold each T-shirt for 7.50.How much profit did Amelia make selling her fancy T-shirts?

Answers

I hope this helpfull dor you...But if this not helpfull,im so sorry...

1. 12x – 8x + 4 = 20
2. 9w + 4w – 5w + w = -9

Answers

Answer:

the answer for just eliminate the variables and to the solving tho get the answer as they get the answer to the number above

Question: 1 out of 10
~!¡! Volume !¡!~

Answers

Answer:

a) 96

Step-by-step explanation:

2 + 2 = 4

4 * 24 = 96

Use the algebra tiles to help you solve the equation 4x -5=3

Answers

Answer:

x=2

Step-by-step explanation:

what is these in simplest form
a) 2a + 4 + 5a + 8 =
b) -2b – 7 + 3b – 8 =

Answers

Answer:

a ) 7a + 12

b) b - 15

Step-by-step explanation:

a)2a+5a +8+8

= 7a + 12

b) b - 7 - 8

= b-15

What time does the clock show?
12
1
11
10
3 -
8
4.
1
7 6
5

Answers

Answer:

6:59

Step-by-step explanation:

Hour : Minute

Small hand is hour hand, large hand is minute hand. Minutes go by the small tic marks, where the hours go off of the numbers.

7:59 I could be wrong so I’m sorry! Have a great day.

Which of the following is a solution for

f + 8 < 10

Answers

Answer: there are no answer choices but f > 2

Step-by-step explanation:

Which angle is a VERTICAL angle to∠8?

Answers

Step-by-step explanation:

alternate angle is vertical to it

In an isosceles trapezoid the base angles are?​

Answers

Answer:

The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary angle of a base angle at the other base

Step-by-step explanation:

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