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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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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please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!will give brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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?
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
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? *
Answer:
4
Step-by-step explanation:
HELP ASAP!!!!!!!!
Find the cite of each variabile
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
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.
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 shelfOnly 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
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?
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
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?
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?
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
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?
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
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!!!
Answer:
Use ratios of corresponding sides:
EH/FH = FH/GHFH² = EH*GH4.
FH² = 6*3 ⇒ FH = √18 = 3√25.
GH = FH²/EH = 6²/12 = 36.
FH = √(19-15)*15 = √60 = 2√15Find the slope of the line between the following points:
(27, 11) and (11, 3)
Record your answer in simplest form.
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]
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.
Answer:
Step-by-step explanation:
the anwser is 1/3
0.25 (771-20q) simplified expression
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!!
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
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?
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
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 !¡!~
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
Answer:
x=2
Step-by-step explanation:
what is these in simplest form
a) 2a + 4 + 5a + 8 =
b) -2b – 7 + 3b – 8 =
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
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.
Which of the following is a solution for
f + 8 < 10
Answer: there are no answer choices but f > 2
Step-by-step explanation:
Which angle is a VERTICAL angle to∠8?
Step-by-step explanation:
alternate angle is vertical to it
In an isosceles trapezoid the base angles are?
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: