A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder’s base. What is the volume of the space remaining in the cylinder after the cone is placed inside it? (Please explain and show work)
Answers
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Work Shown:
A = volume of the cylinder
A = pi*(radius)^2*(height)
A = pi*r^2*h
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The cone's base has diameter r/2, so its radius is (1/2)*(r/2) = r/4
B = volume of the cone
B = (1/3)*(volume of cylinder with radius r/4 and height h)
B = (1/3)pi*(r/4)^2*h
B = (1/3)*pi*(r^2)/(4^2)*h
B = (1/3)*pi*(r^2)/16*h
B = (1/3)*(1/16)*pi*r^2*h
B = (1/48)pi*r^2*h
B = (1/48)*A
B = (1/48)*(volume of cylinder)
-----------
C = volume of the empty space/air inside cylinder, but outside cone
C = A-B
C = A - (1/48)*A
C = (48/48)A - (1/48)A
C = (48A)/48 - (A/48)
C = (48A-A)/48
C = 47A/48
C = (47/48)*A
C = (47/48)*pi*r^2*h
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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O (x+3y-5)
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Step-by-step explanation:
3 units left would be -3 and 5 units down would be +5
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
1,100 miles traveled in 2 hours, 3,300 miles in 6 hours
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Given
3x² + 22x + 35
Consider the factors of the product of the x² term and the constant which sum to give the coefficient of the x- term
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Use these factors to split the x- term
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Answers
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Answers
Answer:
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Step-by-step explanation:
Given
y² + 5y + 4
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Answer:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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First things first, take off 10, 20, 50, and 60.
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Given,
For a given recipe, 12 cups of flour are mixed with 24 cups of sugar
We need to find cups of sugar should be used if 21 cups of flour are used
Let us consider x as cups of sugar should be used if 21 cups of flour are used
Let us form an equation to find x
12/24=21/x
Apply cross multiplication
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12x=504
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To learn more on Ratios click:
https://brainly.com/question/13419413
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Answer:
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B.
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1.5
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Answer:34
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Step-by-step explanation:
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43602
Step-by-step explanation:
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Answers
Answer:
e total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces, which is ... 1: Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm. ... Example 2: Find the surface area of a cuboid of dimensions 4.8 cm, 3.4 cm ... Example 4: The length, breadth and height of a cuboid are 16cm, 14cm and ...
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Where's the cuboid? You left it out.
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Step-by-step explanation:
Answer:
The answer is D. -7.25
Select the symbol that properly compares each pair of numbers:
a. -|-15| ___ -(-15)
• <
• >
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b. |-18| ___ -18
• <
• >
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c. -|-3| ___ -|3|
• <
• >
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d. -|-6| ___ |-6|
• <
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Answer:
a. >
b.<
c.=
Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Convert any mixed numbers to fractions.
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Answers
C
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Answer:
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Step-by-step explanation:
-3(2t - 1) = t + t + t + 3
Answers
isolate the variable
Answer:
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Step-by-step explanation:
Jeremy is saving up to buy a new video game system. Two weeks ago, Jeremy only had $14.75. He has worked for 26 hours at the local grocery store, where he earns $10.15 per hour. If the video game system costs $400.00, how many more hours must Jeremy work before he can purchase the system?
Answers
Answer:
12 more hours
Step-by-step explanation:
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Total needed is now $385.25
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Answer:
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Answer:
B
Step-by-step explanation:
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It takes 40 units of maple sap to produce 1 ounce of maple syrup. Jane and her family are bottling maple syrup in 20 -ounce bottles. She notices that they leave about 2 ounces of air every time they fill a bottle, to avoid overfill. How much maple sap did they need to collect to fill 15 bottles? How much less maple sap did they need than if they would have filled each bottle to the top? Express your answer as a negative number.
Answers
Answer:
10,800
-1200
Step-by-step explanation:
Given that :
40 units of maple sap = 1 ounce of maple syrup
Using a 20 - ounce bottle, 2 ounces of air is left
Ounces of actual syrup = (20 - 2) = 18 ounces
Number of maple sap required to fill 15 bottles :
Number of maple saps required to fill 18 ounces bottle :
40 units = 1 ounce
x = 18 ounces
Hence, for 18 ounces of maple syrup :
(40 * 18).= 720 units of maple sap
For 15 bottles of 18 ounces maple syrup:
(720 * 15) = 10,800 units of maple sap
If they had filled each bottle to the top:
(40 * 20 * 15) = 12000 units of maple sap
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What’s the volume of this shape?
Answers
Answer:
V=72x³y³
Step-by-step explanation:
The formula to apply is;
V= l * w * h where
V= volume in units cubed.
l= length = 3xy
w=width = 4xy
h= height = 6xy
Substitute values in the formula as;
V= l*w*h
V=3xy * 4xy * 6xy ----find product for the numbers {3*4*6=72} then multiply by the product for x's {x*x*x =x³} that of y's {y*y*y=y³}
V= 72*x³*y³
V= 72x³y³ --------where xy are the units used.