Answer:
The expression 
represents the radius of the soap dispenser.
The expression 
represents the height of the soap dispenser.
Step-by-step explanation:
The question says that the soap dispenser is in the form of a cylinder.
Now, we find the volume of the cylinder by using the given formula:
, where V represents the volume, 'r' represents the radius, and 'h' represents the height of the cylinder.
Now, the volume is the product of radius squared and the height, if they both are functions of 
, then the function to represent the volume must have cubic exponents.
Since, the radius is squared in the formula and it is a function of that implies that the function of radius must have square as the exponent of , therefore, the expression will represent the radius of the soap dispenser and the expression 
represents the height of the soap dispenser.
Answer:
Velocity of the 24.6 g marble is 31 cm/s.
Step-by-step explanation:
Given:
Marble 1:
Mass of the marble 
= 12.3 gm
Velocity of 
before collision 
= 15.5 cm/s
Velocity of after collision 
= 77.5 cm/s
Marble 2:
Mass of the marble 
= 24.6 gm
Velocity of 
before collision 
= 62 cm/s
Velocity of after collision 
= ?
From the law of conservation of momentum, we know that momentum before equals the momentum after :
So,
⇒ 
⇒ 
⇒ Plugging the values.
⇒ 
⇒ 
⇒ 
⇒ 
...subtracting both sides 953.25
⇒ 
⇒ 
...dividing both sides with 24.6
⇒ 
⇒ 
cm/s
The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.
Answer:
5x^2 -3x +9
Step-by-step explanation:
(5x2 + 7) - (3x - 2)
Distribute the minus sign
5x^2 +7 -3x +2
Combine like terms
5x^2 -3x +9
Volume = Area * height
= width * length * height
= 8 * 4 * 7
= 224 cm^3
Answer:
Step-by-step explanation:
5x+10-7=-32
5x+3=-32
5x+3-3=-32-3
5x=-35
X=-35/5
X=-7
Check:
5(-7+2)-7=32
5(-5)-7=32
-25-7=-32
-32=-32
This is correct
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