Answer:
(m³/3 + 5m/2 + 3)pi
Step-by-step explanation:
pi integral [(f(x))² - (g(x))²]
Limits 0 to 1
pi × integral [(2+mx)² - (1-mx)²]
pi × integral[4 + 4mx + m²x² - 1 + 2mx - m²x²]
pi × integral [m²x² + 5mx + 3]
pi × [m²x³/3 + 5mx²/2 + 3x]
Upper limit - lower limit
pi × [m²/3 + 5m/2 + 3]
Verification:
m = 0
[pi × 2² × 1] - [pi × 1² × 1] = 3pi
[m³/3 + 5m/2 + 3]pi
m = 0
3pi
406 and 411 because there is at least 400 sheets because of the 4 boxes of 100 so there would have to be more than 400 because of the loose sheets
Answer:
y_c = 2 + 10*x
Step-by-step explanation:
Given:
y'' = 0
Find:
- The solution to ODE such that y(0) = 2, y'(0) = 10
Solution:
- Assuming a solution y = Ce^(mt)
So, y' = C*me^(mt)
y'' = C*m^2e^(mt)
- Back substitute into given ODE, we get:
y'' = C*m^2e^(mt) = 0
e^(mt) can not be equal to zero
- Hence, m^2 = 0
m = 0 , 0 - (repeated roots)
- The complimentary function for repeated roots is:
y_c = (C1 + C2*x)*e^(m*t)
y_c = C1 + C2*x
- Evaluate @ y(0) = 2
2 = C1 + C2*0
C1 = 2
-Evaluate @ y'(0) = 10
y'(t) = C2 = 10
Hence, y_c = 2 + 10*x
Answer:
The answer is 125. X= 125 solve it and you get x=125. Have a great day
Step-by-step explanation:
Answer: The volume of cylinder Q is 12 times the volume of Cylinder P.
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
If cylinder Q has radius, r and height, h,
Then
Volume of cylinder Q = πr²h
For cylinder P,
Height = 3h
Radius = 2r
Volume of cylinder P = π(2r)² × 3h
= 4πr²× 3h = 12πr²h
Therefore, the ratio of the volume of cylinder P to the volume of cylinder Q is
12πr²h/πr²h = 12
