Help please solve math equations for middle schoolers in 7th grade!
1 answer:
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Answer:
Ö + θ ( (k/m) + (g/l)) = 0
Step-by-step explanation:
Use the FBD attached:
Apply Newtons 2 nd Law in tangential direction:
Sum ( Ft ) = m*a
Sum of all tangential forces is:
m*g*sin(θ) + k*l*sin(θ)*cos(θ) = - m*l*Ö
Using small angle approximations:
sin (θ) = θ
cos (θ) = 1
Ö = angular acceleration.
m*g*θ + k*l*θ = -m*l*Ö
Ö + θ ( (k/m) + (g/l)) = 0
Answer:
b) π /16 (1-1/e^2)
Step-by-step explanation:
For this case we have the following limits:
And we have semicircles perpendicular cross sections.
The area of interest is the enclosed on the picture attached.
So we are assuming that the diameter for any cross section on the region of interest have a diameter of
And then we can find the volume of a semicircular cross section with the following formula:
And for th volum we can integrate respect to x and the limits for x are from 0 to 1, so then the volume would be given by this:
And evaluating the integral using the fundamental theorem of calculus we got:
And then the best option would be:
b) π /16 (1-1/e^2)
