Answer:
The level of the root beer is dropping at a rate of 0.08603 cm/s.
Explanation:
The volume of the cone is :

Where, V is the volume of the cone
r is the radius of the cone
h is the height of the cone
The ratio of the radius and the height remains constant in overall the cone.
Thus, given that, r = d / 2 = 10 / 2 cm = 5 cm
h = 13 cm
r / h = 5 / 13
r = {5 / 13} h


Also differentiating the expression of volume w.r.t. time as:

Given:
= -4 cm³/sec (negative sign to show leaving)
h = 10 cm
So,



<u>The level of the root beer is dropping at a rate of 0.08603 cm/s.</u>
Stress required to cause slip on in the direction [ 1 1 0 ] is 7.154 MPa
<u>Explanation:</u>
Given -
Stress Direction, A = [1 0 0 ]
Slip plane = [ 1 1 1]
Normal to slip plane, B = [ 1 1 1 ]
Critical stress, Sc = 2.92 MPa
Let the direction of slip on = [ 1 1 0 ]
Let Ф be the angle between A and B
cos Ф = A.B/ |A| |B| = [ 1 0 0 ] [1 1 1] / √1 √3
cos Ф = 1/√3
σ = Sc / cosФ cosλ
For slip along [ 1 1 0 ]
cos λ = [ 1 1 0 ] [ 1 0 0 ] / √2 √1
cos λ = 1/√2
Therefore,
σ = 2.92 / 1/√3 1/√2
σ = √6 X 2.92 MPa = 2.45 X 2.92 = 7.154MPa
Therefore, stress required to cause slip on in the direction [ 1 1 0 ] is 7.154MPa
Answer:
Check the explanation
Explanation:
The beat frequency is
df = f2 - f1
the wavelength is
lamda1 = (v/f1)
and lamda2 = (v/f2)
where v = 340 m/s,f1 = 25.0 kHz and f2 = 20.0 kHz