Answer:
a) 244,140,625 different ways
b) 390,625 different ways
Explanation:
a) If there are 5 ways to place a chip on each location, and there are 12 locations overall, we have:
5^12 ways of placing them
This would mean a total of 244,140,625 different ways
b) If five chips are of the same type, we can first find how many ways we can place chips on the remaining 7 locations:
5^7 = 78,125
Next we can multiply this by the number of ways the next 5 chips could be the same:
78,125 * 5 = 390,625 different ways
Answer:
f=1.59 Hz
Explanation:
Given that
Simple undamped system means ,system does not consists any damper.If system consists damper then it is damped spring mass system.
Velocity = 100 mm/s
Maximum amplitude = 10 mm
We know that for a simple undamped system spring mass system

now by putting the values

100 = ω x 10
ω = 10 rad/s
We also know that
ω=2π f
10 = 2 x π x f
f=1.59 Hz
So the natural frequency will be f=1.59 Hz.
Answer:
A) ΔL = 0.544 mm
B) Δd = -0.0168 mm
Explanation:
We are given;
Elastic modulus; E = 67.1 GPa = 67.1 × 10^(9) Pa
Force; F = 46400 N
Diameter; d = 17.8 mm = 17.8 × 10^(-3) m
Radius; r = d/2 = 17.8/2 = 8.9 mm = 8.9 × 10^(-3) m
Length; L = 196 mm = 0.196 m
Poisson ratio; ν = 0.34
A) We know that formula for elastic modulus is;
E = σ/ε
Where;
σ = F/A
ε = ΔL/L
Thus;
E = (FL/ΔL•A)
ΔL is change in length. Making it the subject of the formula, we have;
ΔL = FL/AE
Now, A = πr²
A = π × (8.9 × 10^(-3))²
ΔL = [(0.196 × 46400)/(π × (8.9 × 10^(-3))² × 67.1 × 10^(9)]
ΔL = 0.544 × 10^(-3) m
ΔL = 0.544 mm
B) formula for Poisson ratio is given as;
ν = -ε_x/ε_z
Where;
ε_x is transverse strain = Δd/d
ε_z is longitudinal strain = ΔL/L
Thus;
ν = -Δd•L/d•ΔL
Making Δd the subject, we have;
Δd = -νdΔL/L
Δd = -(0.34 × 17.8 × 10^(-3) × 0.544 × 10^(-3))/0.196
Δd = -0.0168 × 10^(-3) m = -0.0168 mm
Answer:
hello your question is poorly written hence I will give you a general answer
answer :
Hence the opening price = 140 - ( 14 * 3 )
= 140 - 42 = 98.00
Explanation:
To determine the opening price we will subtract or add the percentage Increase or decrease of the Dow Jones from the Final price of the Dow Jones
Lets assume :
Dow Jones Increased by 30 %
Dow Jones final price = 140
Hence the opening price = 140 - ( 14 * 3 )
= 140 - 42 = 98.00