Damien has 30 coins, all nickels and dimes. The total value of all these coins is $2.05. How many nickels does he have?
1 answer:
Hi there!
nickels:19
We know that there is only nickels and dimes in his coin collection..
<u><em>1.Multiply two terms:</em></u>
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<u><em>Then there would be 20 nickels but 1+1=2 not 2.05.</em></u>
<u><em>2.Multiply the terms:</em></u>
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<u><em>3.Combine the two terms:</em></u>
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Therefore, there would be 19 nickels...
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Answer:
A) C1 = 0.00187 m = 0.187 cm, C2 = 0.0062 m = 0.62 cm
B) A sample of how the graph looks like is attached below ( periodic sine wave )
C) w = is when the amplitude of the forced response is maximum
Step-by-step explanation:
Given data :
mass = 5kg
length of spring = 10 cm = 0.1 m
f(t) = 10sin(t) N
viscous force = 2 N
speed of mass = 4 cm/s = 0.04 m/s
initial velocity = 3 cm/s = 0.03 m/s
Formulating initial value problem
y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m
spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m
f(t) = 10sin(t/2) N
using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion
the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)
A) finding the solution of the initial value
attached below is the solution and
B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like
C attached below
