Answer:
a. y(x,t)= 2.05 mm cos[( 6.98 rad/m)x + (744 rad/s).
b. third harmonic
c. to calculate frequency , we compare with general wave equation
y(x,t)=Acos(kx+ωt)
from ωt=742t
ω=742
ω=2*pi*f
742/2*pi
f=118.09Hz
Explanation:
A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=2.30mmcos[(6.98rad/m)x+(742rad/s)t]. Being more practical-minded, you measure the rope to have a length of 1.35 m and a mass of 3.38 grams. Assume that the ends of the rope are held fixed and that there is both this traveling wave and the reflected wave traveling in the opposite direction.
A) What is the wavefunction y(x,t) for the standing wave that is produced?
B) In which harmonic is the standing wave oscillating?
C) What is the frequency of the fundamental oscillation?
a. y(x,t)= 2.05 mm cos[( 6.98 rad/m)x + (744 rad/s).
b. lambda=2L/n
when comparing the wave equation with the general wave equation , we get the wavelength to be
2*pi*x/lambda=6.98x
lambda=0.9m
we use the equation
lambda=2L/n
n=number of harmonics
L=length of string
0.9=2(1.35)/n
n=2.7/0.9
n=3
third harmonic
c. to calculate frequency , we compare with general wave equation
y(x,t)=Acos(kx+ωt)
from ωt=742t
ω=742
ω=2*pi*f
742/2*pi
f=118.09Hz
Answer:
the yield of product is YP=46.835 % and the concentration of solids is
Cs = 27.33%
Explanation:
Assuming that all the solids and fats remains in the milk after the evaporation, then the mass of product mP will be
Mass of fat in 100 kg of milk = 100 kg* 0.037 = mP* 0.079
mP = 100 kg* 0.037/0.079 = 46.835 kg
then the yield YP of the product is
YP= mP / 100 kg = 46.835 kg / 100 kg = 46.835 %
YP= 46.835 %
the concentration of solids Cs is
Mass of solids in 100 kg of milk = 100 kg* 0.128 = 46.835 kg * Cs
Cs = 100 kg* 0.128 / 46.835 kg = 0.2733 = 27.33%
Cs = 27.33%
Answer:
1. Tienes 1 kg de fruta.
2. Queda por recorrer 1/4 km.
3. Ambos pesan lo mismo.
Explanation:
1. Tienes 1/2 kg y cuando te doy 1/4 te queda:
Ahora cuando te doy 3/4 kg te queda en total:
Por lo tanto, tienes 1 kg de fruta al final.
2. Si falta por recorrer la mitad de la mitad, tenemos:
Entonces, queda por recorrer 1/4 km.
3. El peso (P) del hierro es:
Y el peso de la paja es:
Por lo tanto, ambos pesan lo mismo.
Espero que te sea de utilidad!
Answer:
The astronaut who has a mass of 80 kg without the toolkit do survive with 40 seconds of remaining air
Explanation:
Due the astronaut throws the 10-kg tool kit away with a speed of 8 m/s, it gives a momentum equivalent but in the other direction, so 
, then we can find the speed that the astronaut reaches due to its weight we get, 
.
Finally, as the distance to the space shuttle is 200m, the time taken to the astronaut to reach it at the given speed will be 
, as the remaining air time is 4 min or 240 seconds, The astronaut who has a mass of 80 kg without the toolkit do survive with 40 seconds of remaining air.
