Answer:
A) 5.1*10^10m B) 5.4*10^6m
Explanation:
Utilizing the formula for surface radiation P (energy per second in Watts) = emissivity constant * surface area * Stefan-Boltzmann constant * Temperature in Kelvin^4 *
2.7*10^31 = 1* 5.67*10^-8*A*11000^4
Rearranging to solve for A = 2.7*10^31 / (5.67*10^-8*1.46*10^16) = 0.3261*10^23m^2
Assuming the shape is spherical, the surface area is = 4πR^2 (radius of Rigel)
R = √(0.3261*10^23 / 4*π) = 5.1 * 10^10m
B) repeating the same calculation
2.1 *10^23 = 1*A*5.67*10^-8*10000^4 where A is the surface area of Procyon
Rearranging gives A = 2.1*10^23/(5.67*10^-8*10^16)
A = 0.37*10^15
Assuming the star is spherical;
A = 4πR^2 where R is Procyon's radius
R = √(0.37*10^15/4π) = 5.4*10^6m
The time period for any moon of Jupiter is described by the formula above, which also allows us to calculate Jupiter's mass. For part a, T is 1.77 days, which is equal to 152928 seconds. Applying the formula, we can derive the values needed. For part B, T equals 3.55 days or 306720 seconds, and repeating this with the necessary formula allows us to find the mass of Jupiter. For part c, T is 7.16 days, equating to 618624 seconds. Once again, using the earlier formula, we find Jupiter's mass. Finally, for PART D, T is noted to be 16.7 days or 1442880 seconds, and we can find the mass of Jupiter using the provided formula.
A. The horizontal component of velocity is
vx = dx/dt = π - 4πsin(4πt + π/2)
vx = π - 4πsin(0 + π/2)
vx = π - 4π(1)
vx = -3π
b. vy = 4πcos(4πt + π/2)
vy = 0
c. m = sin(4πt + π/2) / [πt + cos(4πt + π/2)]
d. m = sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]
e. t = -1.0
f. t = -0.35
g. To find t, set
vx = π - 4πsin(4πt + π/2) = 0
Then use this to calculate vxmax
h. To determine t, set
vy = 4πcos(4πt + π/2) = 0
Then use this to find vymax
i. s(t) = [x(t)^2 + y(t)^2]^(1/2)
h. s'(t) = d[x(t)^2 + y(t)^2]^(1/2) / dt
k and l. Determine the values for t
d[x(t)^2 + y(t)^2]^(1/2) / dt = 0
And substitute to find both the maximum and minimum speeds.
The response is outlined below. Audio power amplifiers are present in various sound systems, including those for sound reinforcement, public addresses, home audio, and musical instrument amplifiers like those for guitars. This component is the final electronic element in the audio playback chain before signals reach the loudspeaker. To achieve the loudest possible sound, it is essential to maximize output while maintaining high input and low output impedance.
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