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
According to the principle of energy conservation, the engine's work in moving the scooter is converted into the scooter's kinetic energy, represented as:
Let T be the force exerted on the rope by her. This force induces tension in the rope, which exerts an upward force on the crates, while the weight of the crate pulls downward. Thus, the net force acting on the crate can be expressed as mg - T, acting in the downward direction. According to Newton's law, we can set up the equation: mg - T = ma. Given that a = 0 (the speed remains constant), this simplifies our equation to mg - T = 0, which leads to T = mg. Therefore, T = 25 x 9.8 = 245 N, indicating that the force she needs to apply is 245 N.
To tackle this question, we know the following:
1 Albert equals 88 meters.
1 A = 88 m.
Initially, we square both sides of the equation:
(1 A)^2 = (88 m)^2
1 A^2 = 7,744 m^2
<span>Since 1 acre equals 4,050 m^2, let’s divide both sides by 7,744 to find out how many acres match this value:</span>
1 A^2 / 7,744 = 7,744 m^2 / 7,744
(1 / 7,744) A^2 = 1 m^2
Then multiply both sides by 4,050.
(4050 / 7744) A^2 = 4050 m^2
0.523 A^2 = 4050 m^2
<span>Thus, one acre is approximately 0.52 square alberts.</span>
