Aerobic dance<span> has its foundation in </span>dance<span>-inspired movements. It is a cardiovascular workout set to music in a group </span>exercise<span> setting. You do not have to memorize </span>dance<span> moves, as the classes are taught by instructors who verbally tell and visually show the </span>choreography<span>.</span>
Answer: 500 s
Explanation:
Speed
is defined as a relation between the distance
and time
:
![v=\frac{d}{t}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%7D%7Bt%7D)
Where:
is the speed of light in vacuum
is the distance between the Earth and Sun
is the time it takes to the light to travel the distance
Isolating
:
![t=\frac{d}{v}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7Bv%7D)
![t=\frac{1.5(10)^{11}m}{3(10)^{8}m/s}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B1.5%2810%29%5E%7B11%7Dm%7D%7B3%2810%29%5E%7B8%7Dm%2Fs%7D)
Finally:
![t=500 s](https://tex.z-dn.net/?f=t%3D500%20s)
Answer:
![x=\frac{-y+\sqrt{y^2+4rt} }{2r}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-y%2B%5Csqrt%7By%5E2%2B4rt%7D%20%7D%7B2r%7D)
![x=\frac{-y-\sqrt{y^2+4rt} }{2r}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-y-%5Csqrt%7By%5E2%2B4rt%7D%20%7D%7B2r%7D)
Explanation:
![rx+y=\frac{t}{x}\\\\x(rx+y)=(\frac{t}{x})x\\\\rx^2+yx=t\\\\rx^2+yx-t=t-t\\\\rx^2+yx-t=0](https://tex.z-dn.net/?f=rx%2By%3D%5Cfrac%7Bt%7D%7Bx%7D%5C%5C%5C%5Cx%28rx%2By%29%3D%28%5Cfrac%7Bt%7D%7Bx%7D%29x%5C%5C%5C%5Crx%5E2%2Byx%3Dt%5C%5C%5C%5Crx%5E2%2Byx-t%3Dt-t%5C%5C%5C%5Crx%5E2%2Byx-t%3D0)
Solve using the quadratic formula.
![x=\frac{-y+\sqrt{y^2+4rt} }{2r}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-y%2B%5Csqrt%7By%5E2%2B4rt%7D%20%7D%7B2r%7D)
![x=\frac{-y-\sqrt{y^2+4rt} }{2r}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-y-%5Csqrt%7By%5E2%2B4rt%7D%20%7D%7B2r%7D)
Answer:
DS = 13865.7[J/K]
Explanation:
We can calculate the energy of the rock, like the potential energy relative to the lake level. Which can be calculated by means of the following expression of the potential energy:
![E_{p}=m*g*h\\\\where:\\m = mass = 2000[kg]\\h = elevation = 200 [m]\\g = gravity = 9.81[m/s^2]](https://tex.z-dn.net/?f=E_%7Bp%7D%3Dm%2Ag%2Ah%5C%5C%5C%5Cwhere%3A%5C%5Cm%20%3D%20mass%20%3D%202000%5Bkg%5D%5C%5Ch%20%3D%20elevation%20%3D%20200%20%5Bm%5D%5C%5Cg%20%3D%20gravity%20%3D%209.81%5Bm%2Fs%5E2%5D)
Therefore:
![E_{p}=2000*9.81*200\\E_{p}=3924000 [J]\\](https://tex.z-dn.net/?f=E_%7Bp%7D%3D2000%2A9.81%2A200%5C%5CE_%7Bp%7D%3D3924000%20%5BJ%5D%5C%5C)
This energy is transformed into thermal energy.
we shall remember that isothermal heat transfer processes are internally reversible, so the entropy change of a system during one of these processes can be determined, by the following expression.
![DS=\frac{Q}{T}\\ where:\\DS = entropy change [J/K]\\Q = Heat transfer [J]\\T = temperature [K]](https://tex.z-dn.net/?f=DS%3D%5Cfrac%7BQ%7D%7BT%7D%5C%5C%20where%3A%5C%5CDS%20%3D%20entropy%20change%20%5BJ%2FK%5D%5C%5CQ%20%3D%20Heat%20transfer%20%5BJ%5D%5C%5CT%20%3D%20temperature%20%5BK%5D)
T = 5 + 278 = 283[K]
DS = 3924000 / 283
DS = 13865.7[J/K]