Answer:
m = 0.59 kg.
Explanation:
First, we need to find the relation between the frequency and mass on a spring.
The Hooke's law states that

And Newton's Second Law also states that

Combining two equations yields

The term that determines the proportionality between acceleration and position is defined as angular frequency, ω.

And given that ω = 2πf
the relation between frequency and mass becomes
.
Let's apply this to the variables in the question.

Answer: 4100 Mpc
Explanation:
Since H o = 70 km/s/Mpc
Redshift z = 5.82
Recessional velocity vr = 287,000 km/s
Then, the distance to the galaxy in light years will be:
= Recessional velocity / H o
= 287000 / 70
= 4100 Mpc
Water evaporates at 100⁰C
So change in temperature = 100-20 = 80⁰C
Amount of water to be evaporated = 1 liter = 1L*1kg/liter = 1 kg
Specific heat of water is 1 calorie/gram ⁰C = 4.186 joule/gram =4186 J/kg
So heat required E = mcΔT = 1 * 4186 *80= 334880 J =334.88 kJ
So amount of heat require to evaporate water = 334.88 kJ
( 3 yr) · (186,282.397 mile/s) · (86,400 s/day) · (365 day/yr)
= (3 · 186,282.397 · 86,400 · 365) mile
= 1.762380502 x 10¹³ miles
= 1.8 x 10¹³ miles (rounded to the nearest trillion miles)