Answer:
and 
Step-by-step explanation:
The equation of the isotope decay is:

14-Carbon has a half-life of 5568 years, the time constant of the isotope is:


The decay time is:
(There is no a year 0 in chronology).

Lastly, the relative amount is estimated by direct substitution:





First move the terms to get
6m-m=13+2
Then collect the like terms and calculate the sum, 5m=15
Divide both sides by 5
And you get m=3
The distance between the trains is changing at the rate of (70 -60) = 10 mph. They will be in the same place (45 mi)/(10 mi/h) = 4.5 hours after they leave their respective cities. They will be 10 miles apart both 1 hour before that time and one hour after that time.
The trains will be 10 miles apart 3.5 hours after leaving.
They will be 10 miles apart the second time 5.5 hours after leaving.
Answer:
since it takes 1 additional stick to bake a cake,then it takes 84 additional sticks to bake 42 cakes
Answer:
See the explanation
Step-by-step explanation:
We know that
f(x) = 2x⁶ + 3x⁴ - 4x³ + (1/x) - sin2x
Lets calculate the derivatives:
f'(x) = 6(2x⁵) + 4(3x³) - 3(4x²) -( 1/x²) - 2(cos2x)
f'(x) = 12x⁵ + 12x³ - 12x² - (1/x²) - 2cos2x
Similarly:
f''(x) = 60x⁴ + 36x² - 24x + (2/x³) + 4sin2x
f'''(x) = 240x³ + 72x - 24 - (6/x⁴) + 8cos2x
Rearrange:
f'''(x) - 240x³ +72x - (6/x⁴) + 8cos2x - 24
f''''(x) = 720x² + 72 + (24/x⁵) - 16sin2x
Rearrange:
f''''(x) = 720x² + (24/x⁵) - 16sin2x +72