Newton's Law of Cooling
Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.
200=68+(210-68)e^(-10k)
132=142e^(-10k)
132/142=e^(-10k)
ln(132/142)=-10k
k=-ln(132/142)/10
k≈0.0073 so
T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?
180=68+142e^(-0.0073t)
112=142e^(-0.0073t)
112/142=e^(-0.0073t)
ln(112/142)=-0.0073t
t= -ln(112/142)/(0.0073)
t≈32.51 minutes
30,000 to the nearest thousands. The largest number is 30,499 and the lowest number is 29,500.
190/5 = 38
So, they can make 38 quarts in an hour.
38 * 36 = 1,368
They can make 1,368 quarts in 36 hours.
To get rid of

, you have to take the third root of both sides:
![\sqrt[3]{x^{3}} = \sqrt[3]{1}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B1%7D%20)
But that won't help you with understanding the problem. It is better to write

as a product of 2 polynomials:

From this we know, that

is the solution. Another solutions (complex roots) are the roots of quadratic equation.