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
1st Side: 8
2nd Side: 2x - 1
3rd Side: x
(8) + (2x - 1) > x (2x - 1) + x > 8 (x) + (8) > 2x - 1
2x + 7 > x 3x - 1 > 8 8 > x - 1
2x > -7 3x > 9 9 > x
x > -3.5 (disregard) x > 3 x < 9
3rd Side: x ⇒ (3 < x < 9)
2nd Side: 2x - 1 ⇒ 2(3) - 1 < x < 2(9) - 1 ⇒ 5 < x < 17
Answer: the 3rd side must be between 3 and 9, the 2nd side must be between 5 and 17
3/1 is your slope for that
X=k*Y
K*Y=X
K=X/Y
K=20/5
K=4
For Y=3/2
X=k*3/2
X=4*3/2
X=6
