I am having trouble with this problem:
Let T:V->W be a linear transformation. Prove that T is one-to-one if and only if dimension of V = dim(RangeT).
I know that in order to be a linear transformation:
1) T(vector u + vector v) = T(vector u) + T(vector v) and
2) T(c*vector u) =...
this is how I tried to solve the problem:
y'=k(y-68)
dy/dt=k(y-68)
∫(1/y-68)dy=∫kdt
e^ln|y-68|=e^kt+c1
y-68=e^kt+c1
y=68+ce^kt
100=68+ce^k(0)
100=68+c
c=32
when t=1, y=95 when t=2, y=92
95=68+32e^k(1) 92=68+32e^k(2)
27=32e^1k...
a cup of coffee is heated to 100° then left in a room with a constant temperature of 68° after a minute the temperature of the coffee has dropped to 95° after another minute to 92 degrees. how much time must pass before the temperature of the coffee has dropped to 70°?