Answer:
Step-by-step explanation:
The rate of change of temperature of the coffee with respect to time is expressed by the differential equation
dT/dt=k(T−A) when k = -1 and A = 23. The equation will become:
dT/dt = -(T-23)
If the coffee cools at the rate of 1°C per minute, then dT/dt = -1 and T = 70
Substituting into the equation:
-1 = k(70-23)
-1 = 47k
k = -1/47
k = -0.0213
Substituting k = -0.0213 into the original equation, the differential equation will be:
dT/dt=k(T−A)
dT/dt = -0.0213(T-23)
dT/dt = -0.0213T+0.489
To get the value of T, we will use variable separable method
dt = dT/-0.0213T+0.489
Integrate both sides
t = -0.0213ln(-0.0213T+0.489)
At t = 1 minute
1 = -0.0213ln(-0.0213T+0.489)
1/-0.0213 = ln(-0.0213T+0.489)
-46.95 = ln(-0.0213T+0.489)
Apply exp to both sides
e^-46.95 = e^ln(-0.0213T+0.489)
4.073×10^-21= -0.0213T+0.489
-0.0213T = 4.073×10^-21-0.489
-0.0213T = -0.489
T = 0.489/0.0213
T = 22.96°C
<span>I note that this problem starts out with "Which is a factor of ... " This implies that you were given several answer choices. If that's the case, it's unfortunate that you haven't shared them.
I thought I'd try finding roots of this function using synthetic division. See below:
f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35
Please use " ^ " to denote exponentiation. Thanks.
Possible zeros of this poly are factors of 35: plus or minus 1, plus or minus 5, plus or minus 7. Use synthetic division; determine whether or not there is a non-zero remainder in each case. If none of these work, form rational divisors from 35 and 6 and try them: 5/6, 7/6, 1/6, etc.
Provided that you have copied down the function
</span>f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35 properly, this approach will eventually turn up 1 or 2 zeros of this poly. Obviously it'd be much easier if you'd check out the possible answers given you with this problem.
By graphing this function, I found that the graph crosses the x-axis at 7/2. There is another root.
Using synth. div. to check whether or not 7/2 is a root:
___________________________
7/2 / 6 -21 -4 24 -35
21 0 -14 35
----------- ------------------------------
6 0 -4 10 0
Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial. Thus, (x-3.5), or (x-7/2), is a factor.
Answer:
0.074
Step-by-step explanation:
cause in probability when two events are exclusive we use multiplication rule
Answer: 36
Step-by-step explanation:
1) Find the prime factorization of 12
12=2*2*3
2) Find the prime factorization of 18
18=2*3*3
3) Multiply each factor the greater number of times it occurs in the first two steps above to find the LCM.
LCM=2*2*3*3
4) LCM=36
