Detailed derivation:
dA/dt = 6 - 0.02A
dA/dt = -0.02 (A - 300)
Rearranging terms.
dA / (A - 300) = -0.02 dt
Integrate both sides.
ln(A - 300) = -0.02t + C
Isolate A.
A - 300 = Ce^(-0.02t)
A = 300 + Ce^(-0.02t)
Apply initial condition to determine C.
50 = 300 + Ce^(-0.02 × 10)
50 = 300 + Ce^(-0.2)
-250 = Ce^(-0.2)
C = -250e^(0.2)
A = 300 - 250e^(0.2)e^(-0.02t)
A = 300 - 250e^(0.2 - 0.02t)
Answer: 130 degrees
Step-by-step explanation:
Given that
The distance from
Dallas to Charleston = 980 miles, from Charleston to Indianapolis = 595 miles, and from Indianapolis to Dallas is 764 miles.
Assuming that Dallas and Charleston are situated on the same latitude, we need to determine the bearing from Charleston to Indianapolis.
We will utilize the cosine rule to find the angle at Charleston.
764^2 = 980^2 + 595^2 - 2(980)(595)cosØ
583696 = 1314425 - 1166200cosØ
-1166200cosØ = -730729
CosØ = 0.6266
Ø = 51.2
Next, we calculate the angle at Indianapolis using the sine rule:
980/sinI = 764/sin 51.2
Reciprocate both sides:
SinI/980 = sin 51.2/764
Therefore, Sin I = 980 × sin 51.2/764
Sin I = 0.9996
I = 88.5 degrees
The bearing = 270 - (51.2 + 88.5)
= 270 - 140
= 130 degrees.
Answer:
The likelihood that a failure will not take place within the next 30 months is 0.0454.
Step-by-step explanation:
We employ a Poisson distribution where:
t = time units
x = occurrences during t units
λ = average occurrences per unit of time
P(x;λt) = e raised to the power of (-λt) multiplied by λtˣ divided by x!
Here, λt equals 25.
x equals 30.
P(x= 30) = 25³⁰e⁻²⁵/ 30!
P (x= 30) = 8.67 E41 * 1.3887 E-11/30! (where E signifies exponent)
P (x=30) = 1.204 E31/30!
Utilizing a statistical calculator will yield:
P (x=30) = 0.0454
The probability that the next failure will not occur prior to 30 months is 0.0454.
