Kathy was building a bed for her dollhouse. She used her bed, which is 3 feet × 5 feet, as a guide. She scaled down the dimensio
2 answers:
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Answer:
Step-by-step explanation:
The general solution will be the sum of the complementary solution and the particular solution:
In order to find the complementary solution you need to solve:
Using the characteristic equation, we may have three cases:
Real roots:
Repeated roots:
Complex roots:
Hence:
Solving for :
Since we got complex roots, the complementary solution will be given by:
Now using undetermined coefficients, the particular solution is of the form:
Note: was multiplied by x to account for
and
in the complementary solution.
Find the second derivative of in order to find the constants
and
:
Substitute the particular solution into the differential equation:
Simplifying:
Equate the coefficients of and
on both sides of the equation:
So:
Substitute the value of the constants into the particular equation:
Therefore, the general solution is:
Answer:
A) 0.99413
B) 0.00022
Step-by-step explanation:
A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:
Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes
Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:
μ = n*μ_s ample = 42 × 5 = 210 minutes
While the standard deviation for the population would be:
σ = √nσ_sample = √(42 × 6) = 15.8745 minutes
To find the z-score, we will use the formula;
z = (x - μ)/σ
Thus;
z = (250 - 210)/15.8745
z = 2.52
From the z-distribution table attached, we have;
P(Z < 2.52) ≈ 0.99413
B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.
Thus, total time is now 250 + 10 = 260 minutes
Similar to the z-formula in A above, we have;
z = (260 - 210)/15.8745
z = 3.15
P(Z > 3.15) = 0.00022
