Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
1/3= 5/15
2/5= 6/15
5/15 + 6/15 = 11/15
15/15 - 11/15 = 4/15
Part C= 4/15
Answer:
6.0
Step-by-step explanation:
This involves using SOH CAH TOA.
we use Sin as we want to find x (which is side O, and we are given H).
So we get sin37 = O/H
= x/10
so x = 10 sin 37 = 6.018... = 6.0 to the nearest tenth.
Answer:
True.
Step-by-step explanation:
A probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. Probability distribution is associated with the following characteristics or properties;
1. The outcomes are mutually exclusive.
2. The list of outcomes is exhaustive, which simply means that the sum of all probabilities of the outcomes must equal one (1).
3. The probability for a particular value or outcome must be between 0 and 1.
Since a probability distribution gives the likelihood of an outcome or event, a single random variable is divided into two main categories, namely;
I. Probability density functions for continuous variables.
II. Discrete probability distributions for discrete variables.
For example, when a coin is tossed, you can only have a head or tail (H or T).
Also, when you throw a die, the only possible outcome is 1/6 and the total probability for it all must equal to one (1).
