Answer:
see explanation
Step-by-step explanation:
To multiply the vector by a scalar, multiply each of the elements by the scalar.
To add 3 vectors add the corresponding elements of each vector
2a + 3b + 4c
= 2
+ 3
+ 4![\left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
=
+
+ ![\left[\begin{array}{ccc}12\\8\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%5C%5C8%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}4-12+12\\6+3+8\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4-12%2B12%5C%5C6%2B3%2B8%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}4\\17\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C17%5C%5C%5Cend%7Barray%7D%5Cright%5D)
The characteristic solution follows from solving the characteristic equation,

so that

A guess for the particular solution may be

, but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to

which has second derivative

Substituting into the ODE, you have



Therefore the particular solution is

Note that you could have made a more precise guess of

but, of course, any solution of the form

is already accounted for within

.
Answer:
LCM of 42 and 63 is 126.
Step-by-step explanation:
Find the prime factorization of 42
42 = 2 × 3 × 7Find the prime factorization of 63
63 = 3 × 3 × 7Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 3 × 3 × 7LCM = 126
Answer: 10 miles
Step-by-step explanation:
Practically, just look at it. 30 minutes = 5 miles, 60 minutes = 10 miles
Mathmatically, find the constant of proportionality.
- 30 minutes divided by 5 miles = 6 minutes per 1 mile.
- 60 minutes = 10 miles