using the annihilator approach, solve the DE

y'' - 4y' + 4y = e^4x + xe^-2x     , y(0) = 1 , y'(0) = -1

How to show that there are infinitely many prime p of the form p= 1+5k or p=4+5k

Write a one paragraph explanation about why Riemann sums are necessary even though we have FTC from calculus I to get the exact results of an integral.

Determine if there exist a nonempty set S with operation ⋆ on S and a nonempty set S′ ⊂ S, which is closed with respect to ⋆, satisfying the following properties.

1) S has identity e with respect to ⋆. ′

2) e ∈/ S .

3) S′ has an identity with respect to ⋆.

Cliffs of Insanity Point is located 194 miles from the Pedimaxus International Airport at a bearing of N8.7ºE. The wind is blowing from the southeast to the northwest at 23 miles per hour. What speed and bearing should the pilot take so that she makes the trip in 2 hours? Round the speed to the nearest hundredth of a mile per hour and your angle to the nearest tenth of a degree.

speed = mph

bearing=   

How do you wrap your head around the poorly written chapter 9.3 in 'Contemporary Linear Algebra'?

10. Solve the following initial value problem:

y''' − 2y '' + y ' = 2e ^x − 4e^ −x

y(0) = 3, y' (0) = 1, y''(0) = 6

BOTH LINES ARE PART OF A SYSTEM OF EQUATIONS

Let α, β be cuts as defined by the following:

1) α ≠ ∅ and α ≠ Q

2) if r ∈ α and s ∈ Q satisfies s < r, then s ∈ α.

3) if r ∈ α, then there exists s ∈ Q with s > r and s ∈ α.

Let α + β = {r + s | r ∈ α and s ∈ β}.

Show that the set of all cuts R with the addition defined above satisfies the axioms for addition (closed, associative, symmetric, identity, inverse)

Kim Walrath has a nutritional deficiency and is told to take at least 2500 mg of​ iron, 2400 mg of vitamin​ B-1, and 1800 mg of vitamin​ B-2. One Maxivite pill contains 40 mg of​ iron, 8 mg of vitamin​ B-1, an 5 mg of vitamin​ B-2 and costs

$0.05.One Healthovite pill provides 10 mg of​ iron, 12 mg of vitamin​ B-1, and 15 mg of vitamin​ B-2 and costs ​$0.09.

Complete parts​ (a) and​ (b) below.

​(a) What combination of Maxivite and Healthovite pills will meet​ Kim's requirement at lowest​ cost? What is the lowest​ cost?

The best combination is? pills of Maxivite and? pills of Healthovite.

​(Round to the nearest whole number as​ needed.)

The lowest cost is ​$?

​(Round to the nearest cent as​ needed.)

​(b) In your solution for part​ (a), does Kim receive more than the minimum amount she needs of any​ vitamin? If​ so, which vitamin is​ it?

Select the correct answer​ below, and if​ necessary, fill in the answer boxes to complete your choice.

A.Yes. She receives?mg more iron than she​ requires,?mg more vitamin​ B-1 more than she​ requires,? and? mg more vitamin​ B-2 than she requires.

B. No. She does not receive more than she requires of any vitamin.

In general, if p is the number of predictor variables and k is the number of groups for the outcome variable in a DA, how many different discriminant functions can be obtained to differentiate among
groups? (This question assumes that the X predictor variables have a determinant that is nonzero; that is, no individual Xi predictor variable can be perfectly predicted from scores on one or more other X
predictor variables.)

Can a closed linear map be unbounded?