Estimate the dose from CT for a prostate patient (total dose 78 Gy) who undergoes the following:

- 2 CT simulations

- 39 KVCT localization images

- 1 Midcourse Evaluation CT

- 1 Post Treatment CT

Please show all work.

Owen is jumping on a trampoline. When his feet hit the deck of the trampoline, the material depresses to a minimum height of 2cm. On average, Owen is reaching a maximum height of 200cm every 10 seconds. Determine the equation of a sinusoidal function that would model this situation, assuming Owen reaches his first maximum at 6 seconds.

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)