Choose all the Reduce function solutions

I have a simple question that is related to the way to extact and use the values i obtain to plot!

I have a variable A and depending the value the following reduce operation returns 1 or 2 values.

 A = 0.5; Reduce[  {D[-A Cos[\[Theta]] + 0.5 Sin[\[Theta]]^2 -       0.01 Cos[\[Theta]], {\[Theta], 1}] == 0,   D[- A Cos[\[Theta]] + 0.5 Sin[\[Theta]]^2 -       0.01 Cos[\[Theta]], {\[Theta], 2}] > 0,    2 Pi >= \[Theta] > 0}, \[Theta], Reals]  A = 2; Reduce[  {D[-A Cos[\[Theta]] + 0.5 Sin[\[Theta]]^2 -       0.01 Cos[\[Theta]], {\[Theta], 1}] == 0,   D[- A Cos[\[Theta]] + 0.5 Sin[\[Theta]]^2 -       0.01 Cos[\[Theta]], {\[Theta], 2}] > 0,    2 Pi >= \[Theta] > 0}, \[Theta], Reals] 

RETURNS:

\[Theta] == 3.14159 || \[Theta] == 6.28319 \[Theta] == 6.28319 

If i want to plot the result of the reduce operation as function of A, how can i extract the values?

Plot[    Reduce[      {D[-A Cos[\[Theta]] + 0.5 Sin[\[Theta]]^2 -           0.01 Cos[\[Theta]], {\[Theta], 1}] == 0,       D[- A Cos[\[Theta]] + 0.5 Sin[\[Theta]]^2 -           0.01 Cos[\[Theta]], {\[Theta], 2}] > 0,        2 Pi >= \[Theta] > 0}, \[Theta], Reals][[2]], {A,-20,20}] 

If i use the [[2]] it only will plot the values obtained when there is only one solution. how can i plot all the solutions? 1 when there is only 1 and 2 when there are 2 solutions?

Thanks in advance

Enlarge / REduce spell cast on a creature that has its hands and feet tied up to trees around him

The Enlarge/REduce Spell indicates that when you enlarge a creature and there is not enough space available, it just grows to maximum possible size given the space available. This effect seems to maybe temporarily trap a creature but will not cause damage to it. On the opposing effect, if you tie a creature’s limbs to trees in ‘star’ shaped fashion, then cast reduce on it, would the limbs effectively pop out as the creature shrinks or would just the spell fails to shrink the creature because of the rope’s resistance preventing the creature to shrink more without tearing it apart.

To me this is one of the worst written spell in history… can anyoone bring some clarification ? something I am missing here ?

Rearrange items in order reduce fragmentation and reduce wasted space

I have a segment with some offsets at irregular intervals

There are items of various length inside. Items cannot be placed randomly. Instead, their left side must match some offset.

Items are free to go past offests.

As you can see in this image, item number 3 is long enough that it goes through an offset, shown with a dotted line.

I also have some special type of offset that I’ll call “barrier” that items cannot go past and cannot be placed on:

One last constraint is that items cannot overlap each other:

Items can be moved one at a time. So I can pick up an item and place it somewhere else as long as no constraint is violated.

I’m trying to come up with an algorithm/solver/optimizer which would find some good enough sequence of steps to reduce fragmentation and compact up these items. It follows that this procedure will reduce empty space between items and offsets:

Can you give some suggstion on how you would tackle a problem like this or point me in the right direction, give some ideas, name algorithms to take inspiration from, etc..?

reduce printing size

I need to print a shipping label that’s in the form of a PDF. The problem is that it’s too large for the package so it has to be reduced in size. It’s easy to reduce the size of the visual image, but that doesn’t seem to affect the size of the printed page. I’ve tried both Ocular and qpdfview but wasn’t able to get them to do this. How can I reduce that size?

Modifying SharePoint alerts to reduce the details in the email

I’m finally getting my organization to use Alerts. Which is great. We are using SharePoint online. I send each team member a daily summary at 7:00 am.
The following are the settings: Change type: All Changes Send Alerts for These Changes: Anything Changes When to Send Alerts: Daily Summary 7:00 am

From the screen shot below, you can see one team member has been working on a file, and every time the file saves, the alert records it, and if they’ve been working on the file all day, there are several lines for each file. The team members have to scroll a long way down in the email to see all the files that have been modified.

Is there a way for information to be displaying with less information so that you don’t have to scroll down in your email so much? enter image description here

Does the Heavy Armor Master feat reduce damage twice against a mixed damage attack?

Displacer Beasts have a Tentacle attack that does 7 (1d6 + 4) bludgeoning damage plus 3 (1d6) piercing damage. Does the bludgeoning and piercing damage reduction granted by Heavy Armor Master reduce that total damage by 6 or 3? If only 3, what determines which of the two damage types is reduced?

Do Boots of Striding and Springing negate skills, feats, and spells that reduce your movement?

Per the horribly worded description:

While you wear these boots, your walking speed becomes 30 feet, unless your walking speed is higher, and your speed isn’t reduced if you are encumbered or wearing heavy armor.

But there are multiple ways in which a characters speed can be reduced beyond encumbrance. For instance, the Sentinel feat:

  • When you hit a creature with an opportunity attack, the creature’s speed becomes 0 for the rest of the turn.

Another example is being grappled:

  • A grappled creature’s speed becomes 0, and it can’t benefit from any bonus to its speed.

I highlighted the word becomes in these descriptions because, in the English language, it would indicate a one-time change. So a boy BECOMES a man. A seed BECOMES a plant.

But the Boots also say, “While” — A continuous duration. This puts the description at odds.

A character wearing the Boots has there walking speed “become” 30 feet unless encumbered or wearing heavy armor. They are hit by and NPC with the Sentinel feat so there speed “becomes” 0. Now what?

Does the character’s speed re-become 30 feet allowing them to keep moving? Or are they forced to stand still?


I seem to recall there being another magic item that uses the a phrase similar to “cannot be reduced below” but so far my search has come up empty.