dnd 5e – How does the Ancestral Protector's barbarian Ancestral Guardian function work if you hit something before the onset of rage?

The barbarian function of the ancestor guardian ancestral protectors (XGtE, p. 10) reads as follows:

If you choose this path in the 3rd level, spectral warriors will appear when you enter your anger. As you roar, the first creature you attack in your turn becomes the target of the Warrior, hindering their attacks. Until the start of your next turn, this target has a disadvantage on an attack roll that is not aimed at you, and if the target hits a creature other than you with an attack, that creature will have resistance to the damage done by the attack. The effect on the target ends early when your anger ends.

Suppose I have a fighter dip. What would happen if I hit a creature that rages with BA? Would the ancestors choose the creature I hit at the beginning of my turn even though anger was triggered after the hit?

If I acted quickly and made something else, would they target that?

I'm specifically wondering if you can use booming blade to trigger the ability RAW.

Calculus – Tangent of a function in the 1st quadrant forms a triangle. Find the area.

So, I have this specific question, which is based on calculus.
Here is the question below:

Consider the graph of f (x) = exp (-x) for x> = 0. The tangent to the graph of f (x) at x = a and intersects the x-axis at point A and the y-axis at Point B. Determine the area of ​​the triangle AOB with respect to a.

Therefore, the coordinate on the x-axis (A, 0) and the coordinate on the y-axis is (0, B).

I worked on that.
The slope of the tangent would be: m = -exp (-a)
So my equation would be the tangent: y = [-exp(-a)]x + B,
Next I insert the point: (A, 0)
Then you get the relationship B = A * exp (-a), so the full equation of the tangent line is:
y = -exp (-a)[x-A]

Now the surface is a right triangle with vertices AOB,
This area is:
Area = AB / 2.
Insert the relationship B = A
exp (-a).
Then area = [(A^2)*exp(-a)]/ 2

BUT my formula depends on the x-axis coordinate A.
SO not sure if this A can be replaced by being related to & # 39; a & # 39 ;, the tangent point.

Hope someone can contribute to this.

binary – Something is wrong with the implementation of the ThueMorse function

In an attempt to answer this Math.SE question, I have probably found several errors in Mathematica and Alpha that relate to the Thue-Morse sequence.

As a reminder, the $ n ^ { rm th} $ Element of the Thue-Morse sequence $ 1 $ if the sum of its binary digits contains an odd number of $ 1 $s $ 0 $ Otherwise.

Essentially, I entered the function
$$
zeta_ {TM} (s) = sum_ {n geq0} frac {t_ {n}} {(n + 1) ^ s}
$$

in Alpha, which gave surprising
$$
zeta_ {TM} (s) = 2 ^ {- s} zeta (s),
$$

from where $ zeta (s) $ is the Riemann zeta function. This is obviously wrong because the LHS does not converge to RHS for one $ s> 1 $, On closer inspection, Alpha seems to have translated ThueMorse[n] to Mod[Plus @@ IntegerDigits[n, 2], 2]which is perfectly fine, since this is the definition of the Thue-Morse sequence.

When I approached Mathematica to solve this puzzle, I realized that this too is the same mistake. input

total[Mod[Mod[Mod[Mod[Plus @@ IntegerDigits[n, 2], 2]/ (n + 1) ^ s, {n, 0, infinity}]

returns

2 ^ -s Zeta[s]

which of course is wrong again. On the example of $ s = 3 $ and calculating the partial sums up to a positive integer $ m $ and share them $ 2 ^ {- s} zeta (s) $ clearly shows that they diverge:

s = 3
table[N[Total[Mod[N[Sum[Mod[N[Summe[Mod[N[Sum[Mod[Plus @@ IntegerDigits[n, 2], 2]/ (n + 1) ^ s, {n, 0, 10 ^ m}]]/ (2 ^ {- s} * Zeta[s]), {m, 1, 5}]

gives

{{1.15377}, {1.16799}, {1.16814}, {1.16814}, {1.16814}}

which certainly does not converge $ 1 $,

So, what's going on here? Is this really a mistake in Alpha and Mathematica or is something very obvious missing?


For information I use Mathematica 11.

With printf, translation function and date_i18n additional characters are added

That's why I'm trying to make these strings translatable and in the right PHP / WP format

& # 39; you & # 39 ;. date_i18n (jj M,, strtotime ($ date_debut-> format (jj M Y)))). & # 39; & # 39 ;. au date_i18n (get_option (# date_format #), strtotime ($ date_fin-> format (# M YY #)));

The equivalent with printf should look like this:

printf (
__ (& # 39; you% 1 $ s au% 2 $ s & # 39 ;, & # 39; my-plugin & # 39;),
date_i18n (jj M,, strtotime ($ date_debut-> format (jj M Y &))),
date_i18n (get_option (# date_format), strtotime ($ date_fin-> format (# M Y Y #))
);

But for some reason, the year seems the same 201914 or 201920,

What are these extra characters, is it because I try to use one date_i18n () in the __ () Translation feature?

Javascript function that performs the same action is wrong

Hello, I'm doing a college job and it has a file list screen. At the time of deleting, I created a button with a mouse click. I do not understand much of javascript, but follow the logic if it would otherwise only do the action if it were true, even more if I aborted it;

Continuity – is there a homotopy between identity function and a continuous function?

(My question is about the Brouwer checkpoint set.)

To let $ B $ be a closed ball of $ mathbb {R} ^ n $,

F 1. If $ f: B rightarrow B $ Is a continuous function, then there is a homotopy in between $ id_B $ and $ f $?

Suppose the answer to the above question is yes. Then we can designate $ {f_r } $ be a family of continuous functions in which $ 0 leq r leq 1 $ so that $ {f_r } $ make the homotopy between $ id_B $ and $ f $, After the Brouwer checkpoint set is the set $ F_r: = {x ~ | ~ f_r (x) = x } $ is not empty for everyone $ 0 leq r leq 1 $,

Q 2. Is there a continuous function? $ g: [0,1] rightarrow B $ satisfying $ g (r) in F_r $ for each $ 0 leq r leq 1 $? In other words, there is a way $ g $ what happens fixed points in homotopy?

Thank you for your interest.