Physics: How do you simulate continuous gravity using a discrete time step?

This is an example of Euler's method

Using differentiation, you can find a better formula. Since discrete calculations only "derive" if they are not linear, you only need to modify the position / time calculation.

// Repeat once per frame
position += velocity * deltaTime + gravity * Math.pow(deltaTime, 2.0) / 2.0;
velocity += gravity * deltaTime;

Even the large time steps align perfectly with the continuous graph:

Improved code, merged with a continuous graphic. The points are directly on the line.

azure: the published ASP.NET application that sends me to "The application is running, it's time to take the next step to implement"

I have a student account through blue. I have hosted several tasks in blue by publishing them through Visual Studio. I have a blue plan with the free $ 100 credit and I still have a lot of funds left. I have published my tasks many times without problems. Lately, it will take the same process and say it's over and gave me a link to my site. When I click on the link, it takes me to a page that says "Hello, App Service developers! Your application service is up and running. It's time to take the next step and implement your code."

I have never had this before. When I go to my account, it shows all my implemented sites and the correct plan affiliated with them. Why are they doing this suddenly? Even when I try to follow the steps, it doesn't work. I am following the same process that I have been doing for the other published applications. Some of them link to my sites very well, but several of them take me to this strange page. I can't send my assignment links this way. Any help would be very much appreciated.

magento2: the next step button does not appear in the payment

Battery exchange network

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How do I compare different optimization algorithms when the step size is unknown?

I want to compare different optimization algorithms (gradient pending, Newton, quasi-Newton, conjugate gradient, etc.) for a particular problem in question.
My main focus is the speed of convergence.

The problem is that all methods are based on a step size $ gamma $. How do I compare the speed of my algorithms when I don't know what $ gamma $ Would it work better for what model?

cryptography: at what step the private key is transformed into a mnemonic phrase

If I am correct in making a private key, I must first generate a 256-bit random number and then transform it into a WIF private key using the base verification encoding 58, is the mnemonic phrase generated from this WIF private key or Is there a step in between?

I am using this guide http://www.righto.com/2014/02/bitcoins-hard-way-using-raw-bitcoin.html, so maybe it is outdated

calculation – What is the wrong step in the integral $ int { ln x over x sqrt {1-4 ln x – ln ^ 2 x}} dx $?

Evaluate the following integral:
$$
I = int { ln x over x sqrt {1-4 ln x – ln ^ 2 x}} dx
$$

I started with a substitution: $ t = ln x $, then:
$$
dt = {dx over x} iff dx = xdt \
I = int {tdt over sqrt {1 – 4t – t ^ 2}}
$$

Completing the square in the denominator I obtained:
$$
1-4t-t ^ 2 = – (t ^ 2 + 4t – 1 + 5-5) = – (t + 2) ^ 2 + 5 = 5- (t + 2) ^ 2
$$

Then the integral becomes:
$$
int frac {tdt} { sqrt {5- (t + 2) ^ 2}}
$$

Replace $ t + 2 = s $, then $ dt = ds $Y $ t = s-2 $:
$$
int frac {(s-2) ds} { sqrt {5 – s ^ 2}} = int frac {sds} { sqrt {5 – s ^ 2}} – int frac {2ds} { sqrt {5 – s ^ 2}} tag1
$$

So:
$$
I_1 = int frac {sds} { sqrt {5 – s ^ 2}}
$$

Replace $ p = s ^ 2 $, $ dp = 2sds $Y $ ds = {dp over 2s} $:
$$
I_1 = int
frac {dp} {2 sqrt {5-p}} = {1 over 2} arcsin { sqrt {p} over sqrt5} + C = \
{1 over 2} arcsin { ln x + 2 over sqrt5} + C
$$

Back to $ (1) $:
$$
I_2 = int frac {2ds} { sqrt {5 – s ^ 2}} = 2 arcsin {s over sqrt5} + C = \
2 arcsin { ln x + 2 over sqrt5} + C
$$

Meaning:
$$
I = I_1 – I_2 = boxed {{1 over 2} arcsin { ln x + 2 over sqrt5} – 2 arcsin { ln x + 2 over sqrt5} + C}
$$

And that is not correct since the answer suggests:
$$
I = – sqrt {1-4 ln x – ln ^ 2 x} – 2 arcsin { ln x + 2 over sqrt5} + C
$$

I've been trying to detect the error for a while without any success, where did it go wrong? Obviously my answer is incorrect. By the way, I'm supposed to use substitution to solve the integral. Thanks in advance!

The economic data of the euro zone is weakening in general, the trend in the price of gold is increasing step by step

The outgoing president of the European Central Bank (ECB), Draghi, said in a testimony before the European Parliament yesterday (23) that the momentum of economic growth in the euro zone has slowed down more than originally expected, and potential price inflation It is still in a low position, the economy in general. There has been no sign of recovery, and the PMI (Purchasing Managers Index) of the Eurozone yesterday (23) continued to fall to historic lows, so it believes that the euro may continue to weaken against the US dollar.
The German manufacturing industry fell at the end of the decade, the comprehensive PMI index fell to 49.1, and the manufacturing PMI index of 41.4 was below the minimum of 50 years since April 2013, and the lowest point since 2009, the PMI of The service industry. The index has fallen for the first time in four and a half years, and the data clearly shows that general demand in Germany is gradually declining. From the perspective of the PMI in the euro zone, there will be a risk of economic recession in the coming months, so the European Central Bank (ECB) has pressure to stimulate economic measures, so the euro can weaken again in the second half.

Forex – Technical analysis (Gold XAUUSD):
Currency gold today (September 24) early in the morning at 1522.3 US dollars / ounce, according to technical analysis, the 1-hour level observation is in line with yesterday's forecast reversal (23) and continues to rise , the current K stick fell in the middle of the Bollinger Close Band, so there is the possibility of correcting stability and then challenging the gold return level of 0.618.
Currently, the pressure range above the short-term line is 1529 ~ 1529.5 dollars / ounce. In the downward direction, the initial support range is 1513 ~ 1513.5 dollars / ounce. The operating mentality is mainly short. Investors who wish to enter the market for a short time may consider the price of US $ 1520. To buy a lightweight warehouse at $ 1522 / oz, the MT4 operating stop loss can be set below $ 1518.5 / oz.

Forex – Technical analysis (EUR / USD EURUSD):
Currency of today EUR / USD (September 24) Early in the neighborhood of 1,00939, from the technical analysis, the 1 hour level observation trend was affected by the general decrease of the PMI index yesterday (23), there was a strong decline, so there is the possibility of appearing slightly After the rebound, it fell again.
Currently, the pressure range above the short-term line is 1,10050 ~ 1,10100, the direction down, the initial support interval is 1,09650 ~ 1,09700 and the operational mindset is short-term. Investors who wish to enter the market in the short term may consider buying in the range of 1,09860 to 1.9910. The stop loss point of the MT4 operation can be set above 1.09960.

Forex – Technical analysis (GBP / USD GBPUSD):
Today's foreign currency / US dollar (September 24) Early in the vicinity of 1,2291, since technical analysis, the 1-hour line level observation trend has not yet fallen below the uptrend line, by there is the possibility of going back to stabilize and then go back up.
At present, the pressure range above the short-term line is 1,225,100 ~ 1,25150, in the downward direction. The initial support range is 1.23850 ~ 1.23900. The operational mentality is mainly short. Investors who wish to enter the market for a short time may consider buying in the range of 1,24230 to 1,24280. It can be considered that the stop loss point of the MT4 operation is set below 1,24150.

Forex – Technical analysis (NZD / USD NZDUSD):
Today's currencies NZD / USD (September 24) Early in the vicinity of 0.62951, since the technical analysis, the 1-hour line level observation trend is in line with the blue trend forecasted for yesterday (23), after background, there is an increase, currently forming a small W below, so there is the possibility of continuing to rise.
At present, the pressure range above the short-term line is 0.63200 ~ 0.63250, in a downward direction, the initial support interval is 0.62750 ~ 0.62800, and the operational mentality is mainly short. Investors who wish to enter the market for a short time may consider buying in the range 0.62920 to 0.62970. It can be considered that the stop loss point of the MT4 operation is set below 0.62840.

Forex – Technical analysis (Nasdaq Index Nas100):
The currency exchange of today Nasdaq (September 24) early in the morning about 7845.4, from the technical analysis, the 1-hour line level observation trend is in line with yesterday's predicted decline (23) to the range of support chips, there has been a strong rebound, so there is a possibility of rebound The pressure fell again.
At present, the pressure range above the short-term line is 7900 ~ 7910 points, the direction down, the initial support range is 7780 ~ 7790 points, and the operating mindset is short-term. Investors who wish to enter the market in the short term may consider buying in the range 7875 to 7885. In, it can be considered that the stop loss point of the MT4 operation is set above 7908.

Today’s key facts:
1. September IFO business climate index of Germany
2. United Kingdom CBI industrial order difference in September
3. Monthly rate of the FHFA housing price index for July
4. Annual rate of the housing price index of large US cities S & P / CS20 in July
5. Richmond Fed manufacturing index in September
6. Consumer Confidence Index of the September US Conference Conference Board

For more information, see Forex and MT4

from

dnd 5e – Can you escape from a network by Misty Step?

No, they can not.

Misty Step says:

You teleport up to 30 feet to an unoccupied space that you can see.

While this says nothing about clothes and equipment, it is normally assumed, as is logical (who would use this spell in another way?).

Therefore, at least any object you have on you at the time of launch should not be left behind, which would include a network.

Assuming that you apply SageAdvice's responses, Misty could exit the links that are attached to a surface, but a network is not, so it must still teleport with you.

What is the equivalent to the impersonation step in the SPD 2013 template?

I need a WF that sends emails when documents are uploaded and I have used a 2010 template with impersonation step. You may now need to use a function that is only in the 2013 template that does not have the impersonation step. What is the equivalent feature here?

magento2 – Add Merchant T&C to Minicart, Cart and Checkout – Shipping Step

I am building a payment method extension which will appear in the mini-cart, cart and the shipping and review steps of the checkout page.
Can I know how to display merchant's terms and conditions below the payment button in mini-cart, cart and shipping step of the checkout page similar to the image below?

img1