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https://math.answers.com/Q/What_is_one_fourth_plus_four_twelves
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0
# What is one fourth plus four twelves?
Wiki User
2015-01-16 04:19:53
4(12)+.25
48+.25=
48.25 or 48 and one fourth
Wiki User
2011-04-09 00:47:45
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# 12.3: One-Way ANOVA
The purpose of a one-way ANOVA test is to determine the existence of a statistically significant difference among several group means. The test actually uses variances to help determine if the means are equal or not. In order to perform a one-way ANOVA test, there are five basic assumptions to be fulfilled:
1. Each population from which a sample is taken is assumed to be normal.
2. All samples are randomly selected and independent.
3. The populations are assumed to have equal standard deviations (or variances).
4. The factor is a categorical variable.
5. The response is a numerical variable.
## The Null and Alternative Hypotheses
The null hypothesis is simply that all the group population means are the same. The alternative hypothesis is that at least one pair of means is different. For example, if there are k groups:
$$H_{0} : \mu_{1}=\mu_{2}=\mu_{3}=\ldots \mu_{k}$$
$$H_a$$: At least two of the group means $$\mu_{1}, \mu_{2}, \mu_{3}, \dots, \mu_{k}$$ are not equal. That is, $$\mu_{i} \neq \mu_{j}$$ for some $$i \neq j$$.
The graphs, a set of box plots representing the distribution of values with the group means indicated by a horizontal line through the box, help in the understanding of the hypothesis test. In the first graph (red box plots), $$H_{0} : \mu_{1}=\mu_{2}=\mu_{3}$$ and the three populations have the same distribution if the null hypothesis is true. The variance of the combined data is approximately the same as the variance of each of the populations.
If the null hypothesis is false, then the variance of the combined data is larger which is caused by the different means as shown in the second graph (green box plots).
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# Portfolio Optimization with Python using Efficient Frontier with Practical Examples
Portfolio optimization in finance is the technique of creating a portfolio of assets, for which your investment has the maximum return and minimum risk.
Investor’s Portfolio Optimization using Python with Practical Examples. Photo by Markus
In this tutorial you will learn:
## 1. What is portfolio optimization?
Portfolio optimization is the process of creating a portfolio of assets, for which your investment has the maximum return and minimum risk.
Don’t worry if these terms made no sense to you, we will go over each one in detail.
## 2. What does a portfolio mean?
An investor’s portfolio basically is his/her investment in different kinds of assets from different companies.
For example, if you have investments in 3 companies, say, Google, Amazon and Tesla, then these 3 companies make up your investment portfolio.
But how do you invest in a company? You do so by purchasing assets of that company.
## 3. What are assets, returns and risk?
Assets are of various kinds. An asset is what you would purchase if you want to invest in a company.
These include, but are not limited to:
1. Bonds
2. Stocks
3. Cash
4. Real Estate
Usually when you build a portfolio, it is advisable to diversify your assets, or purchase different kinds of assets from different companies. For all assets, you will get a profit after a specified period of time. However, the profit may not be the same for each investment you make.
This profit is what we call returns.
For example, you will get returns from stocks when it’s market value goes up and similarly you will get returns from cash in form of interest.
But what if the company whose stocks you have purchased goes bankrupt?
This will lead to its stocks crashing in the share market and instead of gaining profits, you will also lose your capital investment.
This is what is called risk of investment.
Another aspect of risk is the fluctuations in the asset value. For certain assets, its value is highly volatile, that is, the value increases when the market goes up, and drops accordingly. Whereas certain other assets, like bonds and certain steady stocks, are relatively more resistant to market conditions, but may give lesser returns compared to high risk ones.
A good portfolio is one which gives us maximum return on our investment for minimum risk, as discussed earlier.
The next question is, how do we decide out of an infinite possible combinations for portfolios, the one which is optimum?
## 4. Modern Portfolio Theory (MPT)
Modern Portfolio Theory, or also known as mean-variance analysis is a mathematical process which allows the user to maximize returns for a given risk level.
It was formulated by H. Markowitz and while it is not the only optimization technique known, it is the most widely used.
MPT assumes that all investors are risk-averse, i.e, if there is a choice between low risk and high risk portfolios with the same returns, an investor will choose one with the low risk.
So, what is the MPT all about?
MPT encourages diversification of assets. It says that a high variance asset A if combined with diverse assets B and C, where A, B and C have little to no correlation, can give us a portfolio with low variance on returns.
This is the crux of the Modern Portfolio Theory.
## 5. What is Efficient Frontier?
We know every asset in a portfolio has its own rate expected returns and risks. It is possible to create multiple combinations of assets that can provide high returns for a pre-defined risk level.
Likewise, there can be multiple portfolios that give lowest risk for a pre-defined expected return.
Efficient frontier is a graph with ‘returns’ on the Y-axis and ‘volatility’ on the X-axis. It shows the set of optimal portfolios that offer the highest expected return for a given risk level or the lowest risk for a given level of expected return.
Portfolios that lie outside the efficient frontier are sub-optimal because they do not provide either enough return for the level of risk or have a higher risk for the defined rate of return.
We will revisit this with an example again.
Now that you understand the term of portfolio optimization, let’s see how its actually implemented.
## 6. Fundamental terms in portfolio optimization
There are some statistical terms required in optimization process without which an optimal portfolio can’t be defined. Don’t worry, I will simplify it and make it easy and clear.
We will go through each one through an example.
In this example, we are considering a portfolio made up of stocks from just 2 companies, Tesla and Facebook.
Step 1: Pull the stock price data
The first step is to is to pull the required data from a verified site such as Yahoo or Quandl. The example below uses Yahoo and the dates for which we will be pulling the data is from 1st January, 2018 to 31st December, 2019.
# Load Packages
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
Let’s import the data.
# Read Data
test = data.DataReader(['TSLA', 'FB'], 'yahoo', start='2018/01/01', end='2019/12/31')
As you can see, there are a lot of different columns for different prices throughout the day, but we will only focus on the ‘Adj Close’ column. This colum gives us the closing price of company’s stock on the given day.
# Closing price
Symbols TSLA FB
Date
2018-01-02 64.106003 181.419998
2018-01-03 63.450001 184.669998
2018-01-04 62.924000 184.330002
2018-01-05 63.316002 186.850006
2018-01-08 67.281998 188.279999
Step 2: Calculate percentage change in stock prices
Next, we calculate the percentage change in stock prices of tesla everyday. You will notice that that we take the log of percentage change.
But take log?
The reason for this is that log of the returns is time additive.
That is,
If r13 is the returns for time between t3 and t1.
r12 is the returns between t1 and t2 and
r23 is the returns between t2 and t3.
Then, log(r13) = log(r12) + log(r23)
For example:,
If p1 = 100, p2 = 110 and p3 = 120,
where p1 is price of stock in time 1
Then:
log(r12) = ln(p2/p1) = ln(110/100) = 9.53%,
log(r23) = ln(120/110) = 8.7% and
log(r13) = log(r12) + log(r23) = 9.53 + 8.7 = 18.23%, which is same as ln(120/100).
This means a log change of +0.1 today and then -0.1 tomorrow will give you the same value of stock as yesterday. This is not true if you simply compute percentage change.
It is common practice in portfolio optimization to take log of returns for calculations of covariance and correlation.
# Log of percentage change
tesla = test['TSLA'].pct_change().apply(lambda x: np.log(1+x))
Date
2018-01-02 NaN
2018-01-03 -0.010286
2018-01-04 -0.008325
2018-01-05 0.006210
2018-01-08 0.060755
Name: TSLA, dtype: float64
## Variance
The variance in prices of stocks of Tesla are an important indicator of how volatile this investment will be (how returns can fluctuate).
It can be calculated for each company by using built in .var() function. Under the hood, the formula implemented by this function is given by:
$$s^2 = \sum_{i=1}^N (x_i – \bar{x})^2 / N-1$$
# Variance
var_tesla = tesla.var()
var_tesla
0.0011483734269334596
# Log of Percentage change for Facebook
fb = test['FB'].pct_change().apply(lambda x: np.log(1+x))
Date
2018-01-02 NaN
2018-01-03 0.017756
2018-01-04 -0.001843
2018-01-05 0.013579
2018-01-08 0.007624
Name: FB, dtype: float64
The variance is:
# Variance
var_fb = fb.var()
var_fb
#> .00045697258417022536
## Volatility
Volatility is measured as the standard deviation of a company’s stock.
If you carefully look at the formula for standard deviation, you will understand that it is just the square root of variance.
$$s = \sqrt{ \sum_{i=1}^N (x_i – \bar{x})^2 / N-1}$$
But volatility for the annual standard deviation. What we get from square root of variance is the daily standard deviation. To convert it to annual standard deviation we multiply the variance by 250.
250 is used because there are 250 trading days in a year.
# Volatility
tesla_vol = np.sqrt(var_tesla * 250)
fb_vol = np.sqrt(var_fb * 250)
tesla_vol, fb_vol
#> .5358109337568289 .33799873674698305
We can plot the volatility of both Tesla and Facebook for better visualization.
# Volatility of both stocks
test.pct_change().apply(lambda x: np.log(1+x)).std().apply(lambda x: x*np.sqrt(250)).plot(kind='bar')
## Covariance
Covariance measures the directional relationship between the returns on two assets.
A positive covariance means that returns of the two assets move together while a negative covariance means they move inversely. Risk and volatility can be reduced in a portfolio by pairing assets that have a negative covariance.
We can calculate the covariance of Tesla and Facebook by using the .cov() function.
# Log of Percentage change
test1 = test.pct_change().apply(lambda x: np.log(1+x))
test1.head()
Symbols TSLA FB
Date
2018-01-02 NaN NaN
2018-01-03 -0.010286 0.017756
2018-01-04 -0.008325 -0.001843
2018-01-05 0.006210 0.013579
2018-01-08 0.060755 0.007624
# Covariance
test1['TSLA'].cov(test1['FB'])
#> .00018261623156030972
You can notice that there is small positive covariance between Tesla and Facebook.
## Correlation
Correlation, in the finance and investment industries, is a statistic that measures the degree to which two securities move in relation to each other. Correlations are used in advanced portfolio management, computed as the correlation coefficient, which has a value that must fall between -1.0 and +1.0.
You can think of correlation as a scaled version of covariance, where the values are restricted to lie between -1 and +1.
A correlation of -1 means negative relation, i.e, if correlation between Asset A and Asset B is -1, if Asset A increases, Asset B decreases.
A correlation of +1 means positive relation, i.e, if correlation between Asset A and Asset B is 1, if Asset A increases, Asset B increases.
A correlation of 0 means no relation, i.e, if correlation between Asset A and Asset B is 0, they dont have any effect on each other.
This is calculated using the .corr() function.
test1['TSLA'].corr(test1['FB'])
#> .2520883272466132
In line with the covariance, the correlation between Tesla and Facebook is also positive.
## Expected Returns
Expected returns of an asset are simply the mean of percentage change in its stock prices. So, the value of expected return we obtain here are daily expected returns.
For an yearly expected return value, you will need to resample the data year-wise, as you will see further.
For expected returns, you need to define weights for the assets choosen.
In simpler terms, this means you need to decide what percentage of your total money to you want to hold in each company’s stock.
Usually this decision is done by using the optimization techniques we will discuss later but for now we will consider random weights for Tesla and Facebook.
First, let’s compute the log of percentage change.
test2 = test.pct_change().apply(lambda x: np.log(1+x))
test2.head()
Symbols TSLA FB
Date
2018-01-02 NaN NaN
2018-01-03 -0.010286 0.017756
2018-01-04 -0.008325 -0.001843
2018-01-05 0.006210 0.013579
2018-01-08 0.060755 0.007624
### Weights
Let’s define an array of random weights for the purpose of calculation. These weights will represent the percentage allocation of investments between these two stocks. They must add up to 1.
So, the problem of portfolio optimization is nothing but to find the optimal values of weights that maximizes expected returns while minimizing the risk (standard deviation).
# Define weights for allocation
w = [0.2, 0.8]
e_r_ind = test2.mean()
e_r_ind
Symbols
TSLA 0.000530
FB 0.000246
dtype: float64
The total expected return for a portfolio is given by:
$$E(R_p) = w_1E(R_1) + w_2E(R_2) + ….. w_nE(R_n)$$
Thus, e_r, or total expected return can be calculated as:
# Total expected return
e_r = (e_r_ind*w).sum()
e_r
#> .0003027691524101118
## 7. Building an optimal risky portfolio
Now that you have gone through the building blocks of portfolio optimization, it is time to create an optimal portfolio using the same concepts.
We will be using stocks from 4 companies, namely, Apple, Nike, Google and Amazon for a period of 5 years.
You will learn to calculate the weights of assets for each one. Then, we will calculate the expected returns, minimum variance portfolio, optimal risky portfolio and efficient frontier. You will also learn a new term called Sharpe Ratio.
Let’s get started by pulling the required asset data from Yahoo.
# Import data
df = data.DataReader(['AAPL', 'NKE', 'GOOGL', 'AMZN'], 'yahoo', start='2015/01/01', end='2019/12/31')
df.head()
Just like earlier, we will only keep the ‘Adj Close’ column to perform our calculations.
# Closing price
df.head()
Symbols AAPL NKE GOOGL AMZN
Date
2014-12-31 25.181044 44.454605 530.659973 310.350006
2015-01-02 24.941502 43.936787 529.549988 308.519989
2015-01-05 24.238857 43.229393 519.460022 302.190002
2015-01-06 24.241146 42.975098 506.640015 295.290009
2015-01-07 24.581060 43.862804 505.149994 298.420013
## 8. Covariance and Correlation matrix
The first step is to obtain a covariance and correlation matrix to understand how different assets behave with respect to each other. When we had a 2 asset portfolio, we directly plugged in the names of the assets into .cov() and .corr() functions.
In this case, we will need a matrix for better visualisation. This is also achieved by using the same 2 functions on our dataframe df.
Note that we perform necessary operations to display log change in prices of stocks each day.
# Log of percentage change
cov_matrix = df.pct_change().apply(lambda x: np.log(1+x)).cov()
cov_matrix
Symbols AAPL NKE GOOGL AMZN
Symbols
AAPL 0.000245 0.000084 0.000122 0.000142
NKE 0.000084 0.000219 0.000085 0.000092
GOOGL 0.000122 0.000085 0.000221 0.000176
AMZN 0.000142 0.000092 0.000176 0.000333
The covariance between Apple and Apple, or Nike and Nike is the variance of that asset.
The next step is to create the correlation matrix. Correlation ranges from -1 to 1.
• A correlation of -1 means negative relation, i.e, if correlation between Asset A and Asset B is -1, if Asset A increases, Asset B decreases.
• A correlation of +1 means positive relation, i.e, if correlation between Asset A and Asset B is 1, if Asset A increases, Asset B increases.
• A correlation of 0 means no relation, i.e, if correlation between Asset A and Asset B is 0, they dont have any effect on each other.
corr_matrix = df.pct_change().apply(lambda x: np.log(1+x)).corr()
corr_matrix
Symbols AAPL NKE GOOGL AMZN
Symbols
AAPL 1.000000 0.361145 0.524818 0.496704
NKE 0.361145 1.000000 0.387532 0.341431
GOOGL 0.524818 0.387532 1.000000 0.647952
AMZN 0.496704 0.341431 0.647952 1.000000
As you can see, an asset always has a perfectly positive correlation of 1 with itself.
### 9. Portfolio Variance
The formula for calculating portfolio variance differs from the usual formula of variance. It looks like this:
$$\sigma^2(Rp) = \sum{i=1}^{n} \sum_{j=1}^{n} w_i w_j COV(R_i, R_j)$$
Here, wi and wj denote weights of all assets from 1 to n (in our case from 1 to 4) and COV(Ri, Rj) is the covariance of the two assets denoted by i and j.
The simplest way to do this complex calculation is defining a list of weights and multiplying this list horizontally and vertically with our covariance matrix.
For this purpose, let’s define a random list of weights for all 4 assets. Remember that sum of weights should always be 1.
# Randomly weighted portfolio's variance
w = {'AAPL': 0.1, 'NKE': 0.2, 'GOOGL': 0.5, 'AMZN': 0.2}
port_var = cov_matrix.mul(w, axis=0).mul(w, axis=1).sum().sum()
port_var
0.00016069523003596587
Thus we have found the portfolio variance. But for truly optimizing the portfolio, we cant plug in random weights. We will need to calculate it according to what gives us maximum expected returns.
How will you find the portfolio expected return?
## 9. Portfolio expected returns
The mean of returns (given by change in prices of asset stock prices) give us the expected returns of that asset.
The sum of all individual expected returns further multiplied by the weight of assets give us expected return for the portfolio.
Note that we use the resample() function to get yearly returns. The argument to function, ‘Y’, denotes yearly.
If we dont perform resampling, we will get daily returns, like you saw earlier in the ‘Fundamental Terms’ section.
# Yearly returns for individual companies
ind_er = df.resample('Y').last().pct_change().mean()
ind_er
Output:
Symbols
AAPL 0.282997
NKE 0.195950
GOOGL 0.217545
AMZN 0.472289
dtype: float64
Portfolio returns
# Portfolio returns
w = [0.1, 0.2, 0.5, 0.2]
port_er = (w*ind_er).sum()
port_er
0.27071990038443955
### Plotting the efficient frontier
This is the aim of going through all the topics above, to plot the efficient frontier. Efficient frontier is a graph with ‘returns’ on the Y-axis and ‘volatility’ on the X-axis. It shows us the maximum return we can get for a set level of volatility, or conversely, the volatility that we need to accept for certain level of returns.
The plot of efficient frontier looks something like this:
Below, you can see the calculations and code for finding the optimal weights of assets and plotting the efficient frontier for given portfolio.
But first, lets take a look at the volatiltilty and returns of individual assets for a better understanding.
# Volatility is given by the annual standard deviation. We multiply by 250 because there are 250 trading days/year.
ann_sd = df.pct_change().apply(lambda x: np.log(1+x)).std().apply(lambda x: x*np.sqrt(250))
ann_sd
Symbols
AAPL 0.247734
NKE 0.233798
GOOGL 0.235191
AMZN 0.288559
dtype: float64
assets = pd.concat([ind_er, ann_sd], axis=1) # Creating a table for visualising returns and volatility of assets
assets.columns = ['Returns', 'Volatility']
assets
Returns Volatility
Symbols
AAPL 0.282997 0.247734
NKE 0.195950 0.233798
GOOGL 0.217545 0.235191
AMZN 0.472289 0.288559
Amazon has the maximum risk attached but it also offers the maximum returns. Apple lies somewhere in the middle, with average risk and return rates.
Next, to plot the graph of efficient frontier, we need run a loop. In each iteration, the loop considers different weights for assets and calculates the return and volatility of that particular portfolio combination.
We run this loop a 1000 times.
To get random numbers for weights, we use the np.random.random() function. But remember that the sum of weights must be 1, so we divide those weights by their cumulative sum.
Keep reading further to see how it’s done.
p_ret = [] # Define an empty array for portfolio returns
p_vol = [] # Define an empty array for portfolio volatility
p_weights = [] # Define an empty array for asset weights
num_assets = len(df.columns)
num_portfolios = 10000
for portfolio in range(num_portfolios):
weights = np.random.random(num_assets)
weights = weights/np.sum(weights)
p_weights.append(weights)
returns = np.dot(weights, ind_er) # Returns are the product of individual expected returns of asset and its
# weights
p_ret.append(returns)
var = cov_matrix.mul(weights, axis=0).mul(weights, axis=1).sum().sum()# Portfolio Variance
sd = np.sqrt(var) # Daily standard deviation
ann_sd = sd*np.sqrt(250) # Annual standard deviation = volatility
p_vol.append(ann_sd)
data = {'Returns':p_ret, 'Volatility':p_vol}
for counter, symbol in enumerate(df.columns.tolist()):
#print(counter, symbol)
data[symbol+' weight'] = [w[counter] for w in p_weights]
portfolios = pd.DataFrame(data)
portfolios.head() # Dataframe of the 10000 portfolios created
Returns Volatility AAPL weight NKE weight GOOGL weight AMZN weight
0 0.288656 0.195191 0.130962 0.309140 0.288193 0.271705
1 0.259440 0.191103 0.199891 0.269729 0.394412 0.135968
2 0.342442 0.209105 0.204257 0.231146 0.107200 0.457397
3 0.290496 0.194798 0.264460 0.229882 0.267749 0.237909
4 0.294159 0.196093 0.126596 0.453689 0.113033 0.306682
You can see that there are a number of portfolios with different weights, returns and volatility. Plotting the returns and volatility from this dataframe will give us the efficient frontier for our portfolio.
# Plot efficient frontier
portfolios.plot.scatter(x='Volatility', y='Returns', marker='o', s=10, alpha=0.3, grid=True, figsize=[10,10])
## How to read the Efficient Frontier?
Each point on the line (left edge) represents an optimal portfolio of stocks that maximises the returns for any given level of risk.
The point (portfolios) in the interior are sub-optimal for a given risk level. For every interior point, there is another that offers higher returns for the same risk.
On this graph, you can also see the combination of weights that will give you all possible combinations:
1. Minimum volatility (left most point)
2. Maximum returns (top most point)
And everything in between.
min_vol_port = portfolios.iloc[portfolios['Volatility'].idxmin()]
# idxmin() gives us the minimum value in the column specified.
min_vol_port
Returns 0.236901
Volatility 0.186503
AAPL weight 0.252051
NKE weight 0.393245
GOOGL weight 0.310145
AMZN weight 0.044559
Name: 7553, dtype: float64
The minimum volatility is in a portfolio where the weights of Apple, Nike, Google and Amazon are 26%, 39%, 30% and 4% respectively. This point can be plotted on the efficient frontier graph as shown:
# plotting the minimum volatility portfolio
plt.subplots(figsize=[10,10])
plt.scatter(portfolios['Volatility'], portfolios['Returns'],marker='o', s=10, alpha=0.3)
plt.scatter(min_vol_port[1], min_vol_port[0], color='r', marker='*', s=500)
The red star denotes the most efficient portfolio with minimum volatility.
It is worthwhile to note that any point to the right of efficient frontier boundary is a sup-optimal portfolio.
We found the portfolio with minimum volatility, but you will notice that the return on this portfolio is pretty low. Any sensible investor wants to maximize his return, even if it is a tradeoff with some level of risk.
The question arises that how do we find this optimal risky portfolio and finally optimize our portfolio to the maximum?
This is done by using a parameter called the Sharpe Ratio.
### Sharpe Ratio
The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Volatility is a measure of the price fluctuations of an asset or portfolio.
The risk-free rate of return is the return on an investment with zero risk, meaning it’s the return investors could expect for taking no risk.
The optimal risky portfolio is the one with the highest Sharpe ratio. The formula for this ratio is:
Below is the code for finding out portfolio with maximum Sharpe Ratio. This portfolio is the optimized portfolio that we wanted to find. We define the risk-free rate to be 1% or 0.01.
## Optimal Risky Portfolio
An optimal risky portfolio can be considered as one that has highest Sharpe ratio.
Let’s find out.
# Finding the optimal portfolio
rf = 0.01 # risk factor
optimal_risky_port = portfolios.iloc[((portfolios['Returns']-rf)/portfolios['Volatility']).idxmax()]
optimal_risky_port
Returns 0.393435
Volatility 0.232716
AAPL weight 0.244612
NKE weight 0.110882
GOOGL weight 0.007497
AMZN weight 0.637009
Name: 4775, dtype: float64
You can notice that while the difference in risk between minimum volatility portfolio and optimal risky portfolio is just 6%, the difference in returns is a whopping 17%.
We can plot this point too on the graph of efficient frontier.
# Plotting optimal portfolio
plt.subplots(figsize=(10, 10))
plt.scatter(portfolios['Volatility'], portfolios['Returns'],marker='o', s=10, alpha=0.3)
plt.scatter(min_vol_port[1], min_vol_port[0], color='r', marker='*', s=500)
plt.scatter(optimal_risky_port[1], optimal_risky_port[0], color='g', marker='*', s=500)
The green star represents the optimal risky portfolio.
## References
1. Video series by Finquest
2. Investopedia
Course Preview
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#### Chemical Equations Balanced on 02/10/19
Molecular weights calculated on 02/09/19 Molecular weights calculated on 02/11/19
Calculate molecular weight
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206
Molar mass of C2H5OH is 46,06844
Molar mass of H2CO3 is 62,02478
Molar mass of Sr(OH) is 104,62734
Molar mass of Sn (ClO3)2 is 285,6124
Molar mass of Pt (ClO3)2 is 361,9864
Molar mass of C6H6 is 78,11184
Molar mass of Cr(BO3)3 is 228,4237
Molar mass of H2TeO4 is 193,61348
Molar mass of Pb (ClO3)2 is 374,1024
Molar mass of Ca(OH)2 is 74.09268
Molar mass of Pb (ClO3)4 is 541,0048
Molar mass of H2Co3 is 178,815465
Molar mass of H2TeO4 is 193,61348
Molar mass of Pt (ClO3)4 is 528,8888
Molar mass of NaHPO4 is 118,96907128
Molar mass of NaC7H5O2 is 144.10316928
Molar mass of magnesium chloride is 95.211
Molar mass of Cu (ClO3)2 is 230,4484
Molar mass of CaCO3 is 100,0869
Molar mass of Cl2 is 70.906
Molar mass of calcium hydroxide is 74.09268
Molar mass of Cu (ClO3) is 146,9972
Molar mass of chlorine is 70.906
Molar mass of sulfuric acid is 98.07848
Molar mass of Ni (ClO3)3 is 309,047
Molar mass of Co (ClO3)3 is 309,286795
Molar mass of kMnO is 110,035745
Molar mass of kMnO4 is 158,033945
Molar mass of C2H3 is 27,04522
Molar mass of NaHPO4 nome is 393,10462128
Molar mass of Co (ClO3)2 is 225,835595
Molar mass of Ni (ClO3)2 is 225,5958
Molar mass of NaHPO4 nome is 393,10462128
Molar mass of P2O5 is 141,944524
Molar mass of sodium sulfate is 142.04213856
Molar mass of Au (ClO2)3 is 399,321969
Molar mass of Au (ClO2) is 264,418369
Molar mass of NH3 is 17.03052
Molar mass of Hg (ClO2)2 is 335,4936
Molar mass of Hg (ClO2) is 268,0418
Molar mass of Ca(OH)2 is 74.09268
Molar mass of Sn (ClO2)4 is 388,5172
Molar mass of K2Cu(C2O4)2*2H2O is 353.81116
Molar mass of N2O3 is 76.0116
Molar mass of Al(OH)3 is 78.0035586
Molar mass of Sn (ClO2)2 is 253,6136
Molar mass of H2 is 2.01588
Molar mass of N2(l) is 28.0134
Molar mass of H2O is 18,01528
Molar mass of HBr is 80.91194
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206
Calculate molecular weight
Molecular weights calculated on 02/09/19 Molecular weights calculated on 02/11/19
Molecular masses on 02/03/19
Molecular masses on 01/11/19
Molecular masses on 02/10/18
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0
# What is thirteen over one thousand as a decimal?
Updated: 8/21/2019
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0.013
### How do you write 13.651 in word form?
thirteen thousand six hundred fifty one if { a number not a decimal} {if a decimal} thirteen,six hundred fifty one over one thousand if wrong please correct me in a subscribe
### How do you write thirteen million forty-one thousand?
Ways to write thirteen million forty-one thousand: * thirteen million forty-one thousand (American English text) * thirteen million and forty-one thousand (English text) * 13 041 000 (decimal with comma separators) * 13,041,000 (decimal with space separators) * 110001101111110101101000 (binary) * 220112112220000 (ternary) * 11314303000 (quintal) * 61576550 (octal) * c6fd68 (hexadecimal)
0.001
0.002
0.019
### How do you write in standered form one thousand thirteen decimal eight hundred forty nine thousandths?
It is 1.013849*103.
### What is the decimal for ninetythree over one thousand?
I think it is .093
.081
0.28
.068
### What is one thousand as a decimal?
one thousand as a decimal is 1000.0 one thousandth as a decimal is 0.001
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# NCERT Class 8 Mathematics Solutions: Chapter 10 – Visualising Solid Shapes Exercise 10.3 Part 2
Get top class preparation for IEO right from your home: Get full length tests using official NTA interface: all topics with exact weightage, real exam experience, detailed analytics, comparison and rankings, & questions with full solutions.
Question 4:
(i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?
(i) A cylinder can be thought of as a circular prism, i.e. a prism that has a circle as its base.
(ii) A cone can be thought of as a circular pyramid i.e. a pyramid that has a circle as its base.
Question 5:
Is a square prism same as a cube? Explain.
A square prism has a square as its base. However, its height is not necessarily same as the side of square. Thus, a square prism can also be cuboid.
Question 6:
Verity Euler’s formula for these solids.
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# How to Adjust the Position of Axis Labels in Matplotlib?
When we perform data visualization in Matplotlib using subplots or plots, it is important to label the axis correctly and adjust the position of the labels of the axis if required so that they do not overlap with other elements that are there in the plot. This can help users to easily understand the data that is being presented.
For creating labels and adjusting the labels we will use the Matplotlib library which is used for creating high-quality data visualizations. This article will discuss various methods for adjusting the position of the axis labels in Matplotlib. We will be using subplots for the same.
## Matplotlib
Matplotlib is a library that is mainly used for plotting graphs and plots for the Python programming language and NumPy, its extension for numerical mathematics. Tkinter, wxPython, Qt, and GTK GUI toolkits may include diagrams utilizing its object-oriented API.
The matplotlib.pyplot is a collection of command-style methods that allow matplotlib to function similarly to MATLAB. Each pyplot function alters a figure in some manner, whether it is by adding a plotting area, plotting lines, adding labels, etc. The current graph and plotting area are saved between function calls in matplotlib.pyplot, and the plotting functions are always applied to the active set of axes.
## Subplots
Subplots in Matplotlib allow multiple plots or charts to be displayed within a single figure. We can compare and analyze multiple sets of data at the same time with the help of subplots. This makes spotting or identifying trends, patterns, and relationships easier.
A subplot is a grid of smaller plots that are part of a larger plot. Each subplot has its own place in the grid, which is based on the number of rows and columns in the grid and where the subplot is in that grid.
Matplotlib’s “subplots” method lets us create subplots. This function returns a graph object and an array of subplot objects. We can plot our data in each subplot by using these subplot objects.
### Syntax
fig,ax=plt.subplots(nrows,ncolumns,index)
### Explanation
• nrows − This parameter specifies the number of rows of subplots in the grid.
• ncolumns − This parameter specifies the number of columns of subplots in the grid.
• index − This parameter specifies the index of the current subplot. The index starts at 1 and increases row-wise.
## Adjust the position of axis labels
There are various methods or functions in Matplotlib using which we can adjust the position of Axis labels in Matplotlib graphs, they are −
• .set_label_coords() function
• set_label_position() function
### .set_label_coords()
This method is used to set the coordinates of the label of the subplot.
Tick label boundary boxes determine the default values for the x coordinate of the y label and the y coordinate of the x label. The problem arises, however, when there are many axes and the labels must be aligned across them.
The coordinates of the label can be specified to the transform as well. The axes coordinate system, where (0, 0) is the bottom left corner, (0.5, 0.5) is the middle, etc., is used if None is specified.
### Example 1
import matplotlib.pyplot as p
import numpy as n
# generate some data
x=n.array([11, 22,33, 44, 55,66,77,88,99,100])
# create a subplot and plot the data
f, a = p.subplots(2,2)
a[0,0].plot(x, n.sin(x))
a[0,1].plot(x,n.cos(x))
a[1, 0].plot(x, x)
a[1, 1].plot(x, n.exp(x))
# set the x-axis label and adjust the position
a[0,0].set_xlabel('Sin graph')
a[0,0].xaxis.set_label_coords(0.35, 0)
a[0,1].set_xlabel('Cos graph')
a[0,1].xaxis.set_label_coords(0.65,0)
a[1, 0].set_xlabel('Linear graph')
a[1,0].xaxis.set_label_coords(0.35,-0.24)
a[1, 1].set_xlabel('exponential graph')
a[1,1].xaxis.set_label_coords(0.65,-0.25)
# display the plot
p.show()
### set_label_position() Function
set_position() function is used to set the label position of the axis in the subplots. This method accepts the following parameters −
Position − ‘left’,’ right’,’ top’,’ bottom’.
### Example 2
import matplotlib.pyplot as p
import numpy as n
# generate some data
x=n.array([11, 22,33, 44, 55,66,77,88,99,100])
# create a subplot and plot the data
f, a = p.subplots(2,2)
a[0,0].plot(x, n.sin(x))
a[0,1].plot(x,n.cos(x))
a[1, 0].plot(x, x)
a[1, 1].plot(x, n.exp(x))
# set the x-axis label and y label and adjust the position
a[0,0].set_xlabel('Sin graph')
a[0,0].xaxis.set_label_position('bottom')
a[0,0].yaxis.set_label_position('left')
a[0,0].xaxis.set_label_coords(0.35, 0)
a[0,0].yaxis.set_label_coords(0.35, 0)
a[0,1].set_xlabel('Cos graph')
a[0,1].xaxis.set_label_position('bottom')
a[0,0].yaxis.set_label_position('left')
a[0,1].xaxis.set_label_coords(0.65,0)
a[0,1].yaxis.set_label_coords(0.65,0)
a[1, 0].set_xlabel('Linear graph')
a[1,0].xaxis.set_label_position('bottom')
a[0,0].yaxis.set_label_position('left')
a[1,0].xaxis.set_label_coords(0.35,-0.24)
a[1,0].yaxis.set_label_coords(0.35,-0.24)
a[1, 1].set_xlabel('exponential graph')
a[1,1].xaxis.set_label_position('bottom')
a[0,0].yaxis.set_label_position('left')
a[1,1].xaxis.set_label_coords(0.65,-0.25)
a[1,1].yaxis.set_label_coords(0.65,-0.25)
# display the plot
p.show()
### Output
With the set pad() function, we can change how far apart the axis label and the axis tick labels are.
For example, we can use the following code to change how much space is around the x-axis label in a subplot −
### Example 3
import matplotlib.pyplot as plt
import numpy as np
# generate some data
x=np.array([11, 22,33, 44, 55,66,77,88,99,100])
# create a subplot and plot the data
fig, ax = plt.subplots(2,2)
ax[0,0].plot(x, np.sin(x))
ax[0,1].plot(x,np.cos(x))
ax[1, 0].plot(x, x)
ax[1, 1].plot(x, np.exp(x))
# set the x-axis label and adjust the position
# display the plot
plt.show()
## Conclusion
In conclusion, adjusting the position of axis labels is an important part of using Matplotlib to make plots that are clear and accurate. Set_label_coords(), set_position(), and set_pad() are some of the methods we can use to change the position of axis labels in a plot or subplot.
Updated on: 31-May-2023
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PDA
View Full Version : my box?
Colossus281
06-20-2012, 05:30 PM
Hey guys I need to find out my cubic feet. And what it is tuned to. Subs displacement is .15 I have two so .30. The box is 32w 14.5h 21.5d with port 2w 13h 18d. Thanks
ryanthie
06-20-2012, 05:49 PM
Box volume after subwoofer displacement is 4.28 cubes.
And with the calculator I used, I figured you're tuned to around 26.5 hz which is a very low tuning. Not sure if it was accurate with the calculators I used...
Box Volume = Subwoofer Enclosure Calculators, Fraction to Decimal, Parallel, Series, Port Length and Volume Calculators (http://www.the12volt.com/caraudio/boxcalcs.asp)
Port Tuning = Port Length Calculator (http://www.mobileinformationlabs.com/HowTo-1Woofer-Box-CAL%20Port%20lenth%201.htm)
And I just kept typing in different frequencies until it said a port length of 18.1 which is right at 26.5hz. This number seems low as hell and I might have just put something in wrong, lol.
dbeez
06-20-2012, 06:24 PM
Your box is 3.89 tuning I haven't messed with yet but probably a little higher tuning than you thought
Colossus281
06-20-2012, 07:45 PM
Your box is 3.89 tuning I haven't messed with yet but probably a little higher tuning than you thought
Ya I got 3.78 after displacement of subs and port. Tuned at 28.88hz.
Its a box that I got with my skar audio subs. Its supposed to be tuned to 32hz. And I would think it should be at 4 cubic feet.
if I cut my port back so its at 32hz would that help with the higher bass?
Colossus281
06-20-2012, 07:51 PM
If I cut it back to 12.25 I should be at 32.82hz. And 3.95ft right?
SMS
06-20-2012, 08:22 PM
make a new box. you only have 26 sq" port area. you should have about 14-16 sq in per cu ft. thereby a a 4 cube box should have around 60 sq inch of port area- so a 15" x 4" slot would work much better, also the port would get longer the more area it is.
dbeez
06-20-2012, 08:44 PM
That box is as said above basically junk trash it and build a new better one or have one of us builders build you an accurate box.
Colossus281
06-20-2012, 09:38 PM
That box is as said above basically junk trash it and build a new better one or have one of us builders build you an accurate box.
I can build one I just need help with the design.
06-20-2012, 09:40 PM
pro-rabbit or any of the other box guys will sell you plans for around 15 bucks.
Nut Hair Trick
06-20-2012, 09:52 PM
I got 3.91 cuft tuned to 27.78 hz. Port area is extremely small at 6.65" / ft
Colossus281
06-21-2012, 12:15 AM
Can someone check this for me? Box for two vvx 12. 37w 17h 21d
port 4w 15.5h 32d. Port in the middle of the subs. 45 in port. I got 32.64hz and after all displacement 4.07cuft. 62.0in port area.
Colossus281
06-21-2012, 08:19 AM
Someone? Is that right?
Colossus281
06-21-2012, 01:36 PM
Bump
Colossus281
06-22-2012, 09:14 AM
make a new box. you only have 26 sq" port area. you should have about 14-16 sq in per cu ft. thereby a a 4 cube box should have around 60 sq inch of port area- so a 15" x 4" slot would work much better, also the port would get longer the more area it is.
What should the port area be for round ports?
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# how to do transistor sizing in cadence spectre
Status
Not open for further replies.
#### bharathr87
##### Member level 1
transistor sizing
how to do transistor sizing in cadence spectre
L= 40nm
W=150nm
no. f fingers=1
multiplier=1
#### DDavid
##### Full Member level 5
Re: transistor sizing
In generally you have:
L - length
W - wight
F - fingers
m - number of multiplers
#### bhargava834
##### Junior Member level 1
Re: transistor sizing
Hello Bharath
First of all can u tell me what is your circuit???
As i know
In cadence u cant go beyond 50um for W or L.
Anyway L is in the range below 50um.
and if u want W to be greater than 50um u can play with Nof fingers and multipliers.
W=No: of fingers * multipliers
No: of fingers is in um s
multipliers is a constant number
It is nothing but u are going to arrange similar transistors in parallel..
Regards
Bhargav
#### bharathr87
##### Member level 1
Re: transistor sizing
jus choose the optimum value for w/l...increasin w increases the current n hence the gain n transconductance....increasin l decreases channel length mod. n hence increases rout....
#### Areky_qin
transistor sizing
you could use any value of W, L and m factor,
and in fact you could use .scale option in hspice to shink you transitor size, for example, you use a PMOS as W=1000u, L=500u, m=100, at the same time you define .option scale=0.01, so you final Pmos size is w=10000*0.0001=100u, L=500*0.01=50u, m=100.
sorry for comfuse,
you define w=10000u, l=500u, m=100
and use .option scale=0.01, then
the fize device size is w=10000*0.01=100u,
L=500*0.01=5u,m=100. good luck.
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Numerous studies of chemotherapy patients over the last ten : GMAT Critical Reasoning (CR)
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# Numerous studies of chemotherapy patients over the last ten
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Numerous studies of chemotherapy patients over the last ten [#permalink]
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31 Jul 2011, 13:47
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Numerous studies of chemotherapy patients over the last ten years have shown that patients who had regularly attended support groups or received counseling experienced significantly fewer side effects and shorter recovery times from chemotherapy than did patients who had not. Clearly, although the mainstream scientific community has been slow to acknowledge it, psychological support has an effect on the body's ability to heal.
Which of the following, if true, would most strengthen the argument above?
The survival rates for chemotherapy patients in the study were virtually identical regardless of whether or not they received support.
The patients who did not attend support groups chose not to do so, even though they were healthy enough to attend.
Many medical doctors believe that the mind plays a role in the causation and prevention of illness.
The majority of chemotherapy patients must undergo more than one round of treatment.
Some hospitals do not conduct support groups on their premises for chemotherapy patients and their families.
If you have any questions
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Re: CR - 700 level - cancer [#permalink]
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31 Jul 2011, 15:11
I'd go with B
The conclusion of the argument is - 'psychological support has an effect on the body's ability to heal.'
The survival rates for chemotherapy patients in the study were virtually identical regardless of whether or not they received support. -- does not help the conclusion at all. At best it hurts the argument
The patients who did not attend support groups chose not to do so, even though they were healthy enough to attend.
This says that there patients who did not attend support groups did so by choice only. SO there is no other factor behind their slower recovery after chemotherapy(such as support grps not being available) etc. So this supports the conclusion
Many medical doctors believe that the mind plays a role in the causation and prevention of illness.
We are talking about healing after something has already happened here. causation and prevention of illnesses are irrelevant
The majority of chemotherapy patients must undergo more than one round of treatment. --irrelevant for the argument
Some hospitals do not conduct support groups on their premises for chemotherapy patients and their families. - this actually weaken the argument because if this was a factor then the study and its conclusion will not hold good
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Re: CR - 700 level - cancer [#permalink]
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01 Aug 2011, 09:18
i tend to choose C
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Re: CR - 700 level - cancer [#permalink]
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01 Aug 2011, 09:33
IMO C. Whats the OA?
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Re: CR - 700 level - cancer [#permalink]
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01 Aug 2011, 23:08
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+1 B,
agree with dreambeliever's explanations.
Option C is wrong because it primarily uses the word many in "Many Doctors". many is just a number and proves nothing of a consented opinion. For eg., there are 1 million doctors. Out of those, 1,000 doctors believe in the positive effect of mind on preventing illness, but rest do not. Even 1,000 doctors = "many doctors", but their viewpoint is not representative of the entire community as a whole.
If you search for further reasons to rule out option C, then the option mentions about cause and prevention of illness, whereas the question talks about effect of mind on body's healing capability, which is not mentioned in C.
Though for me the first word "many" was enough to rule out the option as irrelevant.
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Re: CR - 700 level - cancer [#permalink]
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01 Aug 2011, 23:19
Let us look at it like this.
Premise:numerous studies of chemotherapy patients over the last ten years have shown that patients who had regularly attended support groups or received counseling experienced significantly fewer side effects and shorter recovery times from chemotherapy than did patients who had not.
Conclusion:Clearly, although the mainstream scientific community has been slow to acknowledge it, psychological support has an effect on the body's ability to heal.
The answer to this question should strengthen the conclusion.
If you carefully look at B- does that Strengthen the conclusion. It reads: The patients who did not attend support groups chose not to do so, even though they were healthy enough to attend.
The conclusion is talking about the psychological support and if reviewing the answer choices this is something which must be taken note of .
In that sense I chose C. Further, If many doctors believe...... it would strengthen the conclusion that psychological support does play an important role.
Alternate explanations welcome.
Can we have the OA please?
Last edited by chandu4gmat on 01 Aug 2011, 23:50, edited 2 times in total.
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Re: CR - 700 level - cancer [#permalink]
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01 Aug 2011, 23:26
The survival rates for chemotherapy patients in the study were virtually identical regardless of whether or not they received support.: This is at best out of scope and at worst weakening to the argument. argument talks of speed of healing and side effects, not of the survival chances
The patients who did not attend support groups chose not to do so, even though they were healthy enough to attend.: Argument says those who attended support groups healed faster. And those who didnt attend healed slower- and attributes it to the fact that they didnt attend support group.Any option that eliminates other possible reasons for not attending will support/ strengthen. Here the option says that the patients did not NOT attend because they were too ill. If that was the case, then their slow recovery could be attributed to the extent of their illness and not the support group's influence. by eliminating this possible cause, the option strengthens.
Many medical doctors believe that the mind plays a role in the causation and prevention of illness.: Many doesnt mean most, and any way, this sortof conflicts with argument which says mainstream doctors have been slow to acknowledge. again causation, and prevention is not same as healing.
The majority of chemotherapy patients must undergo more than one round of treatment.: Irrelevant, out of scope
Some hospitals do not conduct support groups on their premises for chemotherapy patients and their families.That cannot help us judge whether the support groups are beneficial or not.
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Re: CR - 700 level - cancer [#permalink]
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01 Aug 2011, 23:32
Option B does not say that they were ill rather they were healthy,yet they did not attend.
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Re: CR - 700 level - cancer [#permalink]
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01 Aug 2011, 23:36
Would go with C. OA and OE Pls
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Re: CR - 700 level - cancer [#permalink]
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02 Aug 2011, 01:45
IMO B,
C talks about the prevention and causation of the disease but the prompt talks about the healing process.. these are completely different things.. out of the remaining four choices found B to be most suitable..
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Re: CR - 700 level - cancer [#permalink]
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02 Aug 2011, 03:28
That's an awesome question.
I also got lured for C first but then realized that it should be B.
It is a very good question and that is how they trick you on the real GMAT also
Need to be extra careful
BR
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Re: CR - 700 level - cancer [#permalink]
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02 Aug 2011, 04:17
Although i agree that option C should not be OA but still i am not very sure that option B is an Ans.
Option B never said that, ppl who did not attend grps has slower recovery.
Pls explain
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Re: CR - 700 level - cancer [#permalink]
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02 Aug 2011, 07:47
I will gowith B. OA please
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Re: CR - 700 level - cancer [#permalink]
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02 Aug 2011, 12:00
1 more tricky question from bschool83...
what's the OA buddy?
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Re: CR - 700 level - cancer [#permalink]
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04 Aug 2011, 00:28
Sure this one was tricky one. I also had gone for C but realized it is B
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Re: CR - 700 level - cancer [#permalink]
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04 Aug 2011, 09:38
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I agree this question is tricky but sticking to fundamental of reasoning works here.
Conclusion is 'psychological support helps heal faster'
Evidence: people who attended these events healed faster than those who didn't attend
This is a causal argument. Something that suggests that no other factor caused the attendees to heal faster, should be the answer. B portrays this but saying the healthier people didn't attend, i.e., all attendees were equally ill.
C is 50/50 right. "mind plays a role in the causation of illness" is not mentioned anywhere.
B is the OA.
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Re: CR - 700 level - cancer [#permalink]
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04 Aug 2011, 15:22
+1 B
C is out of scope.
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Re: CR - 700 level - cancer [#permalink]
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04 Aug 2011, 17:25
OA - B
Approach-1
-------------------
B strengthens by creating a representative sample of the 2 groups and eliminating all the possible choices.
People - who attend
People - who did NOT attend
Conclusion - 'psychological support helps heal faster'
Both group should be represented equally that is - People who DID NOT attend should have more SEs and higher RTs than the People who DID ATTEND, ONLY because of SGs/Couns., NOT because they were healthy.
B - tells People who DID NOT attend chose that option because they were HEALTHY. In effect eliminating HEALTH as a factor among the reasons
Approach-2
-------------------
You can use POE....I confirmed by eliminating all the other ones....It was very easy.
Note - The question has already been discussed
cr-chemotherapy-42686.html
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Re: CR - 700 level - cancer [#permalink]
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04 Aug 2011, 17:41
Second thought
I am not sure, but did anyone read the choice-B as a SC question !!!
DO SO - refers to an entire action - So in this case choice-B will mean one of the below choices....
1) The patients who did not attend...chose not to attend, even though they were healthy enough to attend.
OR
2) The patients who did not attend SGs chose not to (not to attend)...
==>The patients who did not attend SGs chose to attend, even though they were healthy enough to attend.
Option (2) is nonsense in meaning...So obviously I will rule that out.
But my question is does DO SO grammatically lead to option (1) ?
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Re: CR - 700 level - cancer [#permalink]
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05 Aug 2011, 12:32
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Re: CR - 700 level - cancer [#permalink] 05 Aug 2011, 12:32
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# How do you calculate RAM and RMM?
## What is RAM and RMM?
RAM is a mass of an atom, relative to the mass of C-12. … RMM is a mass of a molecule, relative to the mass of C-12. Since it is a ratio, it is unitless.
## How do you calculate RAM?
You can always find the relative mass of an element by adding the number of protons to the number of neutrons for the specific isotope of the element you’re considering. For example, a carbon-12 atom has 6 protons and 6 neutrons, and so has a relative atomic mass of 12.
## Is RFM and RMM the same?
It’s basically the same. Relative atomic mass is the summation of the individual masses of the atoms. This mostly applied to molecular compounds like water, ammonia, etc. … Formular mass applies to ionic compounds.
## How do you calculate RMM?
The relative molecular mass/relative formula mass is defined as the sum of all the individual atomic masses of ALL the atoms in the formula (Mr). e.g. for ionic compounds e.g. NaCl = 23 + 35.5 58.5) or molecular mass for covalent elements or compounds …
## What is the unit of RMM?
kg/mol. Other units. g/mol. In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample, measured in moles. The molar mass is a bulk, not molecular, property of a substance.
## What is relative formula?
The relative formula mass of a compound is calculated by adding together the relative atomic mass values for all the atoms in its formula. Moles are units used to measure substance amount. Chemistry (Single Science)
## What do you know about RAM?
RAM, or Random Access Memory, is essentially a piece of hardware that stores your computer’s short-term memory while the computer is running. The difference between a RAM module and a data drive (whether HDD or SSD) is that RAM is volatile memory, meaning that data is completely erased when the power source is cut.
## What is the RAM of oxygen?
A r values of elements
Element Relative atomic mass
Carbon (C) 12
Oxygen (O) 16
Magnesium (Mg) 24
Chlorine (Cl) 35.5
## What is RFM model?
Recency, frequency, monetary value is a marketing analysis tool used to identify a company’s or an organization’s best customers by using certain measures. The RFM model is based on three quantitative factors: Recency: How recently a customer has made a purchase. Frequency: How often a customer makes a purchase.
## What is the total MR of H2O?
Average atomic mass of O: 16.00 g/mol. The number of atoms is an exact number, the number of mole is an exact number; they do not affect the number of significant figures. The average mass of one mole of H2O is 18.02 grams. This is stated: the molar mass of water is 18.02 g/mol.
Read more How can I watch the Packers vs the Rams?
## What is the RFM of methane?
the A r of H = 1. so the relative formula mass (M r) of CH 4 = 12 + (4 × 1) = 16. so 1 mole of methane = 16 g of methane and contains 6.02 × 10 23 molecules.
## What is carbon12 scale?
Carbon-12 is of particular importance in its use as the standard from which atomic masses of all nuclides are measured, thus, its atomic mass is exactly 12 daltons by definition. Carbon-12 is composed of 6 protons, 6 neutrons, and 6 electrons.
## How do you work out the atomic number?
The symbol for an atom can be written to show its mass number at the top, and its atomic number at the bottom. To calculate the numbers of subatomic particles in an atom use its atomic number and mass number: number of protons = atomic number. number of electrons = atomic number.
## What do isotopes mean?
Isotope, one of two or more species of atoms of a chemical element with the same atomic number and position in the periodic table and nearly identical chemical behaviour but with different atomic masses and physical properties. Every chemical element has one or more isotopes.
Рубрики RAM
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# Problems Using Unitary Method
We will learn ‘what unitary method is’ and how to solve problems using unitary method.
The method of finding first the value of one quantity from the value of given quantities and then the value of required quantities is called the unitary method.
While working out the problems using the unitary method, we come across certain variations where the two quantities depend on each other in such a way that changes in one results in the change in other; then the two quantities are said to be in variation.
Types of variation:
The two quantities may be linked in such a way that
● if one increases, other also increases. If one decreases, the other also decreases.
● or if one increases, other decreases. If one decreases, the other increases.
This change results in two variations.
1. Direct variation
2. Inverse variation
Now we will learn what ‘direct variation and inverse variation’ is and their different situations.
Problems Using Unitary Method
Situations of Direct Variation
Direct Variations Using Unitary Method
Direct Variations Using Method of Proportion
Inverse Variation Using Unitary Method
Inverse Variation Using Method of Proportion
Problems on Unitary Method using Direct Variation
Problems on Unitary Method Using Inverse Variation
Mixed Problems Using Unitary Method
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
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# Random vectors with null sum
Asked by Matteo Cacciola on 20 Jun 2012
Latest activity Answered by Matteo Cacciola on 23 Jun 2012
Hello, I have a question for you. I have to initialize a number of 3D vectors, with fixed magnitude (intensity) equal to I, but the sum (in the geometrical sense) of vectors should be null. I prefer to work with angles (azimuth and elevation), but obviously a solution just considering the x-, y- and z-components of the vectors is fine, since thereafter I can make the transformation with cart2sph function.
Thanks a lot to all that could give me a support
Regards Matteo
Walter Roberson on 20 Jun 2012
Is the number of vectors to use known, or should it keep generating until it finds a solution?
Matteo Cacciola on 20 Jun 2012
Yes it is. Let me say that I have to generate N vectors, for instance N=100, each vectors has intensity I, for instance I=2, but the geometrical sum of vectors should be zero. Thanks
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Answer by Matteo Cacciola on 23 Jun 2012
I added a trivial solution. If the number to generate is even, I take couples of vectors. An element of each pair is randomly set, the other in opposite phase. If the number is odd, I do as for even vectors, but excluding three of them, which will be set manually as a null vector according to the rule of parallelogram. Thanks for your help.
Answer by the cyclist on 20 Jun 2012
Even in just one dimension, it's a non-trivial problem to combine random numbers to have a fixed sum. (The question comes up with some frequency here.) The following doesn't do exactly what you want (I don't believe), but you might be able to bend it to your needs.
http://www.mathworks.com/matlabcentral/fileexchange/9700
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P15 - and a force due to air resistence which can be...
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Project 15 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. Examine the functions f ( x ) = x 2 ln | x | and g ( x ) = e x - 1 x . Evaluate the limits lim x 0 f ( x ) and lim x 0 g ( x ) . Which indeterminate forms do these limits represent? Using the limit definition of the derivative, show that each of the functions below are differ- entiable (and hence also continuous) at 0 . h ( x ) = x 2 ln | x | x 6 = 0 0 x = 0 k ( x ) = e x - 1 x x 6 = 0 1 x = 0 What do each of the values h 0 (0) and k 0 (0) turn out to be? 2. For each function below, write the indeterminate form that it represents , then evaluate the limit using the techniques learned in class. The answer to each is given to help you. .. a) lim x 0 ± 1 x - 1 e x - 1 ² = 1 2
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b) lim x 0 ( 1 + x + tan(2 x ) ) 1 x = e 3 c) lim x →∞ 1 + ln( x ) ln(1 + x + x 2 ) = 1 2 3. If an object of mass m falls with air resistence, then it experiences two forces: the force of gravity mg
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Unformatted text preview: and a force due to air resistence, which can be accurately modeled as proportional to the velocity v of the object, say-bv for some constant b > . Here, g is the constant acceleration of gravity near the earth’s surface. By Newton’s second law, the force should be equal to the mass of the object times its acceleration dv dt . a) Show that the function v ( t ) = mg b ± 1-e-bt/m ² satisfies m dv dt = mg-bv for all t . b) Calculate lim t →∞ v ( t ) . What does it imply about the velocity of the object as time passes? c) For any fixed (constant) time t , calculate lim b → + v ( b ) . What does it imply about an object falling without air resistence?...
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Best method for impedence matching?
Impedance matching is one of the major application of common collector configuration. Is Common Collector configuration the best method for impedance matching? why?
• +1 for good question! I eager to see a good answer.
– Roh
Feb 28, 2014 at 8:01
• You can't ask for 'the best' without specifying your context and criteria. A CCC is a good solution when you have a high source impedance, a low required output impedance, a transformer is not a good option, you can live with ~1 voltage amplification, etc. Feb 28, 2014 at 11:05
Impedance matching is NOT one of the major applications of a common collector circuit. Why should a transistor be able to match an impedance? Impedance matching is done with passive components.
A common-collector circuit is good at providing a high input impedance (to a weak signal) and generating a low output impedance (at the emitter) - it is a power amplifier not an impedance matcher.
• You're taking the phrase "impedance matching" too literally. Think of it more as a general impedance transformation. Common-collector (emitter follower) matches a high-impedance source to a low-impedance load (unity voltage gain). Common-base matches a low-impedance source to a high-impedance load (unity current gain). Common-emitter is used for intermediate impedances (can have both voltage and current gain). Feb 28, 2014 at 13:13
• @DaveTweed "Making one impedance equal to another" is what the tag for impedance matching says. Feb 28, 2014 at 13:26
See let us take an example for a basic analog circuit where the voice signal is amplified and sent to the loudspeaker.
Now your voice signal is not a electrical signal so to process it we require a transducer which give the electrical equivalent of your voice signal. Let the output impedance of the transducer be 100k (assume). Say we connect a CC (common collector) amplifier in the next stage.
As the input impedance of the CC amplifier is very high so the combination of its input impedace and the transducer output impedance will be equal to the transducer output impedance only (Parallel combination ). Hence the CC amplifier doesnt create any loading effect for the transducer output stage.
Now consider the output of CC amplifier . The input impedance of the output device say a loudspeaker is low which matches with the low output impedance of the CC amplifier . Now there is a condition by Maximum Power Transfer Theorem that if the load impedance is same as the circuit impedance the maximum power transfer will take place . Hence the CC transfers maximum power to the output , which is also known as impedance matching.
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What is 207 Months in Minutes?
Convert 207 Months to Minutes
To calculate 207 Months to the corresponding value in Minutes, multiply the quantity in Months by 43829.1 (conversion factor). In this case we should multiply 207 Months by 43829.1 to get the equivalent result in Minutes:
207 Months x 43829.1 = 9072623.7 Minutes
207 Months is equivalent to 9072623.7 Minutes.
How to convert from Months to Minutes
The conversion factor from Months to Minutes is 43829.1. To find out how many Months in Minutes, multiply by the conversion factor or use the Time converter above. Two hundred seven Months is equivalent to nine million seventy-two thousand six hundred twenty-three point seven Minutes.
Definition of Month
A month (symbol: mo) is a unit of time, used with calendars, which is approximately as long as a natural period related to the motion of the Moon; month and Moon are cognates. The traditional concept arose with the cycle of moon phases; such months (lunations) are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth-Sun line, are still the basis of many calendars today, and are used to divide the year.
Definition of Minute
The minute is a unit of time or of angle. As a unit of time, the minute (symbol: min) is equal to 1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to 1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time. In contrast to the hour, the minute (and the second) does not have a clear historical background. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of "precision" timepieces (mechanical and water clocks). However, no consistent records of the origin for the division as 1⁄60 part of the hour (and the second 1⁄60 of the minute) have ever been found, despite many speculations.
Using the Months to Minutes converter you can get answers to questions like the following:
• How many Minutes are in 207 Months?
• 207 Months is equal to how many Minutes?
• How to convert 207 Months to Minutes?
• How many is 207 Months in Minutes?
• What is 207 Months in Minutes?
• How much is 207 Months in Minutes?
• How many min are in 207 mo?
• 207 mo is equal to how many min?
• How to convert 207 mo to min?
• How many is 207 mo in min?
• What is 207 mo in min?
• How much is 207 mo in min?
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# To what depth will the bullet penetrate the block in this case?
1. Nov 30, 2008
### frosti
1. The problem statement, all variables and given/known data
A 7.00 g bullet, when fired from a gun into a 1.00 kg block of wood held in a vise, penetrates the block to a depth of 7.60 cm. This block of wood is next placed on a frictionless horizontal surface, and a second 7.00 g bullet is fired from the gun into the block. To what depth will the bullet penetrate the block in this case?
2. Relevant equations
m1v1 + m2v2 = (m1+m2)vf
3. The attempt at a solution
I have no clue how to solve this problem. I don't really know what to do with the depth of penetration by the bullet. Can anyone please help?
2. Dec 1, 2008
### PhanthomJay
Re: collision
There's a significant loss of KE in part 1....like all of it, 1/2mv_b^2. In part 2 , apply conservation of momentum, and determine the total loss of KE. It' ll be a bit less; how does that ratio difference relate to the new depth of penetration?
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# Free Godzilla Coloring Mixed Word Problems Worksheets Calendar Math Kindergarten Work Algebra
Clair Alexia November 1, 2020 Math Worksheet
What are math worksheets and what are they used for? These are math forms that are used by parents and teachers alike to help the young kids learn basic math such as subtraction, addition, multiplication and division. This tool is very important and if you have a small kid and you don’t have a worksheet, then its time you got yourself one or created one for your kid. There are a number of sites over the internet that offer free worksheets that are downloadable and printable for use by parents and teachers at home or at school.
If you have read my article ”Helping Your Child With Basic Arithmetic? Stay Away From Worksheets” then you know that I am not a fan of traditional worksheets. After writing that article, I found another credible teacher who has written many ezine articles expounding on the benefits of worksheets. I decided some clarification of position is in order. The primary problem with most math worksheets is that the problems are already written out and the child need only write the answers. For learning and practicing the basic skills of addition, subtraction, multiplication, and division, it is much more beneficial for the child to write out the entire fact and say the entire fact out loud. A child will learn a multiplication fact much faster if they are writing out 6 x 8 = 48 at the same time they are saying ”six times eight is forty-eight” than if they just see 6 x 8 = ___ and only have to supply the 48.
The use of math worksheets can help solve numerous arithmetic problems. ”Practice makes an individual perfect,” is the best motto to be kept in mind while studying math. The motto will help a person to reinforce his desire to better himself in the subject. Without the help of these online resources, one will not be able to achieve the mastery of math. Since education is one of those areas which receive little or no funding from the government, it is essential for parents to look for various options that can help give their child a better education. Some sites do offer math online quiz that is sure to bring about an inclination towards math among children. It is a common practice for parents around the world to send their children to special math training centers. Invariably, every parent is unaware of the actual quality of training provided by these centers. To help parents combat this problem, there are a lot of online resources available that offer math assignment help exclusively for children.
Another problem with almost all worksheets is that they don’t prevent incorrect answers. Self-checking worksheets just let the student know they did something wrong–after the fact. I am a firm believer in the concept that, if at all possible, learning should be structured in small chunks in such a way that there is very little possibility for error. Worksheets often allow for mistakes to be made and then to be repeated many times. A mistake that gets practiced is extremely difficult to correct. This especially happens when worksheets are used as time fillers or baby sitters and the work isn’t really being supervised.
### Free Math Worksheets For 4th And 5th Graders
Nov 06, 2020
#### Free Printable Math Worksheets For Teachers
Nov 06, 2020
##### Graphing Worksheets For 6th Grade Math
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###### Apples Pears Plums 10 Partner Math Worksheet
Nov 06, 2020
Once downloaded, you can customize the math worksheet to suit your kid. The level of the child in school will determine the look and content of the worksheet. Use the school textbook that your child uses at school as a reference guide to help you in the creation of the math worksheet. This will ensure that the worksheet is totally relevant to the kid and will help the child improve his or her grades in school. The math worksheet is not only for the young children in kindergarten and early primary school; they are also used for tutoring high school and university students to keep the students’ math skills sharp. The sites that offer these worksheets have helped a lot and this resource is now a common thing to use for all kinds and levels of educators. The formats for the worksheets differ according to the level and content of the worksheets. For the young kids it is preferable to have the worksheet in large print, while the older students commonly use the small print ones that are simple and uncluttered.
In my 5th grade classroom, we use a math review series that’s engaging and entertaining at the same time. In essence they are simply halfpage handouts with ten standards based math problems woven into a special picture or exciting scene. Remember, I want to keep the math review time quick, but effective. My students are engaged in the activity because they are always eager to find out what the next scene will be, and how the math problems will be nestled within. They also like how within each handout I inscribe the title in a way that fits with the theme of that particular scene – another attention catching technique. And since this review activity only takes about fifteen minutes of class time, it is quick yet extremely beneficial.
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# Question
At first,
Brenda -> 11u
Diana -> 7u
Together, they have 18u.
18u ÷ 3 = 6u
Brenda -> 6u
Diana -> 12u
Celine -> no change at 5u
(a) B : C : D = 6 : 5 : 12
Brenda gave Diana (11u – 6u) = 5u candies
5u = 240
1u = 48
Total -> 11u + 5u + 7u = 23u
(b) There were (23 × 48) = 1104 candies
0 Replies 0 Likes
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{br} STUCK with your assignment? {br} When is it due? {br} Get FREE assistance. Page Title: {title}{br} Page URL: {url}
+1 917 8105386 [email protected]
Select Page
1. Develop a descriptive model that shows, for any given demand level and any quantity ordered by Predicto, the following measures: (i) Predicto’s profit; (ii) InTech’s profit; (iii) the total profit of Predicto and InTech. In order to do so:
Clearly list all inputs (i.e., decision variables), parameters, and outputs (objective function) and assign them a symbol if necessary. [2 pts]
Hint: You can refer to Art’s newsstand for an example.
Express the algebraic relationship between inputs/parameters and constraints/outputs/objective function. [6 pts]
Hint: Please list ALL relevant equations. You can refer to Art’s newsstand for an example.
1. Implement the model you developed in Q1. In the cell representing the demand, set its value to generate a random demand from a normal distribution with a mean of 10,000 and a standard deviation of 4,000. Do not worry about non-integer values, but use the function =max(mean+std*NORMINV(RAND(),0,1),0), to ensure that you do not get negative demand values. Run the simulation for an order quantity of 8,000 units, and provide a 99% confidence interval for Predicto’s expected profit, InTech’s expected profit, and total expected profit. Consider 5,000 runs of simulation. [12 pts]
Instruction: Please clearly indicate different component of your model (parameters, inputs, calculation, output). Seven points will be given for correctness and five points will be given for clarity of your implementation.
1. Create a table (or a graph) in which you show the estimated expected profits (Predicto’s, InTech’s, and total) for all possible order quantities (5,000, 5,500, 6,000, …, 11,500, 12,000). Based on your estimates, what should be Predicto’s optimal order quantity if it wanted to maximize its expected profit? [7 pts]
Instruction: Five points will be given for correctness and two points will be given for clarity of your implementation. You may include your answer to Q2 and Q3 in the same spreadsheet.
Questions 4-5 are related to the Quantity Discount Contract:
1. Modify your benchmark model in Q1 to represent the new setting. Specifically, list new parameters and adjust the algebraic relationship between inputs/parameters and constraints/outputs/objective function to incorporate all-unit quantity discount. We are still interested in (i) Predicto’s profit; (ii) InTech’s profit; (iii) the total profit of Predicto and InTech. [5 pts]
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# Curl
(redirected from makes hair curl)
Also found in: Dictionary, Thesaurus, Medical, Idioms.
## curl
Maths a vector quantity associated with a vector field that is the vector product of the operator ∇ and a vector function A, where ∇ = i∂/∂x + j∂/∂by + k∂/∂z, i, j, and k being unit vectors. Usually written curl A, rot A
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.
## Curl
of a vector field A, the vector characteristic of a “rotating component” of field A. The curl is represented by the symbol rot A. It can be interpreted in the following manner: Let A be the velocity field of a fluid flow. At a given point of the flow we place a small wheel with blades and orient its axis in the direction of rot A at that point. Then the angular velocity of the wheel’s rotation from the action of the current will be maximum, and its value will equal (| rot A |)/2. If the field A has the coordinates P(x, y, z), Q(x, y, z), and R(x, y, z), then the curl has the coordinates
E. G. POZNIAK
## curl
[kərl]
(forestry)
A block of timber cut from a crotch for cutting into veneers.
(materials)
A defect of paper caused by unequal alteration in the dimensions of the top and underside of the sheet.
(mathematics)
The curl of a vector function is a vector which is formally the cross product of the del operator and the vector. Also known as rotation (rot).
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
## curl
A winding, swirling, or circling in the grain of wood, usually obtained from the crotch or fork of a tree; also see fiddleback.
McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.
## Curl
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Author Message
Jan Bielawski
science forum Guru
Joined: 08 May 2005
Posts: 388
Posted: Fri Jul 14, 2006 3:08 am Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
LEJ Brouwer wrote:
Quote: Bilge wrote: LEJ Brouwer: Tom Roberts wrote: No physical anything happens. Merely the labels of coordinates get shuffled. As I said before, if you are going to 'merely' shuffle the labels of the coordinates, then you would have to 'merely' shuffle them in the Einstein field equations too - which means that what you are now solving are not the Einstein field equations. Don't be ridiculous. The metric has one timelike and three spacelike coordinates. For a spacelike metric, -+++, the entry with the - sign is timelike, regardless of what label you give it. Good grief. I despair for humanity. If dy/dx = x is solved by y = x^2 / 2 + c, and then I changed the x into a z wrote, y = z^2 / 2 + c, would I not have to change the original problem to dy/dz = z for the new solution to be valid? What is so ridiculous about that?
You missed the point. As I said earlier - you need to get the new
edition of Spivak, take a year off from posting nonsense on Usenet, and
study the basics.
Quote: The proof is in the papers I reference in post #1, and I have also outlined the proof in another post. WHY DON'T YOU TRY READING IT???
They are no "proofs", just incompetent ramblings. It's not my fault
that I cannot prove to you that you are wrong as any such proof
requires by definition that you have already understood the errors
you've made.
--
Jan Bielawski
LEJ Brouwer
science forum Guru Wannabe
Joined: 07 May 2005
Posts: 120
Posted: Fri Jul 14, 2006 4:01 am Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
JanPB wrote:
Quote: LEJ Brouwer wrote: Good grief. I despair for humanity. If dy/dx = x is solved by y = x^2 / 2 + c, and then I changed the x into a z wrote, y = z^2 / 2 + c, would I not have to change the original problem to dy/dz = z for the new solution to be valid? What is so ridiculous about that? You missed the point. As I said earlier - you need to get the new edition of Spivak, take a year off from posting nonsense on Usenet, and study the basics.
I do not feel any great urge to revise elementary differential geometry
simply because you cannot be bothered to check a simple proof.
Quote: The proof is in the papers I reference in post #1, and I have also outlined the proof in another post. WHY DON'T YOU TRY READING IT??? They are no "proofs", just incompetent ramblings. It's not my fault that I cannot prove to you that you are wrong as any such proof requires by definition that you have already understood the errors you've made.
Yet you know mention no specifics of mathematical errors in these
"incompetent ramblings".
Quote: -- Jan Bielawski
- Sabbir.
LEJ Brouwer
science forum Guru Wannabe
Joined: 07 May 2005
Posts: 120
Posted: Fri Jul 14, 2006 4:17 am Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
Tom Roberts wrote:
Quote: LEJ Brouwer wrote: As I said before, if you are going to 'merely' shuffle the labels of the coordinates, then you would have to 'merely' shuffle them in the Einstein field equations too - which means that what you are now solving are not the Einstein field equations. This is not true. Re-labeling the coordinates is of no consequence, and the field equation is invariant under such a shuffling. It does not matter how you label the individual coordinates, except that it can be confusing if you re-use a given label for different coordinates, such as is done in the two sets of Schw. coordinates.
I must admit I haven't check whether the field equation is invariant. I
would be surprised if it was, though it is not impossible. HOWEVER, if
the r in the field equation is spacelike - how can the r in the
solution be timelike? (And similarly for t). And even if this seems
fine to you, this argument is still a red herring and does not remove
the constraint r>2m.
Quote: What you still don't seem to realise is that r<2m does not physically exist, Hmmm. We are discussing the Schwarzschild solution of the Einstein field equation, not any real, physical system. This is all _theoretical_, and the manifold in the region r<2M is every bit as much a manifold as that in r>2M. So is the entire "second half" of the Kruskal extension.
Well, it's usually associated with the gravitational field outside a
spherical mass distribution (and typically a point mass). Even if you
disagree that this is a physical system, 2M is still a constant of
integration, and the condition r>2M arises from the _mathematical_ fact
that one cannot have a negative radial distance from the origin.
Quote: so there is only ONE valid set of coordinates, i.e. r>2m. That is just plain wrong.
My, what a powerfully convincing argument.
Quote: pointed this out at the start of the thread (in fact this is the whole point of bringing the matter up), and I even went through the proof of it in another post. Your "proof" assumed that it is possible to escape from any point in the manifold. This assumption is not valid for the Schwarzschild spacetime. shrug
What do you mean by 'escape' here? The proof involves measuring the
radial distance of any point from the origin and ensuring that this is
not negative.
Quote: Tom Roberts
- Sabbir.
N:dlzc D:aol T:com (dlzc)
science forum Guru
Joined: 25 Mar 2005
Posts: 2835
Posted: Fri Jul 14, 2006 4:41 am Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
Dear LEJ Brouwer:
"LEJ Brouwer" <intuitionist1@yahoo.com> wrote in message
news:1152850629.183256.303340@s13g2000cwa.googlegroups.com...
Quote: Tom Roberts wrote: LEJ Brouwer wrote: As I said before, if you are going to 'merely' shuffle the labels of the coordinates, then you would have to 'merely' shuffle them in the Einstein field equations too - which means that what you are now solving are not the Einstein field equations. This is not true. Re-labeling the coordinates is of no consequence, and the field equation is invariant under such a shuffling. It does not matter how you label the individual coordinates, except that it can be confusing if you re-use a given label for different coordinates, such as is done in the two sets of Schw. coordinates. I must admit I haven't check whether the field equation is invariant. I would be surprised if it was, though it is not impossible. HOWEVER, if the r in the field equation is spacelike
* outside the horizon *
Quote: - how can the r in the solution be timelike?
* inside the horizon *
That is the problem with the choice of "simple" coordinates.
Choose Kruskal coordinates and there is no such problem.
Consider what you are straining at is equivalent to using the LT
to evaluate something for the range 0 <= v <= oo, noting that
gamma blows up at c, and beyond c things become imaginary.
Quote: (And similarly for t). And even if this seems fine to you,
It is just a mathematical *map*, using a certain type of *ruler*,
not some fundamental desciption of "reality".
Quote: this argument is still a red herring
No, it is your fundamental misunderstanding, and until you can
see past this, you will coninue to be frustrated. I ought to
know, as I am still struggling with this too.
Quote: and does not remove the constraint r>2m.
Or what happens to gamma when v -> c.
Maybe I'm helping, maybe I'm not...
David A. Smith
LEJ Brouwer
science forum Guru Wannabe
Joined: 07 May 2005
Posts: 120
Posted: Fri Jul 14, 2006 9:45 am Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
N:dlzc D:aol T:com (dlzc) wrote:
Quote: Dear LEJ Brouwer: "LEJ Brouwer" wrote in message news:1152850629.183256.303340@s13g2000cwa.googlegroups.com... I must admit I haven't check whether the field equation is invariant. I would be surprised if it was, though it is not impossible. HOWEVER, if the r in the field equation is spacelike * outside the horizon * - how can the r in the solution be timelike? * inside the horizon *
Actually, I meant it as I said it - in the Einstein field equation, r
is spacelike and t is timelike. It is not possible therefore for r to
be timelike in the solution to the Einstein field equation, which means
that only the exterior solution is correct, and that the interior
solution is wrong.
Quote: That is the problem with the choice of "simple" coordinates. Choose Kruskal coordinates and there is no such problem. Consider what you are straining at is equivalent to using the LT to evaluate something for the range 0 <= v <= oo, noting that gamma blows up at c, and beyond c things become imaginary.
Even the Kruskal coordinates has problems - in this case two quadrants
of the solution (i.e. those corresponding to r<2m) are invalid - the
change in coordinates cannot change that. I don't understand your
analogy with the Lorentz transformation.
Quote: (And similarly for t). And even if this seems fine to you, It is just a mathematical *map*, using a certain type of *ruler*, not some fundamental desciption of "reality".
I disagree - the radial distance is a function of r, and the radius
must be nonnegative, so this constrains the possible range of the
parameter.
Quote: this argument is still a red herring No, it is your fundamental misunderstanding, and until you can see past this, you will coninue to be frustrated. I ought to know, as I am still struggling with this too.
The only thing that frustrates me is that people have become
conditioned not to recognise the blindingly obvious if it jars with
their preconceptions. I am not surprised that you are struggling with
it, as the standard picture is simply inconsistent.
Quote: and does not remove the constraint r>2m. Or what happens to gamma when v -> c. Maybe I'm helping, maybe I'm not... David A. Smith
I don't know, but I appreciate the effort.
Best wishes,
Sabbir.
Sue...
science forum Guru
Joined: 08 May 2005
Posts: 2684
Posted: Fri Jul 14, 2006 11:46 am Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
LEJ Brouwer wrote:
Quote: N:dlzc D:aol T:com (dlzc) wrote: Dear LEJ Brouwer: "LEJ Brouwer" wrote in message news:1152850629.183256.303340@s13g2000cwa.googlegroups.com... I must admit I haven't check whether the field equation is invariant. I would be surprised if it was, though it is not impossible. HOWEVER, if the r in the field equation is spacelike * outside the horizon * - how can the r in the solution be timelike? * inside the horizon * Actually, I meant it as I said it - in the Einstein field equation, r is spacelike and t is timelike. It is not possible therefore for r to be timelike in the solution to the Einstein field equation, which means that only the exterior solution is correct, and that the interior solution is wrong. That is the problem with the choice of "simple" coordinates. Choose Kruskal coordinates and there is no such problem. Consider what you are straining at is equivalent to using the LT to evaluate something for the range 0 <= v <= oo, noting that gamma blows up at c, and beyond c things become imaginary. Even the Kruskal coordinates has problems - in this case two quadrants of the solution (i.e. those corresponding to r<2m) are invalid - the change in coordinates cannot change that. I don't understand your analogy with the Lorentz transformation.
I understand why he makes the analogy but I consider it faulty.
Let's examine the real physical phenomena that gives us a
basis to interchange a spatial and temporal axis. It is not
railroading or philosophy about a rigid grid that god hung the
planets on.
<< Note that the time-dependent solutions, (509) and (510),
are the same as the steady-state solutions, (504) and (505),
apart from the weird way in which time appears in the former.
According to Eqs. (509) and (510), if we want to work out the
potentials at position and time then we have to perform
integrals of the charge density and current density over all
space (just like in the steady-state situation). However, when
we calculate the contribution of charges and currents at position
to these integrals we do not use the values at time , instead
we use the values at some earlier time >>
http://farside.ph.utexas.edu/teaching/em/lectures/node50.html
The freedom we take to resolve this little nearfield issue
with an imaginary time doesn't give us carte' blanche with
anything we can rotate into the Lorenz gauge and demonstrate
a principle of invariance. It only shows that an operation is
Lorenz invariant without any consideration what other absurdities
are created or masked.
The most obvious of which is operating on neutral far-field
objects as though they were charged nearfield objects.
At some point SR's basis of retarded potential has to
be distinguished from GR's notions of mass and
energy density equivalenece.
When I look at something based on the Schawrtzchild solution,
I automatically assume an error because I know a change in
energy was expressed as a change in time. Pound-Sinder
is the perfect example.
Sue...
Quote: (And similarly for t). And even if this seems fine to you, It is just a mathematical *map*, using a certain type of *ruler*, not some fundamental desciption of "reality". I disagree - the radial distance is a function of r, and the radius must be nonnegative, so this constrains the possible range of the parameter. this argument is still a red herring No, it is your fundamental misunderstanding, and until you can see past this, you will coninue to be frustrated. I ought to know, as I am still struggling with this too. The only thing that frustrates me is that people have become conditioned not to recognise the blindingly obvious if it jars with their preconceptions. I am not surprised that you are struggling with it, as the standard picture is simply inconsistent. and does not remove the constraint r>2m. Or what happens to gamma when v -> c. Maybe I'm helping, maybe I'm not... David A. Smith I don't know, but I appreciate the effort. Best wishes, Sabbir.
Daryl McCullough
science forum Guru
Joined: 24 Mar 2005
Posts: 1167
Posted: Fri Jul 14, 2006 5:03 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
LEJ Brouwer says...
Quote: Actually, I meant it as I said it - in the Einstein field equation, r is spacelike and t is timelike. It is not possible therefore for r to be timelike in the solution to the Einstein field equation, which means that only the exterior solution is correct, and that the interior solution is wrong.
Back up here. The Einstein field equations don't say anything about
"r" and "t". They don't say anything about which basis vectors are
spacelike and which are timelike. What they say is that
G_uv = k T_uv
where G_uv is a tensor formed from second derivatives of
the metric tensor g_uv, and T_uv is the stress-energy tensor,
and k is a constant related to Newton's constant G (there
might be a factor of pi or something).
How do you get r is spacelike and t is timelike from that?
--
Daryl McCullough
Ithaca, NY
Tom Roberts
science forum Guru
Joined: 24 Mar 2005
Posts: 1399
Posted: Fri Jul 14, 2006 8:47 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
LEJ Brouwer wrote:
Quote: Tom Roberts wrote: Re-labeling the coordinates is of no consequence, and the field equation is invariant under such a shuffling. I must admit I haven't check whether the field equation is invariant.
It is trivial. <shrug>
Quote: I would be surprised if it was, though it is not impossible.
Then you sure don't know much about this at all. This is a trivial
consequence of the arbitrariness of coordinates and the tensor nature of
the field equation. <shrug>
Quote: HOWEVER, if the r in the field equation is spacelike - how can the r in the solution be timelike? (And similarly for t).
Your question does not make sense, because of the nature of the field
equation.
Whether or not a given coordinate is timelike or spacelike depends on
the metric components, and one is solving the field equation for those
components. So it is not possible to say "the r in the field equation is
spacelike" until you have solved the field equation and _looked_ at the
g_rr metric component. For the Schwarzschild manifold, using the usual
Schw. coordinates, r is spacelike in the region r>2M and is timelike in
the region r<2M, and the coordinate singularity at r=2M makes it
impossible to answer for that value. Yes, this is a PUN on the symbol
"r" -- there are _TWO_ disjoint coordinate systems here, using the same
symbols _WITH_DIFFERENT_MEANINGS_. Sloppy mathematicians (aka many
physicists) do not always make such things clear, and indeed until 1960
or so this was not known by anybody; today is 2006 and you have no
excuse for your ignorance. <shrug>
Quote: And even if this seems fine to you, this argument is still a red herring and does not remove the constraint r>2m.
You remain adamantly confused. You need to _study_. <shrug>
Quote: the condition r>2M arises from the _mathematical_ fact that one cannot have a negative radial distance from the origin.
The Schw. r coordinate is most definitely _NOT_ "radial distance from
the origin". And your _ASSUMPTION_ that there is a "radial distance from
the origin" is _FALSE_ in the Schwarzschild manifold. Indeed, the locus
r=0 is deleted from the manifold and there is no "origin" (and that
locus is NOT a point). One could imagine substituting the limit point(s)
of incoming timelike paths from r=2M to the limit r->0, but there is no
definite value for such paths and that "distance" can have any positive
value (for different paths).
You seem to think that the Schwarzschild manifold is "just like we
perceive outside the earth (neglecting the air, etc.)". This is just
plain not so. You need to learn that this is NON-Euclidean geometry.
Indeed, this manifold is not anywhere close to Euclidean near and inside
its event horizon. The only way to understand the geometry is to study
the metric.
Tom Roberts
dda1
science forum Guru
Joined: 06 Feb 2006
Posts: 762
Posted: Fri Jul 14, 2006 9:25 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
LEJ Brouwer
science forum Guru Wannabe
Joined: 07 May 2005
Posts: 120
Posted: Fri Jul 14, 2006 9:44 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
Daryl McCullough wrote:
Quote: LEJ Brouwer says... Actually, I meant it as I said it - in the Einstein field equation, r is spacelike and t is timelike. It is not possible therefore for r to be timelike in the solution to the Einstein field equation, which means that only the exterior solution is correct, and that the interior solution is wrong. Back up here. The Einstein field equations don't say anything about "r" and "t". They don't say anything about which basis vectors are spacelike and which are timelike. What they say is that G_uv = k T_uv where G_uv is a tensor formed from second derivatives of the metric tensor g_uv, and T_uv is the stress-energy tensor, and k is a constant related to Newton's constant G (there might be a factor of pi or something). How do you get r is spacelike and t is timelike from that? -- Daryl McCullough Ithaca, NY
Hi, I think the semantics are getting a little mixed up here. I am not
claiming that r is spacelike *because* of the Einstein field equation -
I am simply stating the *fact* that r is spacelike in the Einstein
field equation - and indeed in any other equation in which r is a
radial parameter. The radial direction is spacelike by definition and
the temporal direction is timelike by definition. That's all there is
to it. The fact that the radial direction is timelike in the interior
Schwarzschild solution is further evidence that this solution is not a
valid one.
- Sabbir.
LEJ Brouwer
science forum Guru Wannabe
Joined: 07 May 2005
Posts: 120
Posted: Fri Jul 14, 2006 10:02 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
Tom Roberts wrote:
Quote: LEJ Brouwer wrote: Tom Roberts wrote: Re-labeling the coordinates is of no consequence, and the field equation is invariant under such a shuffling. I must admit I haven't check whether the field equation is invariant. It is trivial.
Well, maybe all the signs just happen to cancel - frankly I don't
really
Quote: I would be surprised if it was, though it is not impossible. Then you sure don't know much about this at all. This is a trivial consequence of the arbitrariness of coordinates and the tensor nature of the field equation.
No, it's because working out curvature components etc is usually pretty
boring and time-consuming and I see no reason to do so when the outcome
will not affect the present discussion in any way.
Quote: HOWEVER, if the r in the field equation is spacelike - how can the r in the solution be timelike? (And similarly for t). Your question does not make sense, because of the nature of the field equation.
I really don't know what you are talking about.
Quote: Whether or not a given coordinate is timelike or spacelike depends on the metric components, and one is solving the field equation for those components. So it is not possible to say "the r in the field equation is spacelike" until you have solved the field equation and _looked_ at the g_rr metric component.
Ignoring for a moment the fact that this entire thread of reasoning is
a separate argument from the one which I began to explain why r<2m is
physically invalid, your statement is completely wrong. If I have to
solve an equation for x where x is subject to some constraint, then the
solution had better satisfy that constraint. As I said elsewhere, the
radial direction is spacelike by definition.
Quote: For the Schwarzschild manifold, using the usual Schw. coordinates, r is spacelike in the region r>2M and is timelike in the region r<2M, and the coordinate singularity at r=2M makes it impossible to answer for that value. Yes, this is a PUN on the symbol "r" -- there are _TWO_ disjoint coordinate systems here, using the same symbols _WITH_DIFFERENT_MEANINGS_. Sloppy mathematicians (aka many physicists) do not always make such things clear, and indeed until 1960 or so this was not known by anybody; today is 2006 and you have no excuse for your ignorance.
I am sorry, but you are very very confused. This is probably not your
fault, as the textbooks must say the same things to have even the
semblence of consistency. If r had a single 'meaning' in the equation
to be solved, how can it have two different 'meanings' in the solution?
<shrug>
Quote: And even if this seems fine to you, this argument is still a red herring and does not remove the constraint r>2m. You remain adamantly confused. You need to _study_.
<shrug>
Quote: the condition r>2M arises from the _mathematical_ fact that one cannot have a negative radial distance from the origin. The Schw. r coordinate is most definitely _NOT_ "radial distance from the origin".
Ah, so you finally figured that out did you? Well done. Slow, but
you're getting there...
Quote: And your _ASSUMPTION_ that there is a "radial distance from the origin" is _FALSE_ in the Schwarzschild manifold. Indeed, the locus r=0 is deleted from the manifold and there is no "origin" (and that locus is NOT a point).
Ah, you had me fooled for a moment - you haven't figured it out at all,
have you? r is just a parameter. r=0 need not be the origin. In the
Schwarzschild solution, the origin is at r=2m. r=0 does not exist -
because r<2m does not exist - that is why the interior solution does
not exist. I suggest you go back to the start of the thread and try
again. <shrug>
Quote: One could imagine substituting the limit point(s) of incoming timelike paths from r=2M to the limit r->0, but there is no definite value for such paths and that "distance" can have any positive value (for different paths). You seem to think that the Schwarzschild manifold is "just like we perceive outside the earth (neglecting the air, etc.)". This is just plain not so. You need to learn that this is NON-Euclidean geometry. Indeed, this manifold is not anywhere close to Euclidean near and inside its event horizon. The only way to understand the geometry is to study the metric.
Umm, I think you will find that I was the one that pointed out that
this point is non-Euclidean - which is why the radial distance and the
area do not satisfy the usual relationship. So there is little point in
lecturing me about it when you are the one that has clearly
misunderstood what is going on. Can I suggest that you review your
differential geometry? <shrug>
Quote: Tom Roberts
I am sorry Tom, but you are totally clueless <shrug>.
LEJ Brouwer
science forum Guru Wannabe
Joined: 07 May 2005
Posts: 120
Posted: Fri Jul 14, 2006 10:05 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
dda1 wrote:
Quote: snipped. Why is that you Pakis never admit to error? Is it your religion? You afraid that you loose face? Well, you already lost a lot of face by continuing to post, you have been exposed as a fraud by several of us already. Why do you think that you can't publish your stuff in any peer reviewed journal? Eh?
I don't know - maybe it's because you don't like Pakis?
dda1
science forum Guru
Joined: 06 Feb 2006
Posts: 762
Posted: Fri Jul 14, 2006 10:09 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
LEJ Brouwer wrote:
Quote: dda1 wrote: snipped. Why is that you Pakis never admit to error? Is it your religion? You afraid that you loose face? Well, you already lost a lot of face by continuing to post, you have been exposed as a fraud by several of us already. Why do you think that you can't publish your stuff in any peer reviewed journal? Eh? I don't know - maybe it's because you don't like Pakis?
This is why no peer reviewed journal would publish your stuff? This is
why you get kicked of moderated forums? Because we all don't like Pakis?
LEJ Brouwer
science forum Guru Wannabe
Joined: 07 May 2005
Posts: 120
Posted: Fri Jul 14, 2006 11:00 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
dda1 wrote:
Quote: LEJ Brouwer wrote: dda1 wrote: snipped. Why is that you Pakis never admit to error? Is it your religion? You afraid that you loose face? Well, you already lost a lot of face by continuing to post, you have been exposed as a fraud by several of us already. Why do you think that you can't publish your stuff in any peer reviewed journal? Eh? I don't know - maybe it's because you don't like Pakis? :) This is why no peer reviewed journal would publish your stuff? This is why you get kicked of moderated forums? Because we all don't like Pakis?
Well, YOU certainly don't seem to like Pakis.
A major reason for my 'stuff' not being published could be that I tend
to question knowledge that has become 'established' when the
foundations of that knowledge are dubious. For example:
I claim that there is a luminiferous aether, when it has been
'established' that there isn't one.
I claim that quantum theory has a classical basis, when it has already
been 'established' that quantum theory is more fundamental than
classical mechanics.
I claim that classical black holes have been seriously misunderstood,
even though their nature has already been 'well established'.
I claim that classical electrodynamics is a direct consequence of
general relativity, which is just pretty hard to believe.
I claim that antigravity exists, even though it is generally taken for
granted that it does not.
I claim that general relativity is responsible for the existence of the
standard model gauge group, and that the elementary particles are
solitonic solutions of GR, when clearly such a claim is absurd.
I claim that string theory is a red herring, and a great sapper of
funding, resources and manpower, even though it is the only theory
currently considered to be a possible 'theory of everything'.
I claim that cold dark matter consists of neutrinos, which are
gravitational dipoles responsible for MOND, and which can be predicted
from first principles from GR, which is also pretty hard to believe.
I speculate that there was probably no 'big bang', but that it is more
likely that 'in the beginning' there was a 'big collapse'.
....and so on (I am sure you get the picture).
In general, I don't blindly assume that everything I am told or read in
books is correct, and am willing to question when things are not clear
or do not seem right.
And as it happens, yes, I was born in East Pakistan (now Bangladesh)
and am also a practising Muslim - I believe that there is no God but
Allah, and that the prophet Muhammad (may peace be upon him), is His
messenger, and I believe in all the prophets sent by Allah to guide
mankind, from the first prophet Adam (pbuh), all the way through to
Jesus (pbuh) and Muhammad (pbuh), who was the final prophet. Some
people might not like that.
And I think that's more than enough reason for establishment folk to
discard my work without looking at it. Don't you? Besides, my writing
style and my tendency to make imaginative extrapolations isn't
necessarily to everyone's liking. Not all my ideas turn out to be right
it's true, but I still think it's good to come up with bright new
ideas, and to always question the status quo, as that is ultimately
what leads to progress.
- Sabbir.
Tom Roberts
science forum Guru
Joined: 24 Mar 2005
Posts: 1399
Posted: Fri Jul 14, 2006 11:10 pm Post subject: Re: Misinterpretation of the radial parameter in the Schwarzschild solution?
LEJ Brouwer wrote:
Quote: I am simply stating the *fact* that r is spacelike in the Einstein field equation - and indeed in any other equation in which r is a radial parameter.
Where does the symbol "r" obtain this magical power???
You _really_ need to learn the basics. Symbols have no power whatsoever,
they mean merely what we designate them to mean, and in the case of GR,
as I said before, we don't know whether a given corodinate is timelike
or spacelike until we solve the field equation and examint the relevant
metric components. <shrug>
Quote: The radial direction is spacelike by definition
Your definition of words and symbols has no power over the mathematics.
Tom Roberts
Google
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Question
The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the numbers?
1. thuthuy
The first number is 16
The second number is 6
The third number is 64
Step-by-step explanation:
The information from the word problem are;
The count of the numbers in the sum = 3 numbers
The value of the sum of the three numbers = 86
The value of the third number = 4 × The value of the first number
The value of the first number = 10 + The value of the second
Let ‘x’ represent the first number, let ‘y’ represent the second number and let ‘z’ represent the third number, we have;
x + y + z = 86…(1)
z = 4 × x…(2)
x = y + 10…(3)
From equation (3), we get;
x = y + 10
∴ y = x – 10…(4)
Substituting the value of z from equation (2) and the value of y from equation (4) in equation (1) gives;
x + y + z = 86
z = 4 × x = 4·x
y = x – 10
∴ x + y + z = x + (x – 10) + 4·x = 86
x + (x – 10) + 4·x = x + x – 10 + 4·x = 6·x – 10 = 86
6·x = 86 + 10 = 96
∴ x = 96/6 = 16
x = 16
From equation (2), we get;
z = 4 × x
∴ z = 4 × 16 = 64
z = 64
From equation (4), we get
y = x – 10
∴ y = 16 – 10 = 6
y = 6
Therefore; x = 16, y = 6, and z = 64
The numbers are 16, 6, and 64
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### BEC Study Group Q1 2017
CPA Exam Forum BEC BEC Review BEC Study Group Q1 2017
This topic contains 813 replies, has 143 voices, and was last updated by drkarm 7 months, 2 weeks ago.
Viewing 30 posts - 481 through 510 (of 814 total)
• Author
Posts
• #1477999
Trucker90
Participant
@jsn3004
I think the key here is ‘flexibility.' The question emphasizes that XYZ's ‘[s]ales and services vary greatly' – implying that flexibility is an important factor when choosing financing sources. Credit card debt, LT Debt, and A/R factoring all have a rigid payment schedule.
#1478004
Rosy0407
Participant
@trucker90 referring to @ksc168 for the second question are you including depreciation? My answer was B no including depreciation.
#1478050
wei ng
Participant
Help me understand this question please!!
The following information is available on Crain Co.’s two product lines:
Chairs Tables
Sales \$180,000 \$48,000
Variable costs (96,000) (30,000)
Contribution margin 84,000 18,000
Fixed costs:
Avoidable (36,000) (12,000)
Unavoidable (18,000) (10,800)
Operating income (loss) \$ 30,000 (\$4,800)
Assuming the tables line is discontinued, and the factory space previously used to make tables is rented for \$24,000 per year, operating income will increase by what amount?
\$13,200
\$18,000
\$24,000
\$28,800
This answer is correct. To make the determination you would compare the amount of revenue from renting the factory space to the contribution margin less the avoidable costs from producing tables. The unavoidable costs allocated to the tables line would be incurred regardless of the decision and therefore are irrelevant. This answer is correct because income would increase by \$18,000 [\$24,000 rent − (\$18,000 contribution margin − \$12,000 avoidable costs].
I know you are supposed to ignore sunk costs in determining these type of questions but if the tables line is discontinued then the 18,000 revenue that it produces would not be generated nor the 12,000 costs that are avoidable if the line is discontinued. Therefore wouldnt operating income increase by the 24,000 net of the unavoidable costs (10,800)?
#1478086
A1lessio
Participant
For all the Becker users how do you feel about the B4 lecture and MCQs? I did fairly well the first time around scoring 68-70% and sometimes higher. I printed out the IT Appendix at the end of the chapter and plan to memorize and read a few pages a night. For people who have taken the test already, will that be enough for the IT?
#1478130
iamstrong
Participant
I went through the Becker lectures and MCQ. I'm now going through the NINJA MCQ. I feel NINJA MCQ are more diccicult- lots more on IT and it covered items not mentioned in Becker. I know people who passed BEC with just Becker but I did not want to take any chances so I'm NINJA MCQ'ing.
I do have a questions- I'm about 2 1/2 weeks from the exam- when do I start rewriting my notes? I've been making “nuggets” and was going to rewrite after I go through all NINJA MCQ. I was thinking of going less on MCQ to rewrite notes and then get to the review stage of NINJA.
Thanks
Rachel
#1478241
Tarheel83
Participant
@trucker90 unfortunately I did not attend UNC for as much as I wanted to. I am a graduate of University of South Florida. The reason for the name is that I was born and raised in eastern NC. I'm originally from New Bern, NC but live in Sarasota, FL now.
Sad week for the Tarheels though. Took a beating by Duke. Hopefully we get them when they play in the Dean dome.
#1478313
Econ_student
Participant
Hi all, does anyone know if due to the new format change that's coming in Q2, if I received my NTS in February, is it only valid for this current quarter?
I went on prometric today and it looks like I can't schedule anything beyond March.
#1478508
CPAIN2K17
Participant
@econ_student You just can’t schedule REG or BEC for after Q1 until after March 11.
#1478604
marimia22
Participant
thanks
#1478940
Tncincy
Participant
just got my nts for Reg, I thought I was going to squeeze it in this window with BEC, nope tax season really busy, hurt my foot, ordered to stay off of it, have to hop to work anyway (it's tax time)….Oh Lord my nerves….can I take any more!!!!! So I think I have to do just one at a time :-(…Determined to get it done.
#1478967
mtaylo24
Participant
Good luck to you Cincy. My nerves are starting to kick in. Rematch next Friday!
#1479031
Tncincy
Participant
Good luck to you mtaylo24, you got this….
#1479336
mcdylan02
Participant
@wei ng The answer to this problem can be difficult to understand. The way that it works is you have to take the net income that is given up minus the new income that is derived from renting the space out. So you toke the contribution margin (18,000) less the avoidable costs (12,000) and it gets you the income that was given up (6,000). You take that less the 24,000 and you get \$18,000 in increased revenue.
#1479516
Jsn3004
Participant
@wei ng
I think i'm going about the question differently than other people.
Think of it this way. If we rent out the facility that's 24,000.
We have unavoidable fixed costs of 10,800.
24,000-10,800=13,200
Now what's the difference between 13,200 and negative 4,800?… Answer: 18,000
I didn't include the contribution margin or avoidable fixed costs because i'm not going to include those when i'm figuring out my profit for renting out the facilities.
Let me know if this makes sense because I know there's other ways of going about this problem.
#1479522
Tarheel83
Participant
@mtaylo24 your going to kill it this time around man!
I got the retake on 3/6 so I won't be too far behind you. I feel good on Corporate Governance and IT, so I am trying to finish up financial Management by tomorrow night, then work on economics. Hopefully u next week I can just run questions non stop until the exam.
#1479532
wei ng
Participant
@jns3004
My mind is freaking blown!! thanks that makes way more sense to me now.
#1479634
mtaylo24
Participant
@tarheel83 Sounds like a plan. I can beast in Gleim but I'm getting slaughtered in Ninja right now. Hoping to turn everything around by the time the weekend is over, or I may be sitting in the extended window as well.
#1479639
bhuekels
Participant
Anybody else worried about the written communication? I'm just worried that they're going to throw something out of left field. I guess you do get points for the format, and as a written question, you can probably try to bs it, even if it is something unexpected.
#1479810
Tarheel83
Participant
Ok I found this post to be really helpful and have tried to post to this forum a few times and it must be too long or something, so I am going to split it up. I got it from the CPA Excel forum for VARIANCES and I love it. I memorized it heading into my first attempt at BEC and although I was close I didnt pass (74), but I know that this formula helped me back then.
Yes – that's my preferred way to calculate the variances. Personally, I find that the following format works particularly well for CPA exam questions – particularly those which provide you with the variance and ask you to solve for the actual/standard quantity or cost.
Here's an example of using this format to solve one of your past exam questions (and one of the most difficult ones, to boot!):
AICPA.060214BEC
Virgil Corp. uses a standard cost system. In May, Virgil purchased and used 17,500 pounds of materials at a cost of \$70,000. The materials usage variance was \$2,500 unfavorable, and the standard materials allowed for May production was 17,000 pounds. What was the materials price variance for May?
Step 1: Fill in blank format with information supplied in question:
____________Qty/Hrs_______Price/Rate_______Total
+ Standard______17,000_____X____???_______=______???
– Actual ________17,500_____X____???_______=_____\$70,000
= Difference_______???___________???______________???
Usage/Efficiency Variance = Difference in Qty/Hrs X Standard Price/Rate
(\$2,500) = ??? X ???
Price/Rate Variance = Difference in Price/Rate X Actual Qty/Hrs
___???__=__??? X ???
Step 2: Wherever you have 2 out of the 3 numbers in an equation, calculate the missing value:
____________Qty/Hrs_______Price/Rate_______Total
+ Standard______17,000_____X____???_______=______???
– Actual ________17,500_____X___\$4.00_______=_____\$70,000
= Difference_______(500)_________???______________???
Usage/Efficiency Variance = Difference in Qty/Hrs X Standard Price/Rate
(\$2,500) = ??? X ???
Price/Rate Variance = Difference in Price/Rate X Actual Qty/Hrs
___???__=__??? X ???
#1479843
Tarheel83
Participant
Ok, well I tried. Now I cant post steps 3 and 4.
#1479781
Tarheel83
Participant
BTW, for anyone having trouble with Variances, or just looking for a sure fire way to approach variance problems, I found this on the CPA Excel Forum when I first took BEC and I remember it helping a lot. I am just getting into Variances again so I figured I would post this to see if it helps anyone else.
I find that the following format works particularly well for CPA exam questions – particularly those which provide you with the variance and ask you to solve for the actual/standard quantity or cost.
Here's an example of using this format to solve one of your past exam questions (and one of the most difficult ones, to boot!):
AICPA.060214BEC
Virgil Corp. uses a standard cost system. In May, Virgil purchased and used 17,500 pounds of materials at a cost of \$70,000. The materials usage variance was \$2,500 unfavorable, and the standard materials allowed for May production was 17,000 pounds. What was the materials price variance for May?
Step 1: Fill in blank format with information supplied in question:
____________Qty/Hrs_______Price/Rate_______Total
+ Standard______17,000_____X____???_______=______???
– Actual ________17,500_____X____???_______=_____\$70,000
= Difference_______???___________???______________???
Usage/Efficiency Variance = Difference in Qty/Hrs X Standard Price/Rate
(\$2,500) = ??? X ???
Price/Rate Variance = Difference in Price/Rate X Actual Qty/Hrs
___???__=__??? X ???
Step 2: Wherever you have 2 out of the 3 numbers in an equation, calculate the missing value:
____________Qty/Hrs_______Price/Rate_______Total
+ Standard______17,000_____X____???_______=______???
– Actual ________17,500_____X___\$4.00_______=_____\$70,000
= Difference_______(500)_________???______________???
Usage/Efficiency Variance = Difference in Qty/Hrs X Standard Price/Rate
(\$2,500) = ??? X ???
Price/Rate Variance = Difference in Price/Rate X Actual Qty/Hrs
___???__=__??? X ???
Step 3: Check to see if any of the newly calculated values can be used to complete other formulas and/or identify other components in the equations:
a)__________Qty/Hrs_______Price/Rate_______Total
+ Standard______17,000_____X____???_______=______???
– Actual ________17,500_____X___\$4.00_______=_____\$70,000
= Difference_______(500)_________???______________???
Usage/Efficiency Variance = Difference in Qty/Hrs X Standard Price/Rate
(\$2,500) = (500) X ??? = \$5.00==>>Standard Price/Rate
Price/Rate Variance = Difference in Price/Rate X Actual Qty/Hrs
___???__=__??? X ???
b)__________Qty/Hrs_______Price/Rate_______Total
+ Standard______17,000_____X___\$5.00______=______\$85,000
– Actual ________17,500_____X___\$4.00_______=_____\$70,000
= Difference_______(500)________ \$1.00_____________\$15,000
Usage/Efficiency Variance = Difference in Qty/Hrs X Standard Price/Rate
(\$2,500) = (500) X ??? = \$5.00==>>Standard Price/Rate
Price/Rate Variance = Difference in Price/Rate X Actual Qty/Hrs
___???__=__\$1.00 * 17,500 = \$17,500 Favorable
Step 4 (optional): You can check the accuracy of your calculations by adding the Usage/Efficiency and Price/Rate variances to see if they equal the Total Variance (per the Standard/Actual/Difference matrix):
\$2,500 Unfavorable + \$17,500 Favorable = \$15,000 Favorable Total Variance==>>matches with separately calculated Total Variance
Though this format may seem like overkill for some of the easy variance questions, I find it EXTREMELY helpful for more difficult questions.
#1480228
pnc123
Participant
I got the exam in a week and i am using Becker. I still haven't touched B6. Since the time is short and i need to focus on reviewing now instead of going through new material, which parts of B6 should you think i better not skip given that B6 is less frequently tested on the exam. If you took BEC this year, did you get any questions from B6?
#1491820
michelleq6130
Participant
Hey! We are on the same boat! I have reread the notes a couple of times and have done countless MCQs.. I am just not sure when to start writing down those notes! For some reason I am so excited. 🙂
#1492011
ignaciopc
Participant
Hi,
I applied to do the BEC exam, this is my first application ever. I will do it at PA State,my status appears at the official website (NASBA) as ATTSENT. I don't know what it means. Can somebody be so kind to tell which status should appear when I have approved to attend the exam?. Thanks a lot and good luck everybody!
#1492012
Jsn3004
Participant
@wei ng It's unfortunate that many of the explanations get too complicated when there are better ways of explaining a solution.
#1492018
ignaciopc
Participant
1 Dollar = 0.95 euros, as you said, that means that the euro is stronger vs Dollar
0.95 Dollar= 1 euro, means that the is the opposite, Dollar is stronger.
I know that it is almost what you said, but just is case that this helps you.
Good luck everybody
#1492033
Krakebo007
Participant
You'll get ‘NTS issued ‘ and with an email included your NTS details
#1492239
S6
Participant
Re-taking BEC beginning of March and using Ninja MCQ.
Barely finishing capital budgeting and its kicking my beeeeeeehind.
Whyyyy
#1492240
ignaciopc
Participant
Thank you!
#1492246
mperez102204
Participant
Hey everyone, I am taking the exam on the 10th of march. I using the Nina Plus videos instead of reading the books that I have with Wiley. Do you think this is a bad choice? I just can not learn by readying. I learn better by watching and doing.
EH, i just want to pass an exam. I am so freaking far from it. I really do not want to do BEC with SIMS.
Also, you guys think about 3 weeks of final review is okay. I work full time so i can allocate about 2 hours during the week and 4-6 on each weekend night.
panic mode??? lol
Viewing 30 posts - 481 through 510 (of 814 total)
The topic ‘BEC Study Group Q1 2017’ is closed to new replies.
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# Number 15456103
### Properties of number 15456103
Cross Sum:
Factorization:
Divisors:
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 2 (Binary):
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
ebd767
Base 32:
enlr7
sin(15456103)
0.93740050836734
cos(15456103)
0.34825319368621
tan(15456103)
2.6917212113552
ln(15456103)
16.553514499491
lg(15456103)
7.1891000032344
sqrt(15456103)
3931.4250596953
Square(15456103)
### Number Look Up
Look Up
15456103 (fifteen million four hundred fifty-six thousand one hundred three) is a impressive figure. The cross sum of 15456103 is 25. If you factorisate 15456103 you will get these result 13 * 1188931. 15456103 has 4 divisors ( 1, 13, 1188931, 15456103 ) whith a sum of 16645048. The number 15456103 is not a prime number. 15456103 is not a fibonacci number. 15456103 is not a Bell Number. 15456103 is not a Catalan Number. The convertion of 15456103 to base 2 (Binary) is 111010111101011101100111. The convertion of 15456103 to base 3 (Ternary) is 1002002020210021. The convertion of 15456103 to base 4 (Quaternary) is 322331131213. The convertion of 15456103 to base 5 (Quintal) is 12424043403. The convertion of 15456103 to base 8 (Octal) is 72753547. The convertion of 15456103 to base 16 (Hexadecimal) is ebd767. The convertion of 15456103 to base 32 is enlr7. The sine of the number 15456103 is 0.93740050836734. The cosine of the figure 15456103 is 0.34825319368621. The tangent of the number 15456103 is 2.6917212113552. The square root of 15456103 is 3931.4250596953.
If you square 15456103 you will get the following result 238891119946609. The natural logarithm of 15456103 is 16.553514499491 and the decimal logarithm is 7.1891000032344. You should now know that 15456103 is very amazing number!
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# “Canstruction”
It’s awesome when people get together to build something really cool-looking — and even better when it helps other people. As our friend Suzanne D. shared with us, at Canstruction people around the country build giant statues out of cans of food. Then the cans are given to other folks who don’t have enough food. These Despicable Me minions are made of cans of tuna fish. Maybe Despicable Me is a good guy after all.
Wee ones: How many eyes can you count on the Despicable Me guys in the photo?
Little kids: If you stick on a red can, then a blue can then a red, then a blue…what color is the 7th can? Bonus: If the front guy’s arms each have 10 cans, how many cans make up his arms?
Big kids: Each Despicable Me guy has what looks like 41 rows of cans top to bottom. If tuna cans are 2 inches tall, how tall are the statues? Bonus: What does that equal in feet and inches — and how much taller than you are they? (Reminder: A foot has 12 inches.)
The sky’s the limit: How many cans did it take to build each of these statues? Do some guessing and some math, and see what you come up with! (You “can” assume the statue is hollow — just cans around the outside surfaces.)
Wee ones: 3 eyes.
Little kids: Red. Bonus: 20 cans.
Big kids: 82 inches. Bonus: 6 feet 10 inches – and for how much taller, different for everyone.
The sky’s the limit: We got about 750…here’s what we did. We counted about 23 equal layers in the head and shoulders/chest, and 11 cans in the half of the layer we can see, making 22 cans per layer. That comes to 506 cans. For the pants, we assumed each layer has 2 fewer cans than the layer above it. For the 8 layers in the pants, that means adding 20+18+16+14+12+10+8+6. To add that quickly, that’s the same as 20+6, then 18+8, and so on, which is four 26s or 104 more cans. For the head, similar thing: 6 layers would give 20+18+16+14+12+10, which is the same as six 15s, or 90. That gives us 506+104+90, which comes to exactly 700. Then there are 36 in the arms (we count 18 in each) and 12 in the feet (6 in each), bringing us to 748 tuna cans in each statue.
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# CTR Calculator (Click Through Rate)
We have provided a useful online CTR Calculator below to work out your CTR as well as derive the number of impressions and clicks you would need to get a specific Click Through Rate. Feel free to experiment with different scenarios using our Click Through Rate Calculator in order to help you better understand this metric.
## What is a CTR?
A click-through is simply when a user clicks on an ad and goes to the webpage the ad links to.
CTR stands for Click-Through Rate, and is the simplest way to compare the performance on a basic level of different ad campaigns. This is because CTR is a better measure of success than simply the number of clicks an ad has received.
For example:
Ad ONE seen 1,000 times and clicked on 30 times.
Ad TWO – seen 10,000 times and clicked on 275 times.
Although Ad TWO has had more clicks, it has also had ten times more opportunity for clicks. If you multiply Ad ONE‘s clicks by 10, it actually has more! This is why it isn’t fair to judge ads simply by clicks. A CTR tells you how ads with equal opportunities can perform.
CTR is therefore usually used when ad performance is being measured. When clicks are the goal of a campaign, more budget should be spend on placements with a higher CTR where possible.
A higher CTR not only implies a higher level of interest from users on that placement, but it will also save the advertiser on ad serving fees. This is because you can achieve the same amount of clicks while showing an ad fewer times.
## CTR Formula
The CTR equation is:
Click to enlarge
CTR = (Clicks x 100) / Ad impressions
Find out more
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1. Banach algebras question 6
Here is the last my question in this theme.
I've problems with the following statements in red shapes. How can I show/explain this in the easiest way?
Where we used fact that this measure is Radon measure?
PS. Here is link to the original paper http://matwbn.icm.edu.pl/ksiazki/sm/sm29/sm29126.pdf
2. Originally Posted by Arczi1984
Here is the last my question in this theme.
I've problems with the following statements in red shapes. How can I show/explain this in the easiest way?
Where we used fact that this measure is Radon measure?
PS. Here is link to the original paper http://matwbn.icm.edu.pl/ksiazki/sm/sm29/sm29126.pdf
A Radon measure is just a measure for which the formula on the left side of (6) defines a continuous linear functional.
In a function algebra, the spectrum of a function is just the range of the function. So the formula (6) ensures that f(x) is in the spectrum of x.
In a compact space, every sequence has a convergent subsequence. So some subsequence of the sequence $(p_n)$ converges to a limit p, and (since x is continuous) the condition $|x(p_n)-f(x)|\to0$ implies that $x(p) = f(x)$.
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2015-03-17T21:59:06-04:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
28/4 = 7,
36/4 = 9,
Place the 7 over the 9 and you get 7/9!
2015-03-17T22:04:44-04:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
You can easily keep simplifying this fraction by 2 until you can't simplify it anymore, because they're both even.
It can be faster this way for most people, but you can also just find what number goes into both numbers evenly.
4 goes into both numbers.
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+0
# A RECTANGLE COURTYARD IS 20m LONG 18m BROAD.IT IS TO BE PAVED WITH SQUARE TILES OF THE SAME SIZE.FIND THE MAXIMUM SIZE OF THE TILE WHICH CAN
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A RECTANGLE COURTYARD IS 20m LONG 18m BROAD.IT IS TO BE PAVED WITH SQUARE TILES OF THE SAME SIZE.FIND THE MAXIMUM SIZE OF THE TILE WHICH CAN BE USED.
Guest Apr 16, 2017
#1
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The GCF of 18 and 20 is 2, so the maximum size square tile is 2m x 2m.
.
Alan Apr 16, 2017
edited by Alan Apr 16, 2017
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https://www.atheistrepublic.com/forums/debate-room/scientific-purpose-human-species-may-be-replicate-universes?page=2
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# Scientific purpose of human species, may be to replicate universes
154 posts / 0 new
Avant Brown: "In simpler terms, if Cognostic doesn't wish to understand it, it is not worth understanding or isn't understandable?"
Well, I'll be damned. It still ain't got it. AB you are becoming as useful as used tampon.
rmfr
And I watch the sarcasm sail over Avant Brown's head.
My motive is straight forward, I'm skeptical of your claim. I politely asked you for the function several times and I'd still like to see it.
If you are unwilling to provide it, please tell me so, so I can stop asking.
If you don't know it, please tell me so, so I can stop asking.
I already gave a sufficient answer in an earlier response on page 2, as underlined below:
Blue Grey Brain's words:
Mathematical functions are things that may transform some input into some output. Take your pick of a function that looks like it's generating exponential returns. I don't recall mentioning any one particular function.
In case of additional questions: After all, everything is probably numbers. Even if everything isn't numbers, you take some input, pass those to some other numbers that represent some junction or function, then you get some other numbers that in sequence, seem exponential in their distribution.
You can take a look at accelerating returns, and plot the data yourself, if you don't like the plots there. What you seem to be looking for is how some data pertaining to evolving tech is organized, such that it resembles an exponential distribution. (If you want to know what distribution means, you can google that as well.)
@ Avant Brown
since you cannot figure out what Nyarlathotep is talking, he means a "function" like f(x) = x + 1. Although I am giving very simple function, that is an example of what he has been asking you about when he says the "function for the exponential growth" for your deity.
rmfr
arakish - ...[Nyarlathotep] means a "function" like f(x) = x + 1.
Exactly.
When a STEM PhD candidate tells me something pretty important to their field is exponential; I don't think it is unreasonable to ask them what that exponential is.
Am I being unreasonable?
@Avant Brown
Like I said in my first post, it really comes down to how you define "AI"
You could potentially say the first sliding rule, or abacus is "AI" Or you could say AI is human like intelligence but made artificially.
Or somewhere inbetween.
If you take the 2nd option the more extreme end of "human like ai or greater" the experts in the field will tell you: we are nowhere near close. Like I said in my longish post, the latest top of the line supercomputer running self learning, machine learning broad artificial intelligence struggles to operate even at an insect's brain's level.
So far computers are just really fancy calculators. Crunching binary math at blazing speeds, with all kinds of hardware and software tricks that speeds up the more complex calculations, "short cuts" may be the best way to describe it.
The human brain however, is very very different then even the most advanced computer today. At minimum advanced quantum processors that can operate billions of instructions every cycle is needed (currently we have quantum processors that can only do 2-8 qubits and they have not yet left the lab. (good thing too, our cyber security is not anywhere near ready for what quantum processors represent - making all encryption techniques worthless-)
Also another large roadblock. The number of possible connections in a human brain. Far exceeds all the connections of every computer, processor, switch, router, network, ever made in the entire world combined. Trying to replicate a human brain is currently beyond our reach.
Worse still, when it comes to moore's law, it has reached mostly a dead end. We are at 7nm for traditional silicon processors, and it was an incredible effort to get there from just 9-11 n/m processors (billions of dollars!.) You may have noticed, a decent processor from 5 years ago is probably only 10-20 percent slower than a comparable (in price) decent desktop processor of today. So even if there was hope one day our compute capabilities on silicon could begin to rival the human's brain, that hope is gone now, we have reached a "dead end" when it comes to creating more powerful processors. Now we are just lowering power requirements, refining them and of course doubling , quadrupling etc the core counts.
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▮ I am an atheist that always likes a good debate. ▮
▮ Please include @LogicFTW in responses directed to me. ▮
▮ Useful list on forum usage. A.R. Member since 2016. ▮
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2. Moore's law may indeed be seen as dead, but it has been replaced with a better law, or law which indicates computing power is doubling even faster than Moore's law indicated. Enter "Hyper Moore's Law."
---------------------
3. It's not merely about speed. To play the game of "Go" well, you need:
a. Computer size of the universe to brute force search through all Go game states. (The number of possible moves in "Go", surpasses the number of atoms in the known universe!)
b. ...or you need human like intuition; i.e. humans have played the game of "Go" well for millennia.
c. Obviously, alpha go Ai, now the world champion, is not a computer the size of the universe, so alpha go Ai, clearly has human like intuition going on.
---------------------
Most of your arguments demonstrably occur on ignorance.
First I want to say this topic is fascinating to me and I like to read and learn all I can on it. I am by no means an expert at this stuff and I could very easily get something wrong.
1. That is cool, did not know they were up to 2048. They must of made some major advances to stabilizing the qubit to make 2048 qubit possible, or perhaps they went more of the "brute force" route, where many, perhaps most of them spit out bad data, but the numbers are high enough to error correct. I unfortunately did not have time to read the article in its entirety I hope to do so tomorrow. If 2048 qubit every went mass scale, we would all have to update our encryption methods away from prime integers method. Which could end up requiring a lot more overhead for your non quantum computers to remain secure. As I do work in cyber security now, that is a big deal in my line of work.
2. Agreed, but if we are just changing definitions and setting new bars we are not really talking about moore's law anymore. My base point that actual targeted useful improvement by reducing transistor size to realize gains in space, heat issues etc is pretty much at an end. We can however modify, add to, and run stuff in parallel, like what GPU's are good at.
Take Nvidia's latest 20XX series of graphics cards released last summer. The 2080 (retails for at best 750 bucks (and this is months after launch!) but is can only play the latest games maybe 10-20 percent faster than the 1080 that was launched 2.5 years ago for ~\$550. The price to performance ratio for all games has actually gone down! The only real gains in power is for games that utilize ray tracing to a great degree. Basically they just added on more hardware, more transistors to do new things, not a whole lot of "improving upon" what it could do before w/o throwing more memory at it. Now at least part of it is Nvidia cashing in on the cryptocurrency craze which allows them to fatten their profit margins, but overall even for nvidia the "inventor of Hyper moore's law" is having real trouble seeing advancement at a practical usable level. It is a bit like a car manufacture saying: This car is much faster and better then our last model, we added turbo instead of doubling horsepower, and that is fine, but the car also cost a signficant amount more, weighs more etc with the inclusion of turbo.
3. Fully agree with you here. It is pretty cool reading about how they taught the computer how to play GO well enough to beat the top GO players in the world, by having it play many thousands of games and learning based on the outcome of them. Instead of trying to brute force calculate every possible move, as the developers were well aware that the possibilities quickly ballooned to unmanageable numbers even with with a computer that had performance measured in tera flops.
3C. Disagree with you here. That is quite the unevidenced leap, there are many many other possibilities here other then "human intuition going on." We humans still do not even fully understand human intuition.
Most of your arguments demonstrably occur on ignorance.
I never claimed to be an expert and stated these were my own opinions I even learned some new stuff, like the dwave simulation that happened in late august from your post. But how sure are you that there is no gaps in your knowledge? Enough to be certain "most of my arguments demonstrably occur on ignorance?"
As LogicFLW hinted earlier: only someone who has never "gotten their hands dirty" in a computer could think that doubling it's cores, will double its output.
As LogicFLW hinted earlier: only someone who has never "gotten their hands dirty" in a computer could think that doubling it's cores, will double its output.
I think it would benefit both of us in this conversation, if you took a look at "Hyper Moore's Law" and "The laws of accelerating returns".
Btw, the doubling I'm referring to relates to exponential change. Linear change can get you an increment of 1 every step, whereas exponential change gets you powers in doubling terms, or ^2.
You may also want to take a look at Wikipedia/Doubling time.
Avant Brown: "whereas exponential change gets you powers in doubling terms, or ^2."
Well, you just proved you are NOT a STEM PhD candidate. Doubling (×2) is NOT the same as squared (^2).
rmfr
Avant Brown,
"Scientific purpose of human species, may be to replicate universes"
Why has it taken over 13 Billion years for man to even realize what an universe might be? Just 100 years ago people thought that the stars in the night sky was the entire universe. Even today some people don't know how to boil water so the idea that the purpose of humans is to replicate universes seems to be farfetched.
Heck, we have barely begun to explore our universe, and to travel through it is a very big ask.
And if course, if future versions of mankind could actually do it, we now ask the question .. why would they?
If a future race learned enough to perform this task, no doubt they have also learned other things, and may be able to do even more impressive things.
I've read your article on hyper Moore's law and it says that GPUs are advancing in capability but CPUs are not. It also says new types of GPUs are being developed. Also, it was speculation by a CEO, who has investors to please. They always promise things that may or may not actually happen.
Yes, technology, overall, will probably exponentially increase. However, self aware AI might not be possible and I see no advancements in that specific area. So far, AI only do what they are programmed to do. Yes, they can learn, because they are programmed to. We have no examples of AI doing things outside of their programming.
I've read your article on hyper Moore's law and it says that GPUs are advancing in capability but CPUs are not. It also says new types of GPUs are being developed. Also, it was speculation by a CEO, who has investors to please. They always promise things that may or may not actually happen.
Yes, technology, overall, will probably exponentially increase. However, self aware AI might not be possible and I see no advancements in that specific area. So far, AI only do what they are programmed to do. Yes, they can learn, because they are programmed to. We have no examples of AI doing things outside of their programming.
It looks like you don't know that machine learning is evolving exponentially, along with those GPUs.
Now there are TPUs too, btw, which are even better than the fast evolving GPUs.
• While Nvidia does have investors to convince, Nvidia also powers a lot of machine learning stuff. Wanting to please investors is not automatically coupled with being non fast evolving or non-productive, and Nvidia has demonstrably delivered fast evolving computing solutions.
• Yes, CPUs aren't advancing as well as GPUs in particular ways [the whole point of the article was Moore's law transitioning into GPU like evolution], this doesn't change that exponential changes are underway.
• I reiterate. The best they will probably ever do with computers is to create a sophisticated SI (Simulated Intelligence). Never a true AI.
rmfr
I reiterate. The best they will probably ever do with computers is to create a sophisticated SI (Simulated Intelligence). Never a true AI.
rmfr
What do you understand by the word simulation?
It seems you feel your use of the word simulation somehow inhibits the creation of human level surpassing artificial intelligence.
• In particular, perhaps you should check out Wikipedia/Artificial General Intelligence/simulation Or Wikipedia//brain simulation
• This line from the first Wikipedia link may interest you, or at least show you that your use of the word simulation doesn't actually carry the weight you seem to think it does hereafter:
"The computer runs a simulation model so faithful to the original that it will behave in essentially the same way as the original brain, or for all practical purposes, indistinguishably".
• Simulated, NOT simulation. Completely different.
rmfr
Simulated, NOT simulation. Completely different.
rmfr
I think you need to revisit my prior comment.
The words simulated and simulation are used interchangeably on the Wikipedia/brain simulation and Artificial General Intelligence page.
There's a common misconception about the words, which you seem to be servicing throughout your responses.
@ Avant Brown
"There's a common misconception about the words, which you seem to be servicing throughout your responses."
simulated = to create a simulation, likeness, or model of.
simulation = the act or process of pretending
No misconception.
rmfr
The words simulated and simulation are used interchangeably on the Wikipedia/brain simulation and Artificial General Intelligence page.
What does the quote below mean to you? ( ͡° ͜ʖ ͡°)
Blue grey brain's words:
The words simulated and simulation are used interchangeably on the Wikipedia/brain simulation and Artificial General Intelligence page.
@ Avant Brown (Blue Grey Brainless)
It means that whoever wrote the Wikipedia article does not know difference between "simulated" and "simulation." And evidently neither do you.
rmfr
@ Avant Brown (Blue Grey Brainless)
It means that whoever wrote the Wikipedia article does not know difference between "simulated" and "simulation." And evidently neither do you.
rmfr
Or could it mean that for quite a long while you've held on to the misconception that simulations couldn't be highly representative of some original item? ( ͡° ͜ʖ ͡°)
I don't expect myself to be omniscient of any topic at all, and I think you should remember that you are liable to be holding on to misconceptions. The key is to be willing to update your beliefs, especially when you're clearly demonstrated to be wrong, as is the case as is visible on "Wikipedia/Artificial General Intelligence", and "Wikipedia/Brain Simulation".
@ Avant Brown (Blue Grey Brainless)
BGBrainless: "Or could it mean that for quite a long while you've held on to the misconception that simulations couldn't be highly representative of some original item?"
Well, now I know English ain't your first language. For the second time, "No misconception."
• simulatedto create a simulation, likeness, or model of.
• simulationthe act or process of pretending.
Now if I were to stick the definition for simulation into the definition for simulated, we get.
• simulatedto create an act or process of pretending, likeness, or model of.
I do know a university near me that has some of the best ESL classes...
BGBrainless: "I don't expect myself to be omniscient of any topic at all"
Nor do I. However, it seems I have infinitely more knowledge I can tap straight out of my brain than you do by copying and pasting from Wikipedia. Do you see me doing such to fill in my arguments? I was studying computers, computer science, and programming probably decades before you itched your daddy's loins. Even though I am a volcanologist, I still have to know computer programming. I am in the supporting role of field scientist and analyst. I love this role because I do not have to sit on my ass everyday I am at work. Sometimes, if I am needed for such, I get to drive and hike all over Yellowstone. Where are you at? Your mama's basement? Most often, if I ain't needed out in the field, I am at home on a secured server performing analyses for those guys who do write the journal papers. Of course, my name gets included, but I never require it. And in doing those analyses, I am using many different proprietary software that sometimes I actually have to write a new program to perform the analysis.
For the last time, THERE SHALL NEVER, EVER, BE ANY FORM OF TRUE ARTIFICIAL INTELLIGENCE. The best hoped for shall be a SIMULATED intelligence. If in doubt, see the definitions for "simulated" above.
BGBrainless: "I think you should remember that you are liable to be holding on to misconceptions."
Again, no misconceptions. Do you even know how to understand and comprehend English? Or are you going through a translator?
• simulated ‐ to create a simulation, likeness, or model of.
• simulationthe act or process of pretending.
Now if I were to stick the definition for simulation into the definition for simulated, we get.
• simulated ‐ to create aa act or process of pretending, likeness, or model of.
I do know a university near me that has some of the best ESL classes...
BGBrainless: "The key is to be willing to update your beliefs"
My beliefs ain't got a damn thing to do with it.
BGBrainless: "especially when you're clearly demonstrated to be wrong"
Which you have yet to do.
BGBrainless: "as is the case as is visible on "Wikipedia/Artificial General Intelligence", and "Wikipedia/Brain Simulation"."
And I have already read all that shit many years ago and still read scientific journal papers on the matter. Wikipedia is NOT an academic resource. The best Wikipedia can hope for is being referential jumping point for TRUE scientific academic resources.
In all the papers I have read, ALL say the best we shall ever hope for is SIMULATED intelligence, not true artificial intelligence.
It is tiresome dealing with childish, spoiled brats. Go back to school and quit skipping so many classes. Go do some research at some true science journal paper web sites.
And finally, you are a Religiious Absolutist. Just one proselytizing for "artificial intelligence" without even understanding what you are talking about. Someone else, LostLocke (?), has pointed out that you are cloning your posts from the Atheist Forums here at Atheist Republic. That is a sign of being a Religious Absolutist. You are shot down at one forums, thus you try your proselytizing at another forums. Only to get shot down again. If I had the power, I would banish your account and banish you from these boards. Did you notice Forum Guidelines Number 1) No trolling? As far as I concerned, proselytizing is the same as trolling.
Goodbye for now, childish, spoiled brat. Come back in ten years when you have finished primary school and perhaps graduated with a Bachelor's from a university.
rmfr
@ Avant Brown (Blue Grey Brainless)
BGBrainless: "Or could it mean that for quite a long while you've held on to the misconception that simulations couldn't be highly representative of some original item?"
Well, now I know English ain't your first language. For the second time, "No misconception."
simulated — to create a simulation, likeness, or model of.
simulation — the act or process of pretending.
Now if I were to stick the definition for simulation into the definition for simulated, we get.
simulated — to create an act or process of pretending, likeness, or model of.
I do know a university near me that has some of the best ESL classes...
BGBrainless: "I don't expect myself to be omniscient of any topic at all"
Nor do I. However, it seems I have infinitely more knowledge I can tap straight out of my brain than you do by copying and pasting from Wikipedia. Do you see me doing such to fill in my arguments? I was studying computers, computer science, and programming probably decades before you itched your daddy's loins. Even though I am a volcanologist, I still have to know computer programming. I am in the supporting role of field scientist and analyst. I love this role because I do not have to sit on my ass everyday I am at work. Sometimes, if I am needed for such, I get to drive and hike all over Yellowstone. Where are you at? Your mama's basement? Most often, if I ain't needed out in the field, I am at home on a secured server performing analyses for those guys who do write the journal papers. Of course, my name gets included, but I never require it. And in doing those analyses, I am using many different proprietary software that sometimes I actually have to write a new program to perform the analysis.
For the last time, THERE SHALL NEVER, EVER, BE ANY FORM OF TRUE ARTIFICIAL INTELLIGENCE. The best hoped for shall be a SIMULATED intelligence. If in doubt, see the definitions for "simulated" above.
BGBrainless: "I think you should remember that you are liable to be holding on to misconceptions."
Again, no misconceptions. Do you even know how to understand and comprehend English? Or are you going through a translator?
simulated ‐ to create a simulation, likeness, or model of.
simulation – the act or process of pretending.
Now if I were to stick the definition for simulation into the definition for simulated, we get.
simulated ‐ to create aa act or process of pretending, likeness, or model of.
I do know a university near me that has some of the best ESL classes...
BGBrainless: "The key is to be willing to update your beliefs"
My beliefs ain't got a damn thing to do with it.
BGBrainless: "especially when you're clearly demonstrated to be wrong"
Which you have yet to do.
BGBrainless: "as is the case as is visible on "Wikipedia/Artificial General Intelligence", and "Wikipedia/Brain Simulation"."
And I have already read all that shit many years ago and still read scientific journal papers on the matter. Wikipedia is NOT an academic resource. The best Wikipedia can hope for is being referential jumping point for TRUE scientific academic resources.
In all the papers I have read, ALL say the best we shall ever hope for is SIMULATED intelligence, not true artificial intelligence.
It is tiresome dealing with childish, spoiled brats. Go back to school and quit skipping so many classes. Go do some research at some true science journal paper web sites.
And finally, you are a Religiious Absolutist. Just one proselytizing for "artificial intelligence" without even understanding what you are talking about. Someone else, LostLocke (?), has pointed out that you are cloning your posts from the Atheist Forums here at Atheist Republic. That is a sign of being a Religious Absolutist. You are shot down at one forums, thus you try your proselytizing at another forums. Only to get shot down again. If I had the power, I would banish your account and banish you from these boards. Did you notice Forum Guidelines Number 1) No trolling? As far as I concerned, proselytizing is the same as trolling.
Goodbye for now, childish, spoiled brat. Come back in ten years when you have finished primary school and perhaps graduated with a Bachelor's from a university.
rmfr
1. I am now doing PhD work, in artificial intelligence, so it is possible that I know a bit more than you in this scenario.
2. You still refuse to accept that you had misconceived, that simulations couldn't in theory, capture a quite high level of detail of some source. [Wikipedia/Brain simulation, Wikipedia/Artificial General Intelligence.]
3. Now, you can update your beliefs regarding the nature of brain simulations, or continue to supply your feelings on the matter. I've come to learn through many difficult years, that facts don't care about feelings. You should probably stitch that into your being. Also, try using citations/sources in your responses. You may learn a thing or two from practicing this habit, both on these forums, and in life elsewhere.
@ Avant Brown
PhD work, huh? Yeah right. Then you should know that Wikipedia is NOT an academic resource.
rmfr
@ Avant Brown
PhD work, huh? Yeah right. Then you should know that Wikipedia is NOT an academic resource.
rmfr
Yes, that's quite right, PhD work.
This means I can sometimes trivially determine when one is expressing nonsense, as is seen in many of your responses thus far.
It is strange that you feel a resource that may be simplified, is suddenly not academic. By that measure, some silly outcomes arise, such as simplified lectures in pedagogical settings, now being "non-academic" by your imagination.
"I am now doing PhD work, in artificial intelligence, so it is possible that I know a bit more than you in this scenario."
I doubt that for many reasons. The fact that you cite Wiki as your prime reference source reeks of a lack of imagination and ability to be creative. And I cannot see anyone with your abilities as a candidate for a viable thesis.
"I am now doing PhD work, in artificial intelligence, so it is possible that I know a bit more than you in this scenario."
I doubt that for many reasons. The fact that you cite Wiki as your prime reference source reeks of a lack of imagination and ability to be creative. And I cannot see anyone with your abilities as a candidate for a viable thesis.
1. Where did I cite Wikipedia, as a primary source? I particularly mentioned, that Wikipedia is an academic source, not a primary source. [See Wikipedia/Strawman fallacy.]
2. I am the only one on the forum, that encouraged the referencing of sources, as often as possible. You should probably aim to re-evaluate the abilities you feel you have; i.e. I don't recall a single response from you, with valid sources.
3. One can be quite creative, [like the authors of the hypotheses concerning the OP] while still referencing sources to substantiate one's arguments. I too have also come to hypothesize a scientific purpose regarding the human species based on one of the hypotheses presented in the OP, although I did not cite it in the OP.
Have you ever attempted to develop that type of thought, of course, using evidence? Or are you still of the opinion that life is either purposeless, or the usual opinion that the species seeks to enable gene survival?
A human being (like all life forms) has two biological imperatives. That is to survive (food and protection) and propagate by reproduction.
A human being (like all life forms) has two biological imperatives. That is to survive (food and protection) and propagate by reproduction.
• What you note above, is reasonably the strongest, most established scientific picture we have today, although it may not be the most advanced.
For example, the hypothesis in the OP regarding AGI, takes a look at the picture you cite above, and seeks to search for additional possibilities based on evolutionary principle [as included in said picture], but also entropy as it relates to biological general intelligence, which is not explored in the traditional picture except for in the AGI/human purpose hypothesis from the OP, as far as I am aware.
• ~
• Dawkins underlines that genes may not be so concerned for survival, but the AGI/human purpose hypothesis underscores that additionally, that general intelligence may be the thing that survives, and since humans may not necesarily be approximating behaviours that facilitate the survival of genes, general intelligence may "survive" in the form of artificial general intelligence..
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Cody
# David
Rank
Score
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#### Speed Demon+50
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#### Community Group Solver+50
Solve a community group
#### CUP Challenge Master+50
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#### Introduction to MATLAB Master+50
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#### Creator+20
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#### Curator+50
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# 100228900 (number)
100,228,900 (one hundred million two hundred twenty-eight thousand nine hundred) is an even nine-digits composite number following 100228899 and preceding 100228901. In scientific notation, it is written as 1.002289 × 108. The sum of its digits is 22. It has a total of 5 prime factors and 18 positive divisors. There are 40,091,520 positive integers (up to 100228900) that are relatively prime to 100228900.
## Basic properties
• Is Prime? No
• Number parity Even
• Number length 9
• Sum of Digits 22
• Digital Root 4
## Name
Short name 100 million 228 thousand 900 one hundred million two hundred twenty-eight thousand nine hundred
## Notation
Scientific notation 1.002289 × 108 100.2289 × 106
## Prime Factorization of 100228900
Prime Factorization 22 × 52 × 1002289
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 5 Total number of prime factors rad(n) 10022890 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 100,228,900 is 22 × 52 × 1002289. Since it has a total of 5 prime factors, 100,228,900 is a composite number.
## Divisors of 100228900
18 divisors
Even divisors 12 6 6 0
Total Divisors Sum of Divisors Aliquot Sum τ(n) 18 Total number of the positive divisors of n σ(n) 2.17497e+08 Sum of all the positive divisors of n s(n) 1.17268e+08 Sum of the proper positive divisors of n A(n) 1.20832e+07 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 10011.4 Returns the nth root of the product of n divisors H(n) 8.29492 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 100,228,900 can be divided by 18 positive divisors (out of which 12 are even, and 6 are odd). The sum of these divisors (counting 100,228,900) is 217,496,930, the average is 120,831,62.,777.
## Other Arithmetic Functions (n = 100228900)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 40091520 Total number of positive integers not greater than n that are coprime to n λ(n) 5011440 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 5766529 Total number of primes less than or equal to n r2(n) 24 The number of ways n can be represented as the sum of 2 squares
There are 40,091,520 positive integers (less than 100,228,900) that are coprime with 100,228,900. And there are approximately 5,766,529 prime numbers less than or equal to 100,228,900.
## Divisibility of 100228900
m n mod m 2 3 4 5 6 7 8 9 0 1 0 0 4 2 4 4
The number 100,228,900 is divisible by 2, 4 and 5.
• Abundant
• Polite
## Base conversion (100228900)
Base System Value
2 Binary 101111110010101111100100100
3 Ternary 20222121011012111
4 Quaternary 11332111330210
5 Quinary 201124311100
6 Senary 13540130404
8 Octal 576257444
10 Decimal 100228900
12 Duodecimal 29696a04
20 Vigesimal 1b68c50
36 Base36 1no944
## Basic calculations (n = 100228900)
### Multiplication
n×y
n×2 200457800 300686700 400915600 501144500
### Division
n÷y
n÷2 5.01144e+07 3.34096e+07 2.50572e+07 2.00458e+07
### Exponentiation
ny
n2 10045832395210000 1006882730556263569000000 100918748512650685630944100000000 10114975152799614305035333104490000000000
### Nth Root
y√n
2√n 10011.4 464.513 100.057 39.8289
## 100228900 as geometric shapes
### Circle
Diameter 2.00458e+08 6.29757e+08 3.15599e+16
### Sphere
Volume 4.21762e+24 1.2624e+17 6.29757e+08
### Square
Length = n
Perimeter 4.00916e+08 1.00458e+16 1.41745e+08
### Cube
Length = n
Surface area 6.0275e+16 1.00688e+24 1.73602e+08
### Equilateral Triangle
Length = n
Perimeter 3.00687e+08 4.34997e+15 8.68008e+07
### Triangular Pyramid
Length = n
Surface area 1.73999e+16 1.18662e+23 8.18366e+07
## Cryptographic Hash Functions
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Does the fact that we can parametrize surfaces rely on Fubini's theorem?
When learning about double integrals, we learn that the only way we can do them is if Fubini's theorem applies (or maybe I should say, the only way I learned to do them in that one class). But then when we went over surface integrals, we could always find a parametrization so that we could convert our surface integral (which looks an awful lot like a double integral) into an iterated integral.
Is Fubini's theorem the reason we can always convert a surface integral into an iterated integral? If so, how?
No it isn't. There's a theorem that says that all "manifolds" (in your case, ignore this word and substitute the word "surfaces") are locally graphs. That is to say: we can always cut them up into pieces that look like
$$y=f(x_1,\ldots, x_n)$$
in your case this means pieces that look like
$$z=f(x,y)$$
which is a parametrization for that piece of the surface in question. Then you can add up the pieces.
Fubini's theorem only refers to the ability to interchange the order of integration on a given piece.
Edit: I should emphasize: do not try to do this in practice. The theorem is out there to ensure that the parametrizations actually exist so we can satisfy the definition, in real life we find ways around this to do integration in a more intelligent way, and I was just answering the question you asked which was: "is Fubini responsible?"
• This is misleading, as typically we do surface integrals parametrically (e.g., spherical coordinates $(\phi,\theta)$ or cylindrical coordinates $(z,\theta)$) over a region in the parameter space. It is less common to split into explicit graphs. – Ted Shifrin Jul 11 '14 at 20:57
• Yes, I tried to emphasize this is only "possible" from an abstract standpoint, I'll edit to try and put more oomph into "don't actually try to do this in practice." – Adam Hughes Jul 11 '14 at 21:00
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# 2-Variable Inequality
Topics: Dimension, Number, René Descartes Pages: 3 (513 words) Published: February 2, 2014
2-Variable Inequality
Here is an example of a problem very similar to the one in the Week Three Assignment: Catskills Hammock Company can obtain at most 2000 yards of striped canvas for making its full size and chair size hammocks. A full size hammock requires 10 yards of canvas and the chair size requires 5 yards of canvas. Write an inequality that limits the number of striped hammocks of each type which can be made.
(b) First I must define what variables I will be using in my inequality.
Let f = the number of full size hammocks
Let c = the number of chair size hammocks
Since each full size hammock requires 10 yards of canvas I will use 10f, and since each chair hammock requires 5 yards of canvas I will use 5c. The total amount of canvas which can be used is limited to 2000 yards because that is all they can get. Together my inequality will look like this:
10f + 5c ≤ 2000
(d) If we call f the independent variable (on the horizontal axis) and c the dependent variable (on the vertical axis) then we can graph the equation using the intercepts.
The f-intercept is found when c = 0:
10f ≤ 2000
f ≤ 200 The f-intercept is (200, 0).
The c-intercept is found when f = 0:
5c ≤ 2000
c ≤ 400 The c-intercept is (0, 400).
Because this is a “less than or equal to” inequality the line will be solid, sloping downward as it moves from left to right. The region of the graph which is relevant to this problem is restricted to the first quadrant, so the shaded section is from the line towards the origin and stops at the two axes.
(e) Consider the point (105, 175) on my graph. It is inside the shaded area which means the company could fill an order of 105 full size hammocks and 175 chair hammocks. If they made up this many items they would use
105(10) + 175(5) = 1925 yards of striped canvas and have 75 yards left over.
Consider the point (150, 125) on the graph. It is outside the shaded area which means the company...
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https://www.emodel.org.ua/en/archive/2020/42-5/42-5-6
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# FEATURES OF THE ANALYSIS OF PHYSICAL STABILITY OF STEADY-STATE MODES OF AC ELECTRICAL SYSTEMS
S.I. Klipkov
Èlektron. model. 2020, 42(5):82-96
https://doi.org/10.15407/emodel.42.05.082
### ABSTRACT
The mathematical properties of nonlinear complex equations of steady-state modes of electrical systems as monoanalytic functions of many variables are investigated. The existing concepts of formal partial derivatives and the areolar derivative of polyanalytic functions are based on the assumption that complex variables are independent z and , at the same time, do not allow the existence of other complex variables. Therefore, the linearization of the system of nonlinear complex equations for the analysis of their physical stability is proposed to be performed using the pseudo-derivative of complex power, as a polygenic function of many variables with an infinite number of values. A possible approach to the construction of the limiting surface that bounds the region of physically stable modes is proposed. It is shown that splitting complex equations into two real equations is incorrect for the analysis of physical stability, since mathematical operations with real equations do not take into account the composition laws of a system of complex numbers.
### KEYWORDS
steady state, monoanalytical functions of many complex variables, pseudo-derivative of polygenic function, hypercomplex numbers, physical stability.
### REFERENCES
1. Kasner, E. (1936), “A complete characterization of the derivative of a polygenic function”, the Proceedings of the National Academy of Sciences, Vol. 22, pp. 172-177.
https://doi.org/10.1073/pnas.22.3.172
2. Petrov A.M. (2006), Kvaternionnoye predstavleniye vikhrevykh dvizheniy [Quaternion representation of vortex motions, Kompaniya Sputnik+, Moscow, Russia.
3. Klipkov S.I. (2019), “Quaternion Analysis of Electrical System Modes”, Elektronnoye modelirovaniye, Vol. 41, no. 6, pp. 15-35.
https://doi.org/10.15407/emodel.41.06.015
4. Fedorovskiy, K.Yu. (2016), Approksimatsiya polianaliticheskimi mnogochlenami [Approximation by polyanalytic polynomials], IPM im. M.V. Keldysha, Moscow, Russia.
5. Balk M.B. (1991),Polyanalytic functions and their generalizations”, Itogi nauki i tekhn. Sovrem. probl. Matem. Fundam. Napravleniya, Vol. 85, pp. 187-246.
6. Sekene, Y. and Yokojama, A. (1981), “Multisolutions for load flow problem of power System and their physical stability”, the Proceeding of 7th Power Syst. Comput. Conf, Lausanne, pp. 819-826.
7. Klipkov, S.I. (2012), “The use of hypercomplex numerical systems for mathematical modeling of the limiting modes of electrical systems”, Reestratsiya, zberigannya i obrob. danykh, 14, no. 4, pp. 11-23.
8. Klipkov, S.I. (2011), “On a new approach to the construction of hypercomplex number systems of rank two over the field of complex numbers”, Mat. Zhurn, Vol. 63, no. 1, pp. 130-139.
https://doi.org/10.1007/s11253-011-0494-z
9. Sin’kov, M.V., Boyarinova, Yu.Ye. and Kalinovskiy, Ya.A. (2010), Konechnomernyye giperkompleksnyye chislovyye sistemy. Osnovy teorii. Primeneniya [Finite-dimensional hypercomplex number systems. Foundations of the theory. Applications], Infodruk, Kiev, Ukraine.
10. Klipkov,I. (2010),Using a harmonic approach to the analysis of the limit modes of AC electrical systems”, Elektricheskiye seti & sistemy, no. 6, pp. 71-82.
11. Klipkov, S.I. (2015), “Features of harmonic analysis of limiting modes of electrical systems”, Elektronnoye modelirovaniye, Vol. 37, no. 1, pp. 113-127.
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# Electrostatics Chapter 32. Electrical forces arise from particles in atoms Electrons are attracted to protons. This holds electrons in orbits around the.
## Presentation on theme: "Electrostatics Chapter 32. Electrical forces arise from particles in atoms Electrons are attracted to protons. This holds electrons in orbits around the."— Presentation transcript:
Electrostatics Chapter 32
Electrical forces arise from particles in atoms Electrons are attracted to protons. This holds electrons in orbits around the nucleus of an atom Opposite charges attract Like charges repel All electrons are identical Atoms usually have as many electrons as protons, so the atom has a net charge of zero. An ion is produced when an atom gains or loses an electron An atom with more positive charge than negative charge is called a cation An atom with more negative charge than positive charge is called an anion
Electrical vs Gravitational Force Which is stronger? Electrical or Gravitational force? It turns out that Electrical force is 1 x 10 36 times stronger than gravitational force! 1,000,000,000,000,000,000,000,000,000,000,000,000 Newtons law of gravitation states that the force of gravity between two objects is proportional to their mass. We feel a strong pull on us due to Earth’s gravity, but this is because the mass of the Earth is very large compared to us. F G = G m 1 m 2 d 2
Coulomb’s Law When an atom becomes positively or negatively charged, there is a transfer of electrons Conservation of Charge states that at all levels macroscopic or microscopic, electric charge is neither created or destroyed. Electric force between two objects operates similar manner
The coulomb is the SI unit of charge 1 coulomb (C) = 6.24 x 10 18 electrons (q) k = Coulomb’s Law Constant (9 x 10 9 N*m 2 /C 2 ) d = distance between charges q 1 q 2 d 2 F = k
Materials through which electrons are able to move easily are called good conductors of electricity Examples of good conductors: silver copper gold aluminum iron steel Materials that resist the flow of electrons through them are called good insulators of electricity Examples of good insulators rubber wood glass styrofoam Conductors vs Insulators
Friction vs Induction Electrons can be transferred from one surface to another by friction “If the object is a good conductor, the charge will spread to all parts of its surface because the like charges repel each other” - Hewitt p. 509
Lightning in thunderstorms is produced by friction between water droplets and/or hail within a cloud. Lightning can also be produced by friction between ash particles in volcanic eruptions (above). http://www.supertightstuff.com/02/02/pictures/tight-pictures/volcanoes-and-lightning/
Electrons can move in a conducting surface when a charge object is moved close to it. This can occur even without contact between the two surfaces. A charge is said to be induced in the spheres. (see above)
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Starting from some term, all its terms are equal); evidently, this is an equivalent formulation. Let a sequence of pairs (x0 , y0 ) ≥ (x1 , y1 ) ≥ (x2 , y2 ) ≥ · · · be given. By the definition of the ordering (second terms are compared first), we have y0 ≥ y1 ≥ y2 ≥ · · · , and therefore the sequence yi of nonnegative integers stabilizes. After this, the sequence xi must be nonincreasing, and therefore it stabilizes, too. The same argument is applicable to a more general situation. Theorem 16.
The first argument belongs to B, and the second to C. If we fix the second argument, we get a function fc : B → A, defined as fc (b) = f (b, c) (to be formal, we should write f ( b, c ) instead of f (b, c)). The mapping c → fc belongs to (AB )C and corresponds to an element f ∈ AB×C . ) Cardinality of countable sets is denoted by ℵ0 . The continuum cardinality (the cardinality of R or the set of infinite sequences of zeros and ones) is denoted by c. By definition, c = 2ℵ0 . A curious reader would ask: what does subscript 0 in ℵ0 mean?
Theorem 8 has appeared in Cantor’s paper dated 1890/91. Cantor considers functions with values 0 and 1 instead of subsets. Now we have come close to the dangerous point where our intuition about sets becomes self-contradictory. Consider the “universal” set U that consists of all sets. Then all subsets of U are elements of U and therefore P (U ) ⊂ U . This contradicts Cantor’s Theorem. 28 1. Sets and Their Cardinalities We can unfold this argument and get the so-called Russell’s paradox . Traditionally, Russell’s paradox is explained as follows.
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Rock Street, San Francisco
The problem of transport is the particular problem of linear programming must affect the optimal amount of a product that are transported from different points at different points in the request for the cost of transportation of a minimum (Hillier and Liberia, 2001).There is a lot of literature on the subject of the investigation on the issue of transport.Due to certain uncontrollable factors, hunters, and Zadeh (1970), and Zadeh (1978), the concept of a clear solution quantitatively with inaccurate information in decision-making in many situations of demand and/or supply and the cost of coefficients of a transportation problem can be unsafe.Zimmermann (1978), has shown that the solutions through linear programming always effectively. Subsequently, Zimmermann developed a linear programming ambiguous vague in several methods for the optimization of the solution of transport problems.In many real life situations, it is not possible to determine that both the unit cost of transportation and the quantities, but the numbers are unclear, which provides a better approximation of them. OhEigeartaigh (1982) considers that if the composition of demand functions are unclear, triangular shapes of Verkehrsprobleme has been resolved and that the method of the table. And Chanas Kulej (1984) proposed a method for solving a linear programming problem defined at all with triangular membership functions resources. Chanas et al. (1984) presented a model of linear programming confusing to solve transport problems with supply and demand and the values of the coefficient of costs. Lai and Hwang (1992), the transport model, the solution of the problem, when the quantities are unclear and the prices are net prices. Kuchta Chanas and (1996), the concept of the best solution to the problem of the circulation of the coefficients confusing algorithme expressed clear figures and developed to obtain the optimal solution. Kuchta Chanas and (1998), have a algorithme, resolves the problem of the circulation of the values of supply and demand, and the whole of the issue of the solution. Liu and Kao (2004) has established a procedure for the determination of the value of the clear objective clear transportation problem, the amount of the supply and demand and the cost of the coefficients are many, of course, is based on the principle of enlargement.Kumar and Kaur (2011) proposed two new methods to solve transportation unclear to overcome the weaknesses and limitations of current methods. You have shown that it is better to the use of the methods proposed with regard to the current methods to resolve some problems of transport is not clear. Murugesan and Kumar (2012) provided an optimal solution for the transport defined at all with triangular membership functions. Have occupied a new triangular operations arithmetiques confused with figures of the best solutions.
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SI Format Determining Place and Value from Ones to Hundred Millions (Large Print) (C)
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In Progress
Lesson 41, Topic 2
In Progress
# Travelling Sales Person Problem
##### Akash
Lesson Progress
0% Complete
We will be able to apply the branch-and-bound technique to instances of the traveling salesman problem if we come up with a reasonable lower bound on tour lengths. One very simple lower bound can be obtained by finding the smallest element in the intercity distance matrix D and multiplying it by the number of cities n. But there is a less obvious and more informative lower bound for instances with symmetric matrix D, which does not require a lot of work to compute. It is not difficult to show that we can compute a lower bound on the length l of any tour as follows. For each city i, 1 ≤ i ≤ n, find the sum si of the distances from city i to the two nearest cities; compute the sum s of these n numbers, divide the result by 2, and, if all the distances are integers, round up the result to the nearest integer:
lb = [s/2] —formula (a)
For example, for the instance in Figure a, formula (a) yields
lb = [[(1 + 3) + (3 + 6) + (1 + 2) + (3 + 4) + (2 + 3)]/2] = 14.
Moreover, for any subset of tours that must include particular edges of a given graph, we can modify lower bound (a) accordingly. For example, for all the Hamiltonian circuits of the graph in Figure a that must include edge (a, d), we get the following lower bound by summing up the lengths of the two shortest edges incident with each of the vertices, with the required inclusion of edges(a, d) and (d, a):
[[(1 + 5) + (3 + 6) + (1 + 2) + (3 + 5) + (2 + 3)]/2] = 16.
We now apply the branch-and-bound algorithm, with the bounding function given by formula (a), to find the shortest Hamiltonian circuit for the graph in Figure a. To reduce the amount of potential work, we take advantage of two observations. First, without loss of generality, we can consider only tours that start at a. Second, because our graph is undirected, we can generate only tours in which b is visited before c. In addition, after visiting n − 1 = 4 cities, a tour has no choice but to visit the remaining unvisited city and return to the starting one. The state-space tree tracing the algorithm’s application is given in Figure b.
To reiterate the main point: these state-space tree techniques enable us to solve many large instances of difficult combinatorial problems. As a rule, however, it is virtually impossible to predict which instances will be solvable in a realistic amount of time and which will not.
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09_Neural_Networks_Learning
09: Neural Networks - Learning
Neural network cost function
• NNs - one of the most powerful learning algorithms
• Is a learning algorithm for fitting the derived parameters given a training set
• Let's have a first look at a neural network cost function
• Focus on application of NNs for classification problems
• Here's the set up
• Training set is {(x1, y1), (x2, y2), (x3, y3) ... (xn, ym)
• L = number of layers in the network
• In our example below L = 4
• sl = number of units (not counting bias unit) in layer l
• So here
• l = 4
• s1 = 3
• s2 = 5
• s3 = 5
• s4 = 4
Types of classification problems with NNs
• Two types of classification, as we've previously seen
• Binary classification
• 1 output (0 or 1)
• So single output node - value is going to be a real number
• k = 1
• NB k is number of units in output layer
• sL = 1
• Multi-class classification
• k distinct classifications
• Typically k is greater than or equal to three
• If only two just go for binary
• sL = k
• So y is a k-dimensional vector of real numbers
Cost function for neural networks
• The (regularized) logistic regression cost function is as follows;
• For neural networks our cost function is a generalization of this equation above, so instead of one output we generate k outputs
• Our cost function now outputs a k dimensional vector
• hƟ(x) is a k dimensional vector, so hƟ(x)i refers to the ith value in that vector
• Costfunction J(Ɵ) is
• [-1/m] times a sum of a similar term to which we had for logic regression
• But now this is also a sum from k = 1 through to K (K is number of output nodes)
• Summation is a sum over the k output units - i.e. for each of the possible classes
• So if we had 4 output units then the sum is k = 1 to 4 of the logistic regression over each of the four output units in turn
• This looks really complicated, but it's not so difficult
• We don't sum over the bias terms (hence starting at 1 for the summation)
• Even if you do and end up regularizing the bias term this is not a big problem
• Is just summation over the terms
Woah there - lets take a second to try and understand this!
• There are basically two halves to the neural network logistic regression cost function
First half
• This is just saying
• For each training data example (i.e. 1 to m - the first summation)
• Sum for each position in the output vector
• This is an average sum of logistic regression
Second half
• This is a massive regularization summation term, which I'm not going to walk through, but it's a fairly straightforward triple nested summation
• This is also called a weight decay term
• As before, the lambda value determines the important of the two halves
• The regularization term is similar to that in logistic regression
• So, we have a cost function, but how do we minimize this bad boy?!
Summary of what's about to go down
The following section is, I think, the most complicated thing in the course, so I'm going to take a second to explain the general idea of what we're going to do;
• We've already described forward propagation
• This is the algorithm which takes your neural network and the initial input into that network and pushes the input through the network
• It leads to the generation of an output hypothesis, which may be a single real number, but can also be a vector
• We're now going to describe back propagation
• Back propagation basically takes the output you got from your network, compares it to the real value (y) and calculates how wrong the network was (i.e. how wrong the parameters were)
• It then, using the error you've just calculated, back-calculates the error associated with each unit from the preceding layer (i.e. layer L - 1)
• This goes on until you reach the input layer (where obviously there is no error, as the activation is the input)
• These "error" measurements for each unit can be used to calculate the partial derivatives
• Partial derivatives are the bomb, because gradient descent needs them to minimize the cost function
• We use the partial derivatives with gradient descent to try minimize the cost function and update all the Ɵ values
• This repeats until gradient descent reports convergence
• A few things which are good to realize from the get go
• There is a Ɵ matrix for each layer in the network
• This has each node in layer l as one dimension and each node in l+1 as the other dimension
• Similarly, there is going to be a Δ matrix for each layer
• This has each node as one dimension and each training data example as the other
Back propagation algorithm
• We previously spoke about the neural network cost function
• Now we're going to deal with back propagation
• Algorithm used to minimize the cost function, as it allows us to calculate partial derivatives!
• The cost function used is shown above
• We want to find parameters Ɵ which minimize J(Ɵ)
• To do so we can use one of the algorithms already described such as
• To minimize a cost function we just write code which computes the following
• J(Ɵ)
• i.e. the cost function itself!
• Use the formula above to calculate this value, so we've done that
• Partial derivative terms
• So now we need some way to do that
• This is not trivial! Ɵ is indexed in three dimensions because we have separate parameter values for each node in each layer going to each node in the following layer
• i.e. each layer has a Ɵ matrix associated with it!
• We want to calculate the partial derivative Ɵ with respect to a single parameter
• Remember that the partial derivative term we calculate above is a REAL number (not a vector or a matrix)
• Ɵ is the input parameters
• Ɵ1 is the matrix of weights which define the function mapping from layer 1 to layer 2
• Ɵ101 is the real number parameter which you multiply the bias unit (i.e. 1) with for the bias unit input into the first unit in the second layer
• Ɵ111 is the real number parameter which you multiply the first (real) unit with for the first input into the first unit in the second layer
• Ɵ211 is the real number parameter which you multiply the first (real) unit with for the first input into the second unit in the second layer
• As discussed, Ɵijl i
• i here represents the unit in layer l+1 you're mapping to (destination node)
• j is the unit in layer l you're mapping from (origin node)
• l is the layer your mapping from (to layer l+1) (origin layer)
• NB
• The terms destination node, origin node and origin layer are terms I've made up!
• So - this partial derivative term is
• The partial derivative of a 3-way indexed dataset with respect to a real number (which is one of the values in that dataset)
• One training example
• Imagine we just have a single pair (x,y) - entire training set
• How would we deal with this example?
• The forward propagation algorithm operates as follows
• Layer 1
• a1 = x
• z2 = Ɵ1a1
• Layer 2
• a2 = g(z2) (add a02)
• z3 = Ɵ2a2
• Layer 3
• a3 = g(z3) (add a03)
• z4 = Ɵ3a3
• Output
• a4 = hƟ(x) = g(z4)
• This is the vectorized implementation of forward propagation
• Lets compute activation values sequentially (below just re-iterates what we had above!)
What is back propagation?
• Use it to compute the partial derivatives
• Before we dive into the mechanics, let's get an idea regarding the intuition of the algorithm
• For each node we can calculate jl) - this is the error of node j in layer l
• If we remember, ajl is the activation of node j in layer l
• Remember the activation is a totally calculated value, so we'd expect there to be some error compared to the "real" value
• The delta term captures this error
• But the problem here is, "what is this 'real' value, and how do we calculate it?!"
• The NN is a totally artificial construct
• The only "real" value we have is our actual classification (our y value) - so that's where we start
• If we use our example and look at the fourth (output) layer, we can first calculate
• δj= ajyj
• [Activation of the unit] - [the actual value observed in the training example]
• We could also write ajas hƟ(x)j
• Although I'm not sure why we would?
• This is an individual example implementation
• δ= ay
• So here δis the vector of errors for the 4th layer
• ais the vector of activation values for the 4th layer
• With δcalculated, we can determine the error terms for the other layers as follows;
• Taking a second to break this down
• Ɵis the vector of parameters for the 3->4 layer mapping
• δis (as calculated) the error vector for the 4th layer
• g'(z3) is the first derivative of the activation function g evaluated by the input values given by z
• You can do the calculus if you want (...), but when you calculate this derivative you get
• g'(z3) = a. * (1 - a3)
• So, more easily
• δ= (Ɵ3)δ. *(a. * (1 - a3))
• . * is the element wise multiplication between the two vectors
• Why element wise? Because this is essentially an extension of individual values in a vectorized implementation, so element wise multiplication gives that effect
• We highlighted it just in case you think it's a typo!
Analyzing the mathematics
• And if we take a second to consider the vector dimensionality (with our example above [3-5-5-4])
• Ɵ3 = is a matrix which is [4 X 5] (if we don't include the bias term, 4 X 6 if we do)
• (Ɵ3)T = therefore, is a [5 X 4] matrix
• δ4 = is a 4x1 vector
• So when we multiply a [5 X 4] matrix with a [4 X 1] vector we get a [5 X 1] vector
• Which, low and behold, is the same dimensionality as the a3 vector, meaning we can run our pairwise multiplication
• For δwhen you calculate the derivative terms you get
a. * (1 -
a3)
• Similarly For δ2 when you calculate the derivative terms you get
a. * (1 -
a2)
• So to calculate δ2 we do
δ= (Ɵ2)δ3 . *(a. * (1 - a2))
• There's no δ1 term
• Because that was the input!
Why do we do this?
• We do all this to get all the δ terms, and we want the δ terms because through a very complicated derivation you can use δ to get the partial derivative of Ɵ with respect to individual parameters (if you ignore regularization, or regularization is 0, which we deal with later)
• = ajδi(l+1)
• By doing back propagation and computing the delta terms you can then compute the partial derivative terms
• We need the partial derivatives to minimize the cost function!
Putting it all together to get the partial derivatives!
• What is really happening - lets look at a more complex example
• Training set of m examples
• First, set the delta values
• Set equal to 0 for all values
• Eventually these Δ values will be used to compute the partial derivative
• Will be used as accumulators for computing the partial derivatives
• Next, loop through the training set
• i.e. for each example in the training set (dealing with each example as (x,y)
• Set a(activation of input layer) = xi
• Perform forward propagation to compute afor each layer (l = 1,2, ... L)
• i.e. run forward propagation
• Then, use the output label for the specific example we're looking at to calculate δL where δ= a- yi
• So we initially calculate the delta value for the output layer
• Then, using back propagation we move back through the network from layer L-1 down to layer
• Finally, use Δ to accumulate the partial derivative terms
• Note here
• l = layer
• j = node in that layer
• i = the error of the affected node in the target layer
• You can vectorize the Δ expression too, as
• Finally
• After executing the body of the loop, exit the for loop and compute
• When j = 0 we have no regularization term
• At the end of ALL this
• You've calculated all the D terms above using Δ
• NB - each D term above is a real number!
• We can show that each D is equal to the following
• We have calculated the partial derivative for each parameter
• We can then use these in gradient descent or one of the advanced optimization algorithms
• Phew!
• What a load of hassle!
Back propagation intuition
• Some additionally back propagation notes
• In case you found the preceding unclear, which it shouldn't be as it's fairly heavily modified with my own explanatory notes
• Back propagation is hard(ish...)
• But don't let that discourage you
• It's hard in as much as it's confusing - it's not difficult, just complex
• Looking at mechanical steps of back propagation
Forward propagation with pictures!
• Feeding input into the input layer (xiyi)
• Note that x and y here are vectors from 1 to n where n is the number of features
• So above, our data has two features (hence x1 and x2)
• With out input data present we use forward propagation
• The sigmoid function applied to the z values gives the activation values
• Below we show exactly how the z value is calculated for an example
Back propagation
• With forwardprop done we move on to do back propagation
• Back propagation is doing something very similar to forward propagation, but backwards
• Very similar though
• Let's look at the cost function again...
• Below we have the cost function if there is a single output (i.e. binary classification)
• This function cycles over each example, so the cost for one example really boils down to this
• Which, we can think of as a sigmoidal version of the squared difference (check out the derivation if you don't believe me)
• So, basically saying, "how well is the network doing on example "?
• We can think about a δ term on a unit as the "error" of cost for the activation value associated with a unit
• Where cost is as defined above
• Cost function is a function of y value and the hypothesis function
• So - for the output layer, back propagation sets the δ value as [a - y]
• Difference between activation and actual value
• We then propagate these values backwards;
• Looking at another example to see how we actually calculate the delta value;
• So, in effect,
• Back propagation calculates the δ, and those δ values are the weighted sum of the next layer's delta values, weighted by the parameter associated with the links
• Forward propagation calculates the activation (a) values, which
• Depending on how you implement you may compute the delta values of the bias values
• However, these aren't actually used, so it's a bit inefficient, but not a lot more!
Implementation notes - unrolling parameters (matrices)
• Needed for using advanced optimization routines
• Is the MATLAB/octave code
• But theta is going to be matrices
• fminunc takes the costfunction and initial theta values
• These routines assume theta is a parameter vector
• Also assumes the gradient created by costFunction is a vector
• For NNs, our parameters are matrices
• e.g.
Example
• Use the thetaVec = [ Theta1(:); Theta2(:); Theta3(:)]; notation to unroll the matrices into a long vector
• To go back you use
• Theta1 = resape(thetaVec(1:110), 10, 11)
• Backpropagation has a lot of details, small bugs can be present and ruin it :-(
• This may mean it looks like J(Ɵ) is decreasing, but in reality it may not be decreasing by as much as it should
• So using a numeric method to check the gradient can help diagnose a bug
• Gradient checking helps make sure an implementation is working correctly
• Example
• Have an function J(Ɵ)
• Estimate derivative of function at point Ɵ (where Ɵ is a real number)
• How?
• Numerically
• Compute Ɵ + ε
• Compute Ɵ - ε
• Join them by a straight line
• Use the slope of that line as an approximation to the derivative
• Usually, epsilon is pretty small (0.0001)
• If epsilon becomes REALLY small then the term BECOMES the slopes derivative
• The is the two sided difference (as opposed to one sided difference, which would be J(Ɵ + ε) - J(Ɵ) /ε
• If Ɵ is a vector with n elements we can use a similar approach to look at the partial derivatives
• So, in octave we use the following code the numerically compute the derivatives
• So on each loop thetaPlus = theta except for thetaPlus(i)
• Resets thetaPlus on each loop
• Create a vector of partial derivative approximations
• Using the vector of gradients from backprop (DVec)
• Check that gradApprox is basically equal to DVec
• Gives confidence that the Backproc implementation is correc
• Implementation note
• Implement back propagation to compute DVec
• Check they're basically the same (up to a few decimal places)
• Before using the code for learning turn off gradient checking
• Why?
• GradAprox stuff is very computationally expensive
• In contrast backprop is much more efficient (just more fiddly)
Random initialization
• Pick random small initial values for all the theta values
• If you start them on zero (which does work for linear regression) then the algorithm fails - all activation values for each layer are the same
• So chose random values!
• Between 0 and 1, then scale by epsilon (where epsilon is a constant)
Putting it all together
• 1) - pick a network architecture
• Number of
• Input units - number of dimensions x (dimensions of feature vector)
• Output units - number of classes in classification problem
• Hidden units
• Default might be
• 1 hidden layer
• Should probably have
• Same number of units in each layer
• Or 1.5-2 x number of input features
• Normally
• More hidden units is better
• But more is more computational expensive
• We'll discuss architecture more later
• 2) - Training a neural network
• 2.1) Randomly initialize the weights
• Small values near 0
• 2.2) Implement forward propagation to get hƟ(x)i for any xi
• 2.3) Implement code to compute the cost function J(Ɵ)
• 2.4) Implement back propagation to compute the partial derivatives
• General implementation below
for i = 1:m {
Forward propagation on (xiyi) --> get activation (a) terms
Back propagation on (xiyi) --> get delta (δ) terms
Compute Δ := Δl + δl+1(al)T
}
With this done compute the partial derivative terms
• Notes on implementation
• Usually done with a for loop over training examples (for forward and back propagation)
• Can be done without a for loop, but this is a much more complicated way of doing things
• Be careful
• 2.5) Use gradient checking to compare the partial derivatives computed using the above algorithm and numerical estimation of gradient of J(Ɵ)
• Disable the gradient checking code for when you actually run it
• 2.6) Use gradient descent or an advanced optimization method with back propagation to try to minimize J(Ɵ) as a function of parameters Ɵ
• Here J(Ɵ) is non-convex
• Can be susceptible to local minimum
• In practice this is not usually a huge problem
• Can't guarantee programs with find global optimum should find good local optimum at least
• e.g. above pretending data only has two features to easily display what's going on
• Our minimum here represents a hypothesis output which is pretty close to y
• If you took one of the peaks hypothesis is far from y
• Gradient descent will start from some random point and move downhill
• Back propagation calculates gradient down that hill
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Quantitative Skills > Teaching Resources > Activities
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# Show all Resources
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## Quantitative Skills
showing only Vectors and Matrices Show all Quantitative Skills
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# Quantitative Skills Show all Quantitative Skills
Results 1 - 8 of 8 matches
Vectors and slope stability part of Quantitative Skills:Activity Collection
Eric Baer, Highline Community College
An in-class activity or homework for graphically solving slope-stability problems with vectors.
Air-sea Interactions: Activities in Oceanography part of Quantitative Skills:Activity Collection
Steve LaDochy, California State University, Los Angeles
This online set of activities help students learn properties of ocean waves, wind-wave relationships and properties of tsunamis.
Three-Point Problem by Simultaneous Linear Equations part of Quantitative Skills:Activity Collection
Students are introduced to the use of linear algebra in an intuitive and accessible way, through classroom activity and homework set. The familiar three-point problem is cast in terms of three dimensional analytic geometry, fostering understanding of mathematical models for simple geometric forms.
Assessing the error of linear and planar field data using Fisher statistics part of Quantitative Skills:Activity Collection
Vince Cronin, Baylor University
Instruction on use of Fisher statistics to determine the mean and 95% confidence interval of geological vectors, lines or planes, with examples, problems and an Excel spreadsheet for computation.
Radiometric Dating part of Quantitative Skills:Activity Collection
Related Links Radioactive Decay Exponential Growth and Decay Peter Kohn - James Madison University Christopher Gellasch - U.S. Military Academy Jim Sochacki - James Madison University Scott Eaton - James Madison University Richard Ford - Weber State University
This activity leads students through derivations of the equations associated with radiometric dating.
The Metrical Mastrix in Teaching Mineralogy part of Cutting Edge:Courses:Mineralogy:Activities
G. V. Gibbs
The calculation of the d-spacings, the angles between planes and zones, the bond lengths and angles and other important geometric relationships for a mineral can be a tedious task for the student and the ...
Applications of Vector Operators for Surface Atmospheric/Oceanic Processes part of Quantitative Skills:Activity Collection
David Smith, United States Naval Academy
This lab exercise provides students with activities utilizing vector operations within the context of the atmospheric and oceanic environments.
Exercise to Calculate River Discharge part of Spreadsheets Across the Curriculum:General Collection:Examples
Nicholas Baer
Spreadsheets Across the Curriculum module. Students use field data from rivers to understand how river discharge is calculated.
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https://brainly.com/question/204832
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2014-11-30T20:05:20-05:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
You did #1 correctly.
#2). The question gives you the equation, and the numbers to use for 'a' and 'b', and it just wants you to plug in those numbers and do the arithmetic.
It says: The number of tiles needed is (a²) divided by (b²).
Then it says: a = 96 and b = 8. I know you can handle that !
Number needed = (96)² divided by (8)² .
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# Divide 5
Divide 288 in the following ratio
3 : 4 : 5
Correct result:
a = 72
b = 96
c = 120
#### Solution:
We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!
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Check out our ratio calculator.
Do you want to perform natural numbers division - find the quotient and remainder?
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# Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi. and Xii. of Euclid with Exercises and Notes
Rivingtons, 1879 - 349 σελίδες
0 Κριτικές
Οι αξιολογήσεις δεν επαληθεύονται, αλλά η Google ελέγχει και καταργεί ψευδές περιεχόμενο όταν το εντοπίζει
Copy owned by Florence Exton, principle of the college from 1920-1923, when she died unexpectedly in office.
### Τι λένε οι χρήστες -Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
### Περιεχόμενα
INTRODUCTORY REMARKS 77 PROPOSITION 84 EUCLIDS PROPOSITIONS VII TO XIV 93 DEFINITION VII 128 PROPOSITION A EUCL III 134 DEFINITION XIII 142 EUCLIDS PROPOSITIONS XXIII AND XXIV OF BOOK III 175 APPENDIX TO BOOKS I 198 II 211 V 217 EUCL V 7 223 EUCL V 16 229 CONTAINING THE PROPOSITIONS TO WHICH NO REFERENCE IS MADE IN BOOK VI Pp 235 to 235 EUCL V 6 236 EUCL V 17 237 EUCL V 19 238 EUCL V 23 239
EUCL VI 10 259 EUCL VI 11 260 EUCL VI 12 261 EUCL VI 8 262 DEFINITION IV 264 EUCLIDS PROPOSITIONS XIV TO XIX 265 EXERCISES ON PROPOSITION XIX 274 EUCL VI 21 275 EUCL VI 20 276 EUCL VI 31 278 EUCL VI 22 280 PROPOSITION B 284 EUCL VI 25 290 INTRODUCTORY REMARKS 307 EUCL XI 3 313 MISCELLANEOUS EXERCISES ON BOOK XI 334 PAPERS ON EUCLID BOOKS VI AND XI SET IN THE CAM 342
### Δημοφιλή αποσπάσματα
Σελίδα 81 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 160 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 9 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 42 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 25 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Σελίδα 98 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Σελίδα 170 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 48 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Σελίδα 277 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 83 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
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# Tobitzu tv | Accounting homework help
Tobitzu TV produces wall mounts for flat panel television sets. The forecasted income statement for 2009 is as follows:
TOBITZU TV
Budgeted Income Statement
For the Year 2009
Sales (\$43 per unit) \$4,300,000
Cost of good sold (\$32 per unit) (3,200,000)
Gross profit 1,100,000
Selling expenses (\$2 per unit) (200,000)
Net income \$900,000
(1) Of the production costs and selling expenses, \$600,000 and \$100,000, respectively, are fixed. (2) Tobitzu TV received a special order from a hospital supply company offering to buy 15,500 wall mounts for \$28. If it accepts the order, there will be no additional selling expenses, and there is currently sufficient excess capacity to fill the order. The company’s sales manager argues for rejecting the order because “we are not in the business of paying \$32 to make a product to sell for \$28.”
Calculate the net benefit (cost) of accepting the special order.
## Calculate the price of your order
550 words
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Technical Article
# Introduction to the Synchronous Demodulation
December 11, 2019 by Dr. Steve Arar
## This article will discuss the basic idea behind the synchronous demodulation technique.
Sometimes, we need to measure a low-frequency signal. For example, consider a pressure sensor used in an application where the pressure changes very slowly.
The signal we are measuring is almost DC but how is this going to affect our design?
We know that at high frequencies, things can get crazy and we need to pay careful attention to every detail of the design. This might mislead us to the wrong idea that measuring a low-frequency signal is a trivial job. We’ll see that this is not necessarily the case. In fact, there is a technique called synchronous demodulation that intentionally increases the frequency of operation to achieve a more accurate measurement.
This article will discuss the basic idea behind the synchronous demodulation technique.
### Example of Low-Frequency Measurement
There are applications where a sensor with a low-frequency output is measured directly (without applying synchronous demodulation). For example, the electret microphone is a special type of variable capacitance that is measured directly. The capacitance of an electret microphone varies with air pressure variations (sound waves).
A Teflon-like material, called electret, that has a fixed charge bonded to its surface is used in the capacitor structure. Since the charge on the capacitor is fixed, the change in the capacitance value caused by the air pressure variations leads to a corresponding change in the voltage across the capacitor (For a capacitor, we have Q=CV).
As shown in Figure 1, an electret microphone usually has an internal JFET that acts as a buffer.
##### Figure 1. Image courtesy of Texas Instruments.
In this particular application, the signal produced by the sensor (the microphone) is directly applied to the amplifying elements of the circuit. This method for measuring a capacitive sensor is sometimes referred to as the “direct DC” method because the low-frequency signal on the capacitor is measured directly.
One of the main problems that arises when we measure a low-frequency signal is the flicker noise.
### Flicker Noise
The average power of the flicker noise is inversely proportional to the frequency of operation (that’s why the flicker noise is also called 1/f noise). Hence, the lower the signal frequency, the larger the noise power we have to deal with. Figure 2 shows the voltage noise spectral density of the ADA4622-2 that is a precision op-amp.
##### Figure 2. Image courtesy of Analog Devices
Above about 100 Hz, the noise power is almost evenly distributed among different frequencies. This region of the noise profile corresponds to the thermal noise of the device. However, as we move to frequencies below 100 Hz, the noise average power increases due to the flicker noise.
Approximating the two distinct regions of the noise profile with straight lines, we can find an intersection point, called the 1/f noise corner frequency (as shown in Figure 2). The corner frequency allows us to determine the dominant noise type of the device (either flicker or thermal) for a given frequency.
Below the 1/f corner frequency, the small signal produced by the sensor can be completely buried in noise. If we could somehow increase the frequency of the sensor output signal to above the corner frequency, we could make a more accurate measurement. This is the basic idea behind the synchronous demodulation technique.
Figure 3 shows how making the measurement at a higher frequency can bring the desired signal out of the device flicker noise.
##### Figure 3
The flicker noise may not be a serious problem for the “direct DC” measurement illustrated in Figure 1 because the voice signal displays negligible power at very low frequencies (below about 20 Hz). Additionally, we might be able to customize the internal buffer transistor to decrease its 1/f corner frequency.
However, there are applications where the output signal of the sensor is at much lower frequencies (almost DC) and we need a much more accurate measurement. In this case, the flicker noise of the electronic components can completely bury the signal produced by the sensor and we need techniques such as the synchronous demodulation to circumvent the flicker noise problem.
### AC Excitation of the Sensor
Figure 4 illustrates the use of an AC signal for measuring a capacitive sensor. In this figure, the variable capacitance Csense models our capacitive sensor. The input voltage source applies a sine wave with frequency in the 1 kHz-1 MHz range. Depending on the ratio of Csense to C2, a voltage signal appears at the input of the op-amp. In this case, the input signal of the op-amp can be chosen to be sufficiently greater than the 1/f corner frequency of the circuit. This is in contrast to the “direct DC” method where the measured signal can be at very low frequencies.
Since the desired signal is far away from the 1/f corner frequency (as shown in Figure 5), the flicker noise is not a limiting factor and we can detect a much smaller signal.
##### Figure 5
At the op-amp output, we have an amplified signal that can be used to determine the value of the variable capacitance; however, we need a band-pass filter (BPF) to reject the noise components and keep only the desired signal. This is depicted in Figure 6.
##### Figure 6
Note that the center frequency of the BPF is the same as the input frequency. Assuming that the band-pass filter is ideal, we’ll obtain the desired signal along with the thermal noise that falls in the pass-band of the band-pass filter (Figure 7 below).
### Limitations of Using a BPF
In Figure 6, we need a high-Q band-pass filter to sufficiently suppress the noise and keep the desired signal. A very high-Q filter would allow us to reject most of the noise. However, there are two main problems: First, implementing a high-Q continuous-time band-pass filter can be challenging especially at high frequencies. In fact, as the center frequency of the filter increases, it becomes more and more difficult to achieve a given Q-factor. This is due to the fact that at high frequencies (at about a few hundred MHz), op-amps have limited amplification capability and exhibit non-ideal phase response. You might say that the center frequency of the filter in Figure 6 is in the 1 kHz-1 MHz range and this is not really a high-frequency filter. Well, you’re right, we can have a high-Q filter in this frequency range. However, as we move to higher and higher frequencies, we have to burn more power. In other words, for a given Q-factor, we expect a lower frequency filter to exhibit a lower power consumption. Therefore, it could be more power efficient if the filtering after the op-amp could be performed at a lower frequency.
The second problem with the concept illustrated in Figure 6 is tuning the center frequency of the band-pass filter. Note that the center frequency of an analog continuous-time filter depends on the value of resistors, capacitors, and transconductors. The absolute value of these parameters can vary significantly. As a result, the center frequency of the filter might not be exactly at fIN. Since the filter has a narrow pass-band, the desired signal might easily fall outside the filter pass-band due to the variations in the filter center frequency. This second problem with the use of a high-Q BPF can be even more challenging than the power efficiency problem discussed in the previous paragraph. Interestingly, if an application requires a high-Q continuous-time band-pass filter, we have to employ a mechanism for tuning the filter center frequency. For example, some integrated band-pass filter applications employ a feedback loop that is conceptually similar to a phase-locked loop to tune the filter center frequency. However, such a system seems too complex and power-hungry for reading a sensor. In the next section, we’ll see that a clever adjustment can achieve the required filtering operation using a low-pass filter rather than a BPF. In this way, we can have a low-power solution that doesn’t need any frequency tuning circuitry.
### Synchronous Demodulation
The concept of synchronous demodulation is illustrated in Figure 8. In this figure, a multiplier is placed after the op-amp.
##### Figure 8
Assume that the output signal of the op-amp output is $$v_B(t)=Bsin(2\pi f_{in}t+\phi)$$. This signal is multiplied by the input signal $$Asin(2\pi f_{in}t)$$ which gives:
$v_C(t)=Asin(2\pi f_{in}t) \times Bsin(2\pi f_{in}t+ \phi)= \frac {1}{2}ABcos(\phi)-\frac {1}{2}ABcos(4\pi f_{in}t+\phi)$
The first term is DC, however, the second term is at twice the input frequency. Hence, a narrow low-pass filter can remove the second term and we have:
$v_D(t)= \frac {1}{2}ABcos(\phi)$
If we assume that the op-amp is not introducing any delay, i.e. $$\phi = 0$$, we obtain $$v_D(t)=\frac {1}{2}AB$$. As you can see the output of the low-pass filter is proportional to the amplitude of the signal at node A and can be used to measure the value of $$C_{sense}$$. The above method has three advantages:
• The frequency of the sensor output can be chosen to be sufficiently higher than the 1/f corner frequency.
• The filter operates at the lowest possible frequency and should burn the smallest possible power.
• The filter doesn’t need frequency tuning circuitry.
In the next article of this series, we’ll continue this discussion and take a closer look at the implementation of the synchronous demodulation technique.
### Conclusion
The “Direct DC” method measures the low-frequency signal produced by a capacitive sensor directly. The accuracy of such low-frequency measurement can be limited because of the flicker noise. To circumvent this problem, we can use an AC signal to excite the sensor. Since the measurement occurs at a frequency above the 1/f corner frequency, the flicker noise is no longer a limiting factor. In this case, we can use a band-pass filter to select the desired signal; however, the use of high-Q bandpass filters can be challenging. Instead, we can synchronously demodulate the measured signal and use a low-pass filter to perform the required filtering.
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The photo lab offers the prices shown for 4 x 6 and 5 x 7 prints. You have \$70 to spend and you need 100 prints. Write a system of linear equations that describe this situation
1
by Idancer0202
Why are
“the prices shown”?
4x6 is \$0.10 and 5x7 is \$1.60
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# Volume of LEA and PERRINS, STEAK SAUCE, BOLD, UPC: 051600002109
## food weight to volume conversions
### calculate volume of generic and branded foods per weight
#### Volume, i.e. how many spoons, cups,gallons or liters in 100 gram of LEA andPERRINS, STEAK SAUCE, BOLD, UPC:051600002109
centimeter³ 86.98 milliliter 86.98 foot³ 0 US cup 0.37 Imperial gallon 0.02 US dessertspoon 11.76 inch³ 5.31 US fluid ounce 2.94 liter 0.09 US gallon 0.02 meter³ 8.7 × 10-5 US pint 0.18 metric cup 0.35 US quart 0.09 metric dessertspoon 8.7 US tablespoon 5.88 metric tablespoon 5.8 US teaspoon 17.65 metric teaspoon 17.4
#### Weight
gram 100 ounce 3.53 kilogram 0.1 pound 0.22 milligram 100 000
Nutrient (find foodsrich in nutrients) Unit Value /100 g BasicAdvancedAll Proximates Energy kcal 118 Protein g 0 Total lipid (fat) g 0 Carbohydrate,bydifference g 29.41 Sugars, total g 23.53 Minerals Calcium, Ca mg 118 Iron, Fe mg 2.12 Sodium, Na mg 676 Lipids Cholesterol mg 0
#### See how many calories in0.1 kg (0.22 lbs) of LEAand PERRINS, STEAK SAUCE,BOLD, UPC: 051600002109
From kilocalories(kcal) kilojoule(kJ) Carbohydrate 0 0 Fat 0 0 Protein 0 0 Other 118 493.71 Total 118 493.71
• About LEA and PERRINS, STEAK SAUCE, BOLD, UPC: 051600002109
• 287.41919 grams [g] of LEA and PERRINS, STEAK SAUCE, BOLD, UPC: 051600002109 fill 1 metric cup
• 9.59452 ounces [oz] of LEA and PERRINS, STEAK SAUCE, BOLD, UPC: 051600002109 fill 1 US cup
• LEA and PERRINS, STEAK SAUCE, BOLD, UPC: 051600002109 weigh(s) 287.42 gram per (metric cup) or 9.59 ounce per (US cup), and contain(s) 118 calories per 100 grams or ≈3.527 ounces [ weight to volume | volume to weight | price | density ]
• Ingredients: TOMATO PUREE (WATER, TOMATO PASTE), DISTILLED WHITE VINEGAR, LEA and PERRINS WORCESTERSHIRE SAUCE CONCENTRATE (DISTILLED WHITE VINEGAR, ONIONS, ANCHOVIES, SALT, GARLIC, CLOVES, TAMARIND EXTRACT, MOLASSES, NATURAL FLAVORS, CHILI PEPPER EXTRACT), MOLASSES, SUGAR, WATER, CORN STARCH, ONIONS, GARLIC, EVAPORATED CANE SYRUP, XANTHAN GUM, SALT.
• Manufacturer: KRAFT HEINZ FOODS COMPANY
• A few foods with a name containing, like or similar to LEA and PERRINS, STEAK SAUCE, BOLD, UPC: 051600002109:
• LEA and PERRINS, WORCESTERSHIRE SAUCE, UPC: 05160434 contain(s) 100 calories per 100 grams or ≈3.527 ounces [ price ]
• LEA and PERRINS, THE ORIGINAL WORCESTERSHIRE SAUCE, UNWRAP THE FLAVOR, UPC: 051600000013 contain(s) 100 calories per 100 grams or ≈3.527 ounces [ price ]
• LEA and PERRINS, THE ORIGINAL WORCESTERSHIRE SAUCE, UPC: 08951115 contain(s) 100 calories per 100 grams or ≈3.527 ounces [ price ]
• LEA and PERRINS, THE ORIGINAL WORCESTERSHIRE SAUCE, UPC: 05160337 contain(s) 100 calories per 100 grams or ≈3.527 ounces [ price ]
• LEA and PERRINS, WORCESTERSHIRE SAUCE, UPC: 051600000037 contain(s) 100 calories per 100 grams or ≈3.527 ounces [ price ]
• For instance, compute how many cups or spoons a pound or kilogram of “LEA and PERRINS, STEAK SAUCE, BOLD, UPC: 051600002109” fills. Volume of the selected food item is calculated based on the food density and its given weight. Visit our food calculations forum for more details.
• Reference (ID: 55274)
• USDA National Nutrient Database for Standard Reference; National Agricultural Library; United States Department of Agriculture (USDA); 1400 Independence Ave., S.W.; Washington, DC 20250 USA.
#### Foods, Nutrients and Calories
REAL MAYONNAISE, UPC: 071735128390 weigh(s) 236.7 gram per (metric cup) or 7.9 ounce per (US cup), and contain(s) 714 calories per 100 grams or ≈3.527 ounces [ weight to volume | volume to weight | price | density ]
BARBECUE CASHEWS, UPC: 655852008508 weigh(s) 118.35 gram per (metric cup) or 3.95 ounce per (US cup), and contain(s) 571 calories per 100 grams or ≈3.527 ounces [ weight to volume | volume to weight | price | density ]
#### Gravels, Substances and Oils
CaribSea, Marine, Aragonite, Florida Crushed Coral weighs 1 153.3 kg/m³ (71.99817 lb/ft³) with specific gravity of 1.1533 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Diamine [N2H4] weighs 1 004.5 kg/m³ (62.70889 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | density ]
Volume to weightweight to volume and cost conversions for Diesel fuel with temperature in the range of 10°C (50°F) to 140°C (284°F)
#### Weights and Measurements
metric cup is a metric (SI) liquid measure of volume.
Volume is a basic characteristic of any three–dimensional geometrical object.
dwt/yd² to mg/Ų conversion table, dwt/yd² to mg/Ų unit converter or convert between all units of surface density measurement.
#### Calculators
Calculate volume of a quarter cylinder and its surface area
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# Check if a key is present in every segment of size k in an array in C++
## Concept
With respect of a given array arr1[] with size of array N,one another key X and a segment size K, the task is to determine that the key X present in every segment of size K in arr1[].
Input
arr1[] = { 4, 6, 3, 5, 10, 4, 2, 8, 4, 12, 13, 4}
X = 4
K = 3
Output
Yes
There are existence of 4 non-overlapping segments of size K in the array, {4, 6, 3}, {5, 10, 4}, {2, 8, 4} and {12, 13, 4}. 4 is present all segments.
Input
arr1[] = { 22, 24, 57, 66, 35, 55, 77, 33, 24, 46, 22, 24, 26}
X = 24
K = 5
Output
Yes
Input
arr1[] = { 6, 9, 8, 13, 15, 4, 10}
X = 9
K = 2
Output
No
## Method
In this case,the concept is simple, we consider every segment of size K and verify if X is present in the window or not. So we need to carefully tackle the last segment.
## Example
Following is the implementation of the above approach −
Live Demo
// C++ code to determine the every segment size of
// array have a search key x
#include <bits/stdc++.h>
using namespace std;
bool findxinkindowSize1(int arr1[], int X, int K, int N){
int i;
for (i = 0; i < N; i = i + K) {
// Search X in segment starting
// from index i.
int j;
for (j = 0; j < K; j++)
if (arr1[i + j] == X)
break;
// If loop didn't break
if (j == K)
return false;
}
// If N is a multiple of K
if (i == N)
return true;
// Check in last segment if N
// is not multiple of K.
int j;
for (j=i-K; j<N; j++)
if (arr1[j] == X)
break;
if (j == N)
return false;
return true;
}
// main driver
int main(){
int arr1[] = { 4, 6, 3, 5, 10, 4, 2, 8, 4, 12, 13, 4 };
int X = 4, K = 3;
int N = sizeof(arr1) / sizeof(arr1[0]);
if (findxinkindowSize1(arr1, X, K, N))
cout << "Yes" << endl;
else
cout << "No" << endl;
return 0;
}
## Output
Yes
Updated on: 23-Jul-2020
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# Exeter point
In geometry, the Exeter point is a special point associated with a plane triangle. The Exeter point is a triangle center and is designated as the center X(22)[1] in Clark Kimberling's Encyclopedia of Triangle Centers. This was discovered in a computers-in-mathematics workshop at Phillips Exeter Academy in 1986.[2] This is one of the recent triangle centers, having been discovered only in 1986, unlike the classical triangle centers like centroid, incenter, and Steiner point.[3]
## Definition
The Exeter point is defined as follows.[2][4]
Let ABC be any given triangle. Let the medians through the vertices A, B, C meet the circumcircle of triangle ABC at A' , B' and C' respectively. Let DEF be the triangle formed by the tangents at A, B, and C to the circumcircle of triangle ABC. (Let D be the vertex opposite to the side formed by the tangent at the vertex A, E be the vertex opposite to the side formed by the tangent at the vertex B, and F be the vertex opposite to the side formed by the tangent at the vertex C.) The lines through DA' , EB' and FC' are concurrent. The point of concurrence is the Exeter point of triangle ABC.
## Trilinear coordinates
The trilinear coordinates of the Exeter point are
( a ( b4 + c4a4 ), b ( c4 + a4b4 ), c ( a4 + b4c4 ) ).
## References
1. ^ Kimberling, Clark. "Encyclopedia of Triangle Centers: X(22)". Retrieved 24 May 2012.
2. ^ a b Kimberling, Clark. "Exeter Point". Retrieved 24 May 2012.
3. ^ Kimberling, Clark. "Triangle centers". Retrieved 24 May 2012.
4. ^ Weisstein, Eric W. "Exeter Point". From MathWorld--A Wolfram Web Resource. Retrieved 24 May 2012.
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### Measurement Activities {And a NEW Freebie!}
Measurement is one of my most favorite math concepts to teach. Put a ruler in the hands of a student and they are as happy as a peach! When Hope and I were putting together our 2nd Grade math unit on measurement we really wanted to make sure to pull together activities that were hands-on and engaging. We also wanted to incorporate several skills in such as estimating, comparing, adding & subtracting, and more! Here's a little look at our favorite activities from Magic of Math Unit 6:
Students will create a robot then estimate and measure using inches.
Students create a City-Scape and estimate/measure the height of each building. Afterwards students compare the heights of different buildings.
Students will also use a ruler to measure the lengths of different lines.
During Spin, Move, and Measure students decide which unit of measurement would be best to measure in. Students also measure several of the objects that can be found around the classroom.
Using small cars, our friends will host a Meter Derby to measure the length their cars travel using meters.
Students also take a peek at Wacky Line Ups! These pictures will give students a chance to measure objects that aren't lined up perfectly on a ruler.
Building Lego Towers will give our friends an opportunity to estimate and measure using centimeters.
We will also work on comparing lengths in centimeters with a little Twizzler Station activity!
Students are always trying to sneak a little paper airplane making into their day, so why not give them the opportunity to do so?! Paper airplanes will take flight and students will have a blast estimating and measuring!
One of our other skills to master is measuring the area of a rectangle. This also includes partitioning rectangles into equal parts.
Students create their very own dream room and measure the area of each object that they include!
Want an excuse to break out the chocolate?! Using a Hershey's bar, students will partition rectangles and find the area of each new shape using their candy bar :)
We provide many opportunities for students to practice covering a shape appropriately to find the area of different sized rectangles.
We just couldn't leave out the cuteness! Students create a dinosaur and estimate/measure the area of each part.
Your little learners will become Area Royalty after they create their very own Area Crowns!
Let's just face it, word problems can be such a bore, but goodness they are important! We did try to take the pain out of it with different ways to attack those tricky things!
You can find all of the activities shown above HERE... plus there are SOOOO many more that we didn't even show :)
As a little added bonus, I put together this Measurement Review that can be used after your students have learned how to measure length. This can be displayed on the projector or used as a Scoot activity! Find this freebie HERE!
Sr. Layan Collins said...
I love this! Thank you so much for such amazing products!
Christine said...
You have provided some highly engaging activities! My class is going to love our measurement unit! Not only are the hands-on activities centered around topics that children are interested in, but I see potential for differentiated activities. How many students did you have working in each group? Did your class complete one activity a day? Did you have the children rotate between a variety of activities?
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http://mathematicsbhilai.blogspot.in/2015/12/median-to-hypotenuse-of-right-triangle.html
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Monday, December 21, 2015
Median to Hypotenuse of a Right Triangle
Problem : Let us consider the right triangle PQR with the right angle P (Figure 1), and let PS be the median drawn from the vertex P to the hypotenuse QR. We need to find the relationship between the length of the median PS and the the length of the hypotenuse QR.
Solution :Draw a straight line passing through the midpoint S and parallel to the side PR intersecting the side PQ at the point T. (Figure 2).
The angle QPR is given as right angle. The angles QTS and QPR are equal to each other as as they are corresponding angles of the parallel lines PR and TS and the transversal PQ. Hence the angle QTS is a right angle.
As TS passes through the mid-point S and is parallel to PR , it divides the side PQ into two equal parts i.e. PT = TQ. So, the triangles PTS and QTS are right triangle triangles with equal sides PT and TQ , these triangles also have a common side TS. Hence, these triangles are congruent in as per the Side – Angle – Side (SAS) Rule.
From this we can say that the other sides of these triangles are also equal to each other as they are the corresponding parts of the congruent triangles , thus PS = QS. Now QS is equal to half the length of the hypotenuse QR , we can say that the median PS is also equal to half the length of the hypotenuse.
Hence, we can conclude that in a right triangle , the length of median to hypotenuse is half the length of the hypotenuse.
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# Choose the correct answer from the given four options:The list of numbers $-10,-6,-2,2, \ldots$ is(A) an AP with $d=-16$(B) an AP with $d=4$(C) an AP with $d=-4$(D) not an AP
Given:
The list of numbers $-10,-6,-2,2, \ldots$
To do:
We have to choose the correct answer.
Solution:
$a_1 = -10, a_2=-6, a_3=-2$
This implies,
$a_3-a_2=-2-(-6)=-2+6=4$
$a_2-a_1=-6-(-10)=-6+10=4$
Here,
$a_3-a_2=a_2-a_1$
$d=a_3-a_2=a_2-a_1=4$
Therefore, the given list of numbers is an AP with $d=4$.
Updated on: 10-Oct-2022
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Question
## Introduction
Most 8-year-old girls will be about 4’0″ tall (122 cm) and weigh 34 pounds (15 kg).
## Height
The average height for an 8 year old girl is 4 feet, 0 inches. For boys, the average height is 3 feet 6 inches.
Height is a measure of how tall you are and is usually expressed in inches or centimeters.
## Weight
The average weight of an 8-year-old girl is 34 pounds (15 kilograms). This is about the same as a large dog, rabbit, or cat.
## BMI
BMI, or body mass index, is a measure of body fat based on height and weight. It’s calculated by dividing your weight in kilograms by the square of your height in meters.
The BMI is not an exact measurement–it doesn’t take into account muscle mass or bone density, so it can’t be used as a diagnostic tool for obesity. But it has been shown to correlate well with other more accurate measures of body fatness like underwater weighing (dunking yourself in water) or dual energy x-ray absorptiometry (DXA).
## Body fat percentage
Body fat percentage is the amount of fat in relation to the total body weight. A healthy body fat percentage for an 8-year-old girl is between 18 and 25 percent, according to Kids Health. This means that if you weigh 50 pounds, about 10 of them are made up of fat (20%).
It’s easy to measure your own body fat percentage using skinfold calipers or a body fat scale like this one from Tanita (which also measures bone mass). If you’re concerned about whether or not your child’s weight falls within normal ranges and want to check out her BMI, visit this page on WebMD for guidelines regarding how doctors determine whether a child needs medical attention based on their height and weight measurements alone without taking into account other factors such as age or gender differences between individuals within any given population
## An 8-year-old girl is likely to be about 4’0″ tall (122 cm) and weigh 34 pounds (15 kg).
An 8-year-old girl is likely to be about 4’0″ tall (122 cm) and weigh 34 pounds (15 kg). Girls grow quickly between the ages of 8 and 12, gaining about 2 inches per year.
Girls have reached their full height by age 13, but they continue to gain weight until they reach puberty at around age 14.
An 8-year-old girl is likely to be about 4’0″ tall (122 cm) and weigh 34 pounds (15 kg).
1. As a parent, keeping track of your child’s growth is important to ensure they are developing properly. One aspect of this is understanding the average weight and height for their age group. If you have an 8-year-old girl, it’s natural to wonder if she falls within the normal range for her age. In this blog post, we’ll dive into the topic of an average weight for 8-year-old American girls and explore why some may be above or below that range. So let’s get started!
## The average weight of an 8-year-old girl in the United States
The average weight of an 8-year-old girl in the United States can vary depending on various factors such as genetics, lifestyle habits, and nutrition. However, according to the Centers for Disease Control and Prevention (CDC), the average weight for an 8-year-old girl is around 56 pounds.
It’s essential to note that this number is just a guideline and does not apply to every child. Some may weigh more or less than this range while still being healthy and within their normal growth pattern.
Factors like physical activity level, diet quality, sleep patterns, stress levels can influence your child’s weight. It’s important not only to focus on numerical values but also pay attention to these other aspects of their health.
If you are concerned about your child’s weight, it’s always best to consult with a healthcare professional who can help guide you towards making any necessary changes in their lifestyle.
## The average height of an 8-year-old girl in the United States
At 8 years old, a girl’s height can vary greatly depending on various factors such as genetics and nutrition. On average, the height of an 8-year-old American girl is around 4 feet tall (about 122 cm). However, this number may differ based on several aspects.
One critical factor that influences a child’s growth is their environment. If they grow up in a household with poor nutrition or limited access to healthcare and education, it could stunt their physical development. Conversely, if they have proper nourishment and exercise regularly, it can enhance growth.
Another significant factor is genetics. Height tends to run in families; thus, if your parents are tall or short statured, you might likely follow suit.
It’s essential not to worry too much about your child’s height unless there are underlying health issues at play. Instead of focusing solely on their physical appearance and size measurements alone, pay attention to your little one’s overall well-being by ensuring that they lead healthy lifestyles with balanced diets and regular activity levels for optimal growth potential.
## The normal range for weight and height of 8-year-old girls
At the age of 8, girls are beginning to develop their own unique body shapes and sizes. As such, there is a wide range of normal weight and height measurements for 8-year-old girls. The average weight for an 8-year-old girl in the United States is around 56 pounds (25 kg), with a range between approximately 40-80 pounds (18-36 kg).
Similarly, the average height of an 8-year-old girl in the United States is around four feet tall (122 cm), with a range between approximately three and a half to five feet tall (107-152 cm). It’s important to note that these averages can vary based on factors such as genetics, nutrition, physical activity levels, and more.
While it’s natural for parents to be concerned about their child’s growth patterns, it’s important not to focus too much on specific numbers or percentiles. Instead, parents should pay attention to overall trends over time. If your child consistently falls outside of the expected ranges or if you have concerns about their growth development at any point along the way, don’t hesitate to consult with your pediatrician.
Ultimately though every child develops differently so trust in your pediatrician’s guidance and take comfort knowing that there is no one “right” size or shape for an eight-year-old girl!
## Why are some 8-year-old girls above or below the average weight and height?
As we have seen, the average weight and height of an 8-year-old girl in the United States can vary depending on several factors such as genetics, lifestyle choices, and nutrition. It’s important to remember that every child is unique and will develop at their own pace.
If you’re concerned about your child’s weight or height, it’s always best to consult with a pediatrician who can provide personalized recommendations based on your child’s individual needs.
In any case, it’s crucial to promote healthy habits from an early age by encouraging physical activity and a balanced diet rich in fruits, vegetables, whole grains, lean proteins while limiting sugary drinks and snacks. By doing so, parents can help set their children up for a lifetime of good health.
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# Margin Call Price
Guide to Understanding the Margin Call Price Concept
• What is the definition of a margin call?
• Which factors cause a margin call?
• What formula calculates the margin call price?
• If a margin call is not met, what happens?
## Margin Call Definition
Margin calls are triggered when investors trading on margin have an account value below the minimum requirement.
A margin account is a method for investors to purchase securities on margin, i.e. investors can borrow funds from a brokerage to make investments instead of using their money.
For instance, if an investor has contributed \$10,000 of their own capital to the account, which has a margin of 50% — the investor can purchase up to \$20,000 worth of securities because the remaining \$10,000 is borrowed from the broker.
However, the optionality to utilize borrowed capital (i.e. leverage) to make investments comes with certain requirements, namely the initial and maintenance margin.
• Initial Margin: The minimum percentage that investors must contribute before purchasing an asset using the margin loan.
• Maintenance Margin: The minimum percentage that investors must maintain in their margin accounts for their positions to remain open.
With that said, a margin call implies that the securities purchased (and thus, the account value) have declined in value to where the minimum threshold is no longer met.
Certain brokers send out warnings to investors trading on margin if an account is close to no longer meeting a requirement, but margin calls specifically request the investor to either:
• Deposit More Cash Funds (or)
• Sell Portfolio Holdings
## Margin Call Price Formula
The formula for calculating the price at which a margin call is expected is shown below.
###### Margin Call Price Formula
• Margin Call Price = Initial Purchase Price x [(1 – Initial Margin) /(1 – Maintenance Margin)]
The margin call price represents the price below which the margin requirements are not met, and the investor must deposit more money or sell off a certain amount of portfolio holdings to return to compliance with the requirements.
If not, the broker could liquidate the positions, and the investor could be prohibited from trading on margin for non-compliance (and for their refusal to resolve the issue within the set timeframe).
## Margin Call Price Calculator — Excel Template
We’ll now move to a modeling exercise, which you can access by filling out the form below.
Submitting ...
## Margin Call Price Example Calculation
Suppose you opened up a margin account and deposited \$60,000 of your own cash.
At a 50% margin, \$60,000 is borrowed on margin, so the total funding available to be spent on securities is \$120,000, which you decided to spend entirely on a portfolio of stocks.
• Initial Purchase Price (P₀) = \$120,000
Assuming a 50% initial margin and 25% maintenance margin, we can enter our numbers into the margin call price formula.
• Margin Call Price = \$120,000 × [(1 – 50%) /(1 – 25%)]
• Margin Call Price = \$80,000
Therefore, your account value must remain above \$80,000 at all times — otherwise, you are at risk of receiving a margin call.
The maintenance margin is calculated based on the market value of the securities held minus the margin loan, which is \$60,000 in our example.
If the market value of your margin account declines to \$80,000, your equity is only worth \$20,000 after deducting the \$60,000 margin loan.
• Investor Equity = \$80,000 – \$60,000
• Investor Equity = \$20,000
The 25% maintenance margin is still met, so there is no margin call.
## Margin Call Deficit — Downside Case Example
We’ll use the same assumptions in the next exercise as in the previous example, except for the margin account value.
After the investor placed riskier bets on options that were not unsuccessful, the account value has declined from \$120,000 to \$76,000.
• Margin Account Value = \$76,000
If we deduct the margin loan of \$60,000 from the account value, the investor equity is \$16,000.
• Investor Equity = \$76,000 – \$60,000
• Investor Equity = \$16,000
Moreover, \$16,000 divided by \$80,000 equals 20%, which does NOT sufficiently meet the minimum requirement of 25%.
The shortfall, i.e. the deficit that must be addressed promptly, is \$4,000.
• Account Deficit = \$80,000 – \$76,000
• Account Deficit = \$4,000
In this second case, the account value is short \$4,000, as the maintenance margin is just 20% rather than the required 25% — so the broker will soon issue a formal margin call to ensure a deposit is made or securities are sold to make up the difference.
## Failure to Meet Margin Call
Suppose your margin account value falls below the set maintenance requirement.
In that case, the broker will make a margin call requesting a cash deposit or liquidation of securities, so there is no longer a shortfall.
If unable to meet the margin call, the broker can liquidate your securities themselves at their discretion to increase the equity held in your account to meet the maintenance requirement.
If an investor cannot meet the margin, the brokerage firm has the right to close out open positions on behalf of the investor so that the account is back to meeting the minimum value, i.e. a “forced sale.”
As part of the agreement to open a margin account, the broker has the right to liquidate positions without the investor’s approval, albeit the forced sale is the last resort typically done after several unsuccessful attempts to reach the investor.
The fees associated with the transactions are billed to the investor, along with interest on the loan — or in some cases, there are fines charged to the investor for the inconvenience.
If the failure to respond to margin calls is a recurring occurrence, a brokerage firm could sell the investor’s entire portfolio and close the margin account.
Step-by-Step Online Course
#### Everything You Need To Master Financial Modeling
Enroll in The Premium Package: Learn Financial Statement Modeling, DCF, M&A, LBO and Comps. The same training program used at top investment banks.
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John Fox, Applied Regression Analysis, Linear Models, and Related Methods (Sage, 1997)
` Preface `
` Synopsis `
` Computing `
` To Readers, Students, and Instructors `
` Acknowledgments `
` Part I Preliminaries `
` Chapter 1 Statistics and Social Science `
` 1.1 Statistical Models and Social Reality `
` 1.2 Observation and Experiment `
` 1.3 Populations and Samples `
` 1.4 Summary `
` 1.5 Recommended Reading `
` Chapter 2 What Is Regression Analysis? `
` 2.1 Preliminaries `
` 2.2 Naive Nonparametric Regression `
` 2.3 Local Averaging `
` 2.3.1 Weighted Local Averages* `
` 2.4 Summary `
` Chapter 3 Examining Data `
` 3.1 Univariate Displays `
` 3.1.1 Histograms `
` 3.1.2 Density Estimation* `
` 3.1.3 Quantile-Comparison Plots `
` 3.1.4 Boxplots `
` 3.2 Plotting Bivariate Data `
` 3.3 Plotting Multivariate Data `
` 3.4 Summary `
` 3.5 Recommended Reading `
` Chapter 4 Transforming Data `
` 4.1 The Family of Powers and Roots `
` 4.2 Transforming Skewness `
` 4.3 Transforming Nonlinearity `
` 4.4 Transforming Non-Constant Spread `
` 4.5 Transforming Proportions `
` 4.6 Summary `
` 4.7 Recommended Reading `
` Part II: Linear Models and Least Squares `
` Chapter 5 Linear Least-Squares Regression `
` 5.1 Simple Regression `
` 5.1.1 Least-Squares Fit `
` 5.1.2 Simple Correlation `
` 5.2 Multiple Regression `
` 5.2.1 Two Independent Variables `
` 5.2.2 Several Independent Variables `
` 5.2.3 Multiple Correlation `
` 5.2.4 Standardized Regression Coefficients `
` 5.3 Summary `
` Chapter 6 Statistical Inference for Regression `
` 6.1 Simple Regression `
` 6.1.1 The Simple-Regression Model `
` 6.1.2 Properties of the Least-Squares Estimator `
` 6.1.3 Confidence Intervals and Hypothesis Tests `
` 6.2 Multiple Regression `
` 6.2.1 The Multiple-Regression Model `
` 6.2.2 Confidence Intervals and Hypothesis Tests `
` Individual Slope Coefficients `
` All Slopes `
` A Subset of Slopes `
` 6.3 Empirical versus Structural Relations `
` 6.4 Measurement Error in Independent Variables* `
` 6.5 Summary `
` Chapter 7 Dummy-Variable Regression `
` 7.1 A Dichotomous Independent Variable `
` 7.2 Polytomous Independent Variables `
` 7.3 Modeling Interactions `
` 7.3.1 Constructing Interaction Regressors `
` 7.3.2 The Principle of Marginality `
` 7.3.3 Interactions With Polytomous Independent Variables `
` 7.3.4 Hypothesis Tests for Main Effects and Interactions `
` 7.4 A Caution Concerning Standardized Coefficients `
` 7.5 Summary `
` Chapter 8 Analysis of Variance `
` 8.1 One-Way Analysis of Variance `
` 8.2 Two-Way Analysis of Variance `
` 8.2.1 Patterns of Means in the Two-Way Classification `
` 8.2.2 The Two-Way ANOVA Model `
` 8.2.3 Fitting the Two-Way ANOVA Model to Data `
` 8.2.4 Testing Hypotheses in Two-Way ANOVA `
` 8.2.5 Equal Cell Frequencies `
` 8.2.6 Some Cautionary Remarks `
` 8.3 Higher-Way Analysis of Variance* `
` 8.3.1 The Three-Way Classification `
` 8.3.2 Higher-Order Classifications `
` 8.3.3 Empty Cells in ANOVA `
` 8.4 Analysis of Covariance `
` 8.5 Linear Contrasts of Means `
` 8.6 Summary `
` Chapter 9 Statistical Theory for Linear Models* `
` 9.1 Linear Models in Matrix Form `
` 9.1.1 Dummy Regression and Analysis of Variance `
` 9.1.2 Linear Contrasts `
` 9.2 Least-Squares Fit `
` 9.3 Properties of the Least-Squares Estimator `
` 9.3.1 The Distribution of the Least-Squares Estimator `
` 9.3.2 The Gauss-Markov Theorem `
` 9.3.3 Maximum-Likelihood Estimation `
` 9.4 Statistical Inference for Linear Models `
` 9.4.1 Inference for Individual Coefficients `
` 9.4.2 Inference for Several Coefficients `
` 9.4.3 General Linear Hypotheses `
` 9.4.4 Joint Confidence Regions `
` 9.5 Random Regressors `
` 9.6 Specification Error `
` 9.7 Summary `
` 9.8 Recommended Reading `
` Chapter 10 The Vector Geometry of Linear Models* `
` 10.1 Simple Regression `
` 10.1.1 Variables in Mean-Deviation Form `
` 10.1.2 Degrees of Freedom `
` 10.2 Multiple Regression `
` 10.3 Estimating the Error Variance `
` 10.4 Analysis-of-Variance Models `
` 10.5 Summary `
` 10.6 Recommended Reading `
` Part III: Linear-Model Diagnostics `
` Chapter 11 Unusual and Influential Data `
` 11.1 Outliers, Leverage, and Influence `
` 11.2 Assessing Leverage: Hat-Values `
` 11.3 Detecting Outliers: Studentized Residuals `
` 11.3.1 Testing for Outliers in Linear Models `
` 11.3.2 Anscombe's Insurance Analogy `
` 11.4 Measuring Influence `
` 11.4.1 Influence on Standard Errors `
` 11.4.2 Influence on Collinearity `
` 11.5 Numerical Cutoffs for Diagnostic Statistics `
` 11.5.1 Hat-Values `
` 11.5.2 Studentized Residuals `
` 11.5.3 Measures of Influence `
` 11.6 Joint Influence and Partial-Regression Plots `
` 11.7 Should Unusual Data Be Discarded? `
` 11.8 Some Statistical Details* `
` 11.8.1 Hat-Values and the Hat Matrix `
` 11.8.2 The Distribution of the Least-Squares Residuals `
` 11.8.3 Deletion Diagnostics `
` 11.8.4 Partial-Regression Plots `
` 11.9 Summary `
` 11.10 Recommended Reading `
` Chapter 12 Nonlinearity and Other Ills `
` 12.1 Non-Normally Distributed Errors `
` 12.1.1 Confidence Envelopes by Simulated Sampling* `
` 12.2 Non-Constant Error Variance `
` 12.2.1 Residual Plots `
` 12.2.2 Weighted-Least-Squares Estimation* `
` 12.2.3 Correcting OLS Standard Errors for Non-Constant Variance* `
` 12.2.4 How Non-Constant Error Variance Affects the OLS Estimator* `
` 12.3 Nonlinearity `
` 12.3.1 Partial-Residual Plots `
` 12.3.2 When Do Partial-Residual Plots Work? `
` CERES Plots* `
` 12.4 Discrete Data `
` 12.4.1 Testing for Nonlinearity `Lack of Fit') `
` 12.4.2 Testing for Non-Constant Error Variance `
` 12.5 Maximum-Likelihood Methods* `
` 12.5.1 Box-Cox Transformation of Y `
` 12.5.2 Box-Tidwell Transformation of the X's `
` 12.5.3 Non-Constant Error Variance Revisited `
` 12.6 Structural Dimension* `
` 12.7 Summary `
` 12.8 Recommended Reading `
` Chapter 13 Collinearity `
` 13.1 Detecting Collinearity `
` 13.1.1 Principal Components* `
` Two Variables `
` The Data Ellipsoid `
` Summary `
` Diagnosing Collinearity `
` 13.1.2 Generalized Variance Inflation* `
` 13.2 Coping With Collinearity: No Quick Fix `
` 13.2.1 Model Re-Specification `
` 13.2.2 Variable Selection `
` 13.2.3 Biased Estimation `
` Ridge Regression* `
` 13.2.4 Prior Information About the Regression Coefficients `
` 13.2.5 Some Comparisons `
` 13.3 Summary `
` Part IV: Beyond Linear Least Squares `
` Chapter 14 Extending Linear Least Squares* `
` 14.1 Time-Series Regression `
` 14.1.1 Generalized Least-Squares Estimation `
` 14.1.2 Serially Correlated Errors `
` GLS Estimation With Autoregressive Errors `
` Empirical GLS Estimation `
` 14.1.3 Diagnosing Serially Correlated Errors `
` 14.1.4 Concluding Remarks `
` 14.2 Nonlinear Regression `
` 14.2.1 Polynomial Regression `
` 14.2.2 Transformable Nonlinearity `
` 14.2.3 Nonlinear Least Squares `
` 14.3 Robust Regression `
` 14.3.1 M-Estimation `
` Estimating Location `
` M-Estimation in Regression `
` 14.3.2 Bounded-Influence Regression `
` 14.4 Nonparametric Regression `
` 14.4.1 Smoothing Scatterplots by Lowess `
` Selecting the Span `
` Statistical Inference `
` 14.4.2 Additive Regression Models `
` Fitting the Additive Regression Model `
` Statistical Inference `
` Semi-Parametric Models `
` 14.5 Summary `
` Time-Series Regression `
` Nonlinear Regression `
` Robust Regression `
` Nonparametric Regression `
` 14.6 Recommended Reading `
` Chapter 15 Logit and Probit Models `
` 15.1 Models for Dichotomous Data `
` 15.1.1 The Linear-Probability Model `
` 15.1.2 Transformations of pi: Logit and Probit Models `
` 15.1.3 An Unobserved-Variable Formulation `
` 15.1.4 Logit and Probit Models for Multiple Regression `
` 15.1.5 Estimating the Linear Logit Model* `
` 15.1.6 Diagnostics for Logit Models* `
` Residuals in Logit model `
` Residual and Partial-Residual Plots `
` Hat-Values and the Hat-Matrix `
` Studentized Residuals `
` Influence Diagnostics `
` Partial-Regression Plot `
` Constructed-Variable Plot for Transforming an X `
` 15.2 Models for Polytomous Data `
` 15.2.1 The Polytomous Logit Model `
` Details of Estimation* `
` 15.2.2 Nested Dichotomies `
` Why Nested Dichotomies are Independent* `
` 15.2.3 Ordered Logit and Probit Models `
` 15.2.4 Comparison of the Three Approaches `
` 15.3 Discrete Independent Variables `
` 15.3.1 The Binomial Logit Model* `
` 15.4 Generalized Linear Models* `
` 15.5 Summary `
` 15.6 Recommended Reading `
` Chapter 16 Assessing Sampling Variation `
` 16.1 Bootstrapping `
` 16.1.1 Bootstrapping Basics `
` 16.1.2 Bootstrap Confidence Intervals `
` Normal-Theory Intervals `
` Percentile Intervals `
` Improved Bootstrap Intervals* `
` 16.1.3 Bootstrapping Regression Models `
` 16.1.4 Bootstrap Hypothesis Tests* `
` 16.1.5 Bootstrapping Complex Sampling Designs `
` 16.1.6 Concluding Remarks `
` 16.2 Cross-Validation `
` 16.2.1 An Illustration `
` 16.2.2 Concluding Remarks `
` 16.3 Summary `
` 16.4 Recommended Reading `
` Appendix A: Notation `
` Appendix B: Vector Geometry* `
` B.1 Basic Operations `
` B.2 Vector Spaces and Subspaces `
` B.3 Orthogonality and Orthogonal Projections `
` B.4 Recommended Reading `
` Appendix C Multivariable Differential Calculus `
` C.1 Partial Derivatives `
` C.2 Lagrange Multipliers `
` C.3 Matrix Calculus `
` Appendix D Probability and Estimation `
` D.1 Elementary Probability Theory `
` D.1.1 Basic Definitions `
` D.1.2 Random Variables `
` Vector Random Variables* `
` D.1.3 Transformations of Random Variables `
` Transformations of Vector Random Variables* `
` D.2 Discrete Distributions* `
` D.2.1 The Binomial Distribution `
` D.2.2 The Multinomial Distribution `
` D.2.3 The Poisson Distribution `
` D.3 Continuous Distributions `
` D.3.1 The Normal Distribution `
` D.3.2 The Chi-Square Distribution `
` D.3.3 The t-Distribution `
` D.3.4 The F-Distribution `
` D.3.5 The Multivariate-Normal Distribution* `
` D.4 Asymptotic Distribution Theory* `
` D.4.1 Probability Limits `
` D.4.2 Asymptotic Expectation and Variance `
` D.4.3 Asymptotic Distribution `
` D.5 Properties of Estimators `
` D.5.1 Bias `
` Asymptotic Bias* `
` D.5.2 Mean-Squared Error and Efficiency `
` Asymptotic Efficiency* `
` D.5.3 Consistency* `
` D.5.4 Sufficiency* `
` D.6 Maximum-Likelihood Estimation `
` Generalization of the Example* `
` D.6.1 Properties of Maximum-Likelihood Estimators* `
` D.6.2 Wald, Likelihood-Ratio, and Score Tests `
` An Illustration* `
` D.6.3 Several Parameters* `
` D.7 Recommended Reading `
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<meta http-equiv="refresh" content="1; url=/nojavascript/"> Pythagorean Identities | CK-12 Foundation
You are reading an older version of this FlexBook® textbook: CK-12 Trigonometry Concepts Go to the latest version.
# 1.25: Pythagorean Identities
Created by: CK-12
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What if you were working on a problem using the unit circle and had the value of one trig function (such as sine), but wanted instead to find the value of another trig function (such as cosine)? Is this possible?
Try it with $\sin \theta = \frac{1}{2}$
Keep reading, and when this Concept is finished, you'll know how to use this information to help you find $\cos \theta$ .
### Watch This
The final portion of this video reviews the Pythagorean Identities.
### Guidance
One set of identities are called the Pythagorean Identities because they rely on the Pythagorean Theorem. In other Concepts we used the Pythagorean Theorem to find the sides of right triangles. Consider the way that the trig functions are defined. Let’s look at the unit circle:
The legs of the right triangle are $x$ and $y$ . The hypotenuse is 1. Therefore the following equation is true for all $x$ and $y$ on the unit circle:
$x^2 + y^2 = 1$
Now remember that on the unit circle, $\cos \theta = x$ and $\sin \theta = y$ . Therefore the following equation is an identity:
$\cos^2 \theta + \sin^2 \theta = 1$
Note: Writing the exponent 2 after the $cos$ and $sin$ is the standard way of writing exponents. Just keeping mind that $\cos^2 \theta$ means $(\cos \theta)^2$ and $\sin ^2 \theta$ means $(\sin \theta)^2$ .
We can use this identity to find the value of the sine function, given the value of the cosine, and vice versa. We can also use it to find other identities.
#### Example A
If $\cos \theta = \frac{1}{4}$ what is the value of $\sin \theta$ ? Assume that $\theta$ is an angle in the first quadrant.
Solution: $\sin \theta = \frac{\sqrt{15}}{4}$
$\cos^2 \theta + \sin^2 \theta & = 1\\\left ( \frac{1}{4} \right )^2 + \sin ^2 \theta & = 1\\\frac{1}{16} + \sin^2 \theta & = 1\\\sin^2 \theta & = 1 -\frac{1}{16}\\\sin^2 \theta & = \frac{15}{16}\\\sin \theta & = \pm \sqrt{\frac{15}{16}}\\\sin \theta & = \pm \frac{\sqrt{15}}{4}$
Remember that it was given that $\theta$ is an angle in the first quadrant. Therefore the sine value is positive, so $\sin \theta = \frac{\sqrt{15}}{4}$ .
#### Example B
Use the identity $\cos^2\theta + \sin^2\theta = 1$ to show that $\cot^2 \theta + 1 = \csc^2 \theta$
Solution:
$\cos^2\theta + \sin^2\theta & = 1 && \text{Divide both sides by} \sin^2 \theta.\\\frac{\cos^2\theta + \sin^2\theta}{\sin^2\theta} & = \frac{1}{\sin^2 \theta}\\\frac{\cos^2\theta}{\sin^2\theta} + \frac{\sin^2\theta}{\sin^2\theta} & = \frac{1}{\sin^2\theta} && \frac{\sin^2\theta}{\sin^2\theta} = 1\\\frac{\cos^2\theta}{\sin^2\theta} + 1 & = \frac{1}{\sin^2\theta}\\\frac{\cos \theta}{\sin \theta} \times \frac{\cos \theta}{\sin \theta} + 1 & = \frac{1}{\sin \theta} \times \frac{1}{\sin \theta} && \text{Write the squared functions in terms}\\&&& \text{of their factors.}\\\cot \theta \times \cot \theta + 1 & = \csc \theta \times \csc \theta && \text{Use the quotient and reciprocal}\\&&& \text{identities.}\\\cot^2\theta + 1 & = \csc^2 \theta && \text{Write the functions as squared}\\&&& \text{functions.}$
#### Example C
If $\sin \theta = \frac{1}{2}$ what is the value of $\cos \theta$ ? Assume that $\theta$ is an angle in the first quadrant.
Solution: $\cos \theta = \sqrt{\frac{3}{4}}$
$\sin^2 \theta + \cos^2 \theta & = 1\\\left ( \frac{1}{2} \right )^2 + \cos ^2 \theta & = 1\\\frac{1}{4} + \cos^2 \theta & = 1\\\cos^2 \theta & = 1 -\frac{1}{4}\\\cos^2 \theta & = \frac{3}{4}\\\cos \theta & = \pm \sqrt{\frac{3}{4}}\\$
Remember that it was given that $\theta$ is an angle in the first quadrant. Therefore the cosine value is positive, so $\cos \theta = \sqrt{\frac{3}{4}}$ .
### Vocabulary
Pythagorean Identity: A pythagorean identity is a relationship showing that the sine of an angle squared plus the cosine of an angle squared is equal to one.
### Guided Practice
1. If $\cos \theta = \frac{1}{2}$ what is the value of $\sin \theta$ ? Assume that $\theta$ is an angle in the first quadrant.
2. If $\sin \theta = \frac{1}{8}$ what is the value of $\cos \theta$ ? Assume that $\theta$ is an angle in the first quadrant.
3. If $\sin \theta = \frac{1}{3}$ what is the value of $\cos \theta$ ? Assume that $\theta$ is an angle in the first quadrant.
Solutions:
1. The solution is $\sin \theta = \sqrt{\frac{3}{4}}$ . We can see this from the Pythagorean Identity:
$\cos^2 \theta + \sin^2 \theta & = 1\\\left ( \frac{1}{2} \right )^2 + \sin ^2 \theta & = 1\\\frac{1}{4} + \sin^2 \theta & = 1\\\sin^2 \theta & = 1 -\frac{1}{4}\\\sin^2 \theta & = \frac{3}{4}\\\sin \theta & = \pm \sqrt{\frac{3}{4}}\\$
2. The solution is $\cos \theta = \sqrt{\frac{63}{64}}$ . We can see this from the Pythagorean Identity:
$\cos^2 \theta + \sin^2 \theta & = 1\\\left ( \frac{1}{8} \right )^2 + \cos ^2 \theta & = 1\\\frac{1}{64} + \cos^2 \theta & = 1\\\cos^2 \theta & = 1 -\frac{1}{64}\\\cos^2 \theta & = \frac{63}{64}\\\cos \theta & = \pm \sqrt{\frac{63}{64}}\\$
3. The solution is $\cos \theta = \sqrt{\frac{8}{9}}$ . We can see this from the Pythagorean Identity:
$\sin^2 \theta + \cos^2 \theta & = 1\\\left ( \frac{1}{3} \right )^2 + \cos ^2 \theta & = 1\\\frac{1}{9} + \cos^2 \theta & = 1\\\cos^2 \theta & = 1 -\frac{1}{9}\\\cos^2 \theta & = \frac{8}{9}\\\cos \theta & = \pm \sqrt{\frac{8}{9}}\\$
### Concept Problem Solution
Since we now know that:
$\sin^2 \theta + \cos^2 \theta = 1$
we can use this to help us compute the cosine of the angle from the problem at the beginning of this Concept. It was given at the beginning of this Concept that:
$\sin \theta = \frac{1}{2}$
Therefore, $\sin^2 \theta = \frac{1}{4}$
If we use this to solve for cosine:
$\sin^2 \theta + \cos^2 \theta = 1\\\cos^2 \theta = 1 - \sin^2 \theta\\\cos^2 \theta = 1 - \frac{1}{4}\\\cos^2 \theta = \frac{3}{4}\\\cos \theta = \frac{\sqrt{3}}{2}\\$
### Practice
1. If you know $\sin \theta$ , what other trigonometric value can you determine using a Pythagorean Identity?
2. If you know $\sec \theta$ , what other trigonometric value can you determine using a Pythagorean Identity?
3. If you know $\cot \theta$ , what other trigonometric value can you determine using a Pythagorean Identity?
4. If you know $\tan \theta$ , what other trigonometric value can you determine using a Pythagorean Identity?
For questions 5-14, assume all angles are in the first quadrant.
1. If $\sin \theta = \frac{1}{2}$ , what is the value of $\cos \theta$ ?
2. If $\cos \theta = \frac{\sqrt{2}}{2}$ , what is the value of $\sin \theta$ ?
3. If $\tan \theta = 1$ , what is the value of $\sec \theta$ ?
4. If $\csc \theta = \sqrt{2}$ , what is the value of $\cot \theta$ ?
5. If $\sec \theta = 2$ , what is the value of $\tan \theta$ ?
6. If $\cot \theta = \sqrt{3}$ , what is the value of $\csc \theta$ ?
7. If $\cos \theta = \frac{1}{4}$ , what is the value of $\sin \theta$ ?
8. If $\sec \theta = 3$ , what is the value of $\tan \theta$ ?
9. If $\sin \theta = \frac{1}{5}$ , what is the value of $\cos \theta$ ?
10. If $\tan \theta = \frac{\sqrt{3}}{3}$ , what is the value of $\sec \theta$ ?
11. Use the identity $\sin^2\theta + \cos^2\theta = 1$ to show that $\tan^2 \theta + 1 = \sec^2 \theta$
Sep 26, 2012
Aug 17, 2014
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Cody
# Problem 1802. 03 - Matrix Variables 6
Solution 311715
Submitted on 28 Aug 2013 by Jacob
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% user = MatrixFunc(); assert(isequal(size(user),[5 3]))
fMat = -3 1 1 -3 0 2 2 1 -2 3 0 -1 1 -3 -3
2 Pass
%% user = MatrixFunc(); assert(max(max(user))<=3)
fMat = -1 3 -3 3 -3 2 2 -3 -1 2 1 0 -2 0 -2
3 Pass
%% user = MatrixFunc(); assert(min(min(user))>=-3)
fMat = -2 0 -3 -3 3 2 -3 1 1 1 3 2 0 0 -1
4 Pass
%% user = MatrixFunc(); assert(sum(sum(user))==floor(sum(sum(user))))
fMat = -1 0 0 -3 3 3 1 0 0 1 0 -1 1 2 -1
5 Pass
%% user = MatrixFunc(); assert(~all(user(:)==user(1)))
fMat = -1 -2 3 -2 1 1 -2 -2 1 -2 -1 2 1 -2 -1
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# 28834 (number)
28,834 (twenty-eight thousand eight hundred thirty-four) is an even five-digits composite number following 28833 and preceding 28835. In scientific notation, it is written as 2.8834 × 104. The sum of its digits is 25. It has a total of 3 prime factors and 8 positive divisors. There are 13,296 positive integers (up to 28834) that are relatively prime to 28834.
## Basic properties
• Is Prime? No
• Number parity Even
• Number length 5
• Sum of Digits 25
• Digital Root 7
## Name
Short name 28 thousand 834 twenty-eight thousand eight hundred thirty-four
## Notation
Scientific notation 2.8834 × 104 28.834 × 103
## Prime Factorization of 28834
Prime Factorization 2 × 13 × 1109
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 3 Total number of prime factors rad(n) 28834 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 28,834 is 2 × 13 × 1109. Since it has a total of 3 prime factors, 28,834 is a composite number.
## Divisors of 28834
1, 2, 13, 26, 1109, 2218, 14417, 28834
8 divisors
Even divisors 4 4 4 0
Total Divisors Sum of Divisors Aliquot Sum τ(n) 8 Total number of the positive divisors of n σ(n) 46620 Sum of all the positive divisors of n s(n) 17786 Sum of the proper positive divisors of n A(n) 5827.5 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 169.806 Returns the nth root of the product of n divisors H(n) 4.94792 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 28,834 can be divided by 8 positive divisors (out of which 4 are even, and 4 are odd). The sum of these divisors (counting 28,834) is 46,620, the average is 582,7.5.
## Other Arithmetic Functions (n = 28834)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 13296 Total number of positive integers not greater than n that are coprime to n λ(n) 3324 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3136 Total number of primes less than or equal to n r2(n) 16 The number of ways n can be represented as the sum of 2 squares
There are 13,296 positive integers (less than 28,834) that are coprime with 28,834. And there are approximately 3,136 prime numbers less than or equal to 28,834.
## Divisibility of 28834
m n mod m 2 3 4 5 6 7 8 9 0 1 2 4 4 1 2 7
The number 28,834 is divisible by 2.
• Deficient
• Polite
• Square Free
• Sphenic
## Base conversion (28834)
Base System Value
2 Binary 111000010100010
3 Ternary 1110112221
4 Quaternary 13002202
5 Quinary 1410314
6 Senary 341254
8 Octal 70242
10 Decimal 28834
12 Duodecimal 1482a
20 Vigesimal 3c1e
36 Base36 m8y
## Basic calculations (n = 28834)
### Multiplication
n×y
n×2 57668 86502 115336 144170
### Division
n÷y
n÷2 14417 9611.33 7208.5 5766.8
### Exponentiation
ny
n2 831399556 23972574797704 691225221716997136 19930788042987895419424
### Nth Root
y√n
2√n 169.806 30.6644 13.031 7.79796
## 28834 as geometric shapes
### Circle
Diameter 57668 181169 2.61192e+09
### Sphere
Volume 1.00416e+14 1.04477e+10 181169
### Square
Length = n
Perimeter 115336 8.314e+08 40777.4
### Cube
Length = n
Surface area 4.9884e+09 2.39726e+13 49942
### Equilateral Triangle
Length = n
Perimeter 86502 3.60007e+08 24971
### Triangular Pyramid
Length = n
Surface area 1.44003e+09 2.8252e+12 23542.9
## Cryptographic Hash Functions
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recent
### Fundamental laws of Thermodynamics
Classical thermodynamics is based upon four empirical principles called zeroth, first, second and third laws of thermodynamics. These laws define thermodynamic properties, which are of great importance in understanding of thermodynamic principles. Zeroth law defines temperature; first law defines internal energy; second law defines entropy and the third law can be used to obtain absolute entropy values. The above four thermodynamic laws are based on human observation of natural phenomena; they are not mathematically derived equations. Since no exceptions to these have been observed; these are accepted as laws.
Conservation of mass is a fundamental concept, which states that mass is neither created nor destroyed.
The Zeroth law of thermodynamics states that when two systems are in thermal equilibrium with a third system, then they in turn are in thermal equilibrium with each other. This implies that some property must be same for the three systems. This property is temperature. Thus this law is the basis for temperature measurement. Equality of temperature is a necessary and sufficient condition for thermal equilibrium, i.e. no transfer of heat.
Fig. Example of zeroth law
The First law of thermodynamics
It is a statement of law of conservation of energy. Also, according to this law, heat and work are interchangeable. Any system that violates the first law (i.e., creates or destroys energy) is known as a Perpetual Motion Machine (PMM) of first kind.
For a system undergoing a cyclic process, the first law of thermodynamics is given by:
Mathematical expression of first law
Second law of thermodynamics:
The second law of thermodynamics is a limit law. It gives the upper limit of efficiency of a system. The second law also acknowledges that processes follow in a certain direction but not in the opposite direction. It also defines the important property called entropy.
It is common sense that heat will not flow spontaneously from a body at lower temperature to a body at higher temperature. In order to transfer heat from lower temperature to higher temperature continuously (that is, to maintain the low temperature) a refrigeration system is needed which requires work input from external source. This is one of the principles of second law of thermodynamics, which is known as Clausius statement of the second law.
Clausius’ statement of second law
It is impossible to transfer heat in a cyclic process from low temperature to high temperature without work from external source.
It is also a fact that all the energy supplied to a system as work can be dissipated as heat transfer. On the other hand, all the energy supplied as heat transfer cannot be continuously converted into work giving a thermal efficiency of 100 percent. Only a part of heat transfer at high temperature in a cyclic process can be converted into work, the remaining part has to be rejected to surroundings at lower temperature. If it were possible to obtain work continuously by heat transfer with a single heat source, then automobile will run by deriving energy from atmosphere at no cost. A hypothetical machine that can achieve it is called Perpetual Motion Machine of second kind. This fact is embedded in Kelvin-Planck Statement of the Second law.
Kelvin-Planck statement of second law
It is impossible to construct a device (engine) operating in a cycle that will produce no effect other than extraction of heat from a single reservoir and convert all of it into work.
Mathematically, Kelvin-Planck statement can be written as:
Third law of thermodynamics:
This law gives the definition of absolute value of entropy and also states that absolute zero cannot be achieved. Another version of this law is that “the entropy of perfect crystals is zero at absolute zero”.
#### Definitions of Entropy :
1. is a state variable whose change is defined for a reversible process at T where Q is the heat absorbed.
2. a measure of the amount of energy which is unavailable to do work.
3. a measure of the disorder of a system.
For imperfect crystals however there is some entropy associated with configuration of molecules and atoms even when all motions cease, hence the entropy in this case does not tend to zero as T → 0, but it tends to a constant called the entropy of configuration.
The third law allows absolute entropy to be determined with zero entropy at absolute zero as the reference state. In refrigeration systems we deal with entropy changes only, the absolute entropy is not of much use. Therefore entropy may be taken to be zero or a constant at any suitably chosen reference state.
Another consequence of third law is that absolute zero cannot be achieved. One tries to approach absolute zero by magnetization to align the molecules. This is followed by cooling and then demagnetization, which extracts energy from the substance and reduces its temperature. It can be shown that this process will require infinite number of cycles to achieve absolute zero. In a later chapter it will be shown that infinitely large amount of work is required to maintain absolute zero if at all it can be achieved.
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# Basic Math & Pre-Algebra Extras For Dummies
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### Basic Math & Pre-Algebra For Dummies Cheat Sheet
With arithmetic a little understanding can go a long way toward helping master math. Some math concepts may seem complicated at first, but after you work with them for a little bit, you may wonder what
### Using Prime Factorizations
Every whole number greater than 1 has a prime factorization — that is, the list of prime numbers (including repeats) that equal that number when multiplied together. For example, here are the prime factorizations
### Introducing the Percent Circle
The percent circle is a simple visual aid that helps you make sense of percent problems so that you can solve them easily. The trick to using a percent circle is to write information into it. For example
### Using Probability to Calculate the Odds in the Game of Craps
Probability is the mathematics of deciding how likely an event is to occur. You can calculate the probability of an event by using the following formula:
### Simplifying and Factoring Expressions
In algebra, simplifying and factoring expressions are opposite processes. Simplifying an expression often means removing a pair of parentheses; factoring an expression
### 10 Math Concepts You Can't Ignore
Math itself is one big concept, and it's chock full of so many smaller mathematical concepts that no one person can possibly understand them all — even with a good dose of studying. Yet certain concepts
### How to Convert between Fractions and Repeating Decimals
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number), using either calculator or pencil and paper. For example, here’s how to convert the fraction
### Making Sense of Weird Exponents
Exponents are a quick way to represent repeated multiplication. Raising a base number to the power of an exponentmeans multiplying the base by itself the number of times indicated by the exponent. For
### Solving Systems of Equations in Algebra
In most cases, an algebraic equation is solvable only when one value is unknown — that is, when the equation has only one variable. In rare cases, you can solve an equation with two or more variables because
### 10 Great Mathematicians
Mathematics is an ongoing journey of thousands of years and millions of minds. The list below is by no means complete, but here are ten great mathematicians whose work forever changed not only math but
Education & Languages
### Inside Dummies.com
About us More From Dummies Topics A-Z
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# Transform point position in trapezoid to rectangle position
I am trying to find out how I can transform a coordinate Pxy within the green trapezoid below into the equivalent coordinate on the real ground plane.
I have the exact measures of the room, meaning I can exactly say how long A,B,C and D are in that room shown below. Also I know how long A,B,C and D are in that green triangle (coordinate wise).
I have already been reading about homography and matrix transformation, but can't really wrap my head around it. Any input steering me into the right direction would be appreciated.
Thanks!
-
I think I need to clarify, that I am not looking to transform an image here. I am looking for a method to transform A,B,C,D into a rectangle of known size and alongside transform Pxy into the known rectangle. – Sebastian Borggrewe Feb 12 '13 at 14:26
See stackoverflow.com/a/14178717/1832154, it presents code to find the coefficients for the homographic transform as well a link that explains it. By achieving this matrix, you can directly find to where your point `Pxy` will be mapped to. – mmgp Feb 12 '13 at 16:06
add comment
## 3 Answers
Just for the sake of completion. I ended up looking at the thread suggested by @mmgp and implemented a solution that is equivalent to the one presented by Christopher R. Wren:
Perspective Transform Estimation
This turned out to work really well for my case, although there was some distortion from the camera.
-
add comment
If I understand your question correctly, you are looking for the transform matrix that expresses the position and orientation (aka the "pose") of your camera in relation to the world. If you have this matrix - lets call it M - you could map any point from your camera coordinate frame to the world coordinate frame and vice versa. In your case you'll want to transform a rectangle onto the plane (0, 1, 0)^T + 0 in world coordinates.
There are several ways to derive this pose Matrix. First of all you'll need to know another matrix - K - which describes the internal camera parameters to convert positions in the camera coordinate frame to actual pixel positions. This involves a standard pinhole projection as well as radial distortion and a few other things.
To determine both K and M you have to calibrate your camera. This is usually done by taking a calibration pattern (e.g. a chessboard-pattern) for which the positions of the chessboard-fields are known. Then you can establish so called Point-Correspondences between the known positions on the pattern and the observed pixel-positions. Once you have enough of these point-pairs you can solve a Matrix H = KM. This is your Homography matrix you've mentioned already. Once you have that, you can reconstruct K and M.
So much for the theory. For the practical part I would suggest to have a look at the OpenCV-Documentations (e.g. you could start here: OpenCV Camera calibration and here: OpenCV Pose estimation).
I hope this will point you in the right directions ;)
-
add comment
There is the code computes the affine transformation matrix using the library Opencv (it shows how to trasform your trapezoid to rectangle and how to find transformation matrix for futher calculations):
``````//example from book
// Learning OpenCV: Computer Vision with the OpenCV Library
// by Gary Bradski and Adrian Kaehler
// Published by O'Reilly Media, October 3, 2008
#include <cv.h>
#include <highgui.h>
#include <stdlib.h>
#include <stdio.h>
int main(int argc, char* argv[])
{
IplImage *src=0, *dst=0;
// absolute or relative path to image should be in argv[1]
char* filename = argc == 2 ? argv[1] : "Image0.jpg";
// get the picture
src = cvLoadImage(filename,1);
printf("[i] image: %s\n", filename);
assert( src != 0 );
// points (corners of )
CvPoint2D32f srcQuad[4], dstQuad[4];
// transformation matrix
CvMat* warp_matrix = cvCreateMat(3,3,CV_32FC1);
// clone image
dst = cvCloneImage(src);
// define all the points
//here the coordinates of corners of your trapezoid
srcQuad[0].x = ??; //src Top left
srcQuad[0].y = ??;
srcQuad[1].x = ??; //src Top right
srcQuad[1].y = ??;
srcQuad[2].x = ??; //src Bottom left
srcQuad[2].y = ??;
srcQuad[3].x = ??; //src Bot right
srcQuad[3].y = ??;
//- - - - - - - - - - - - - -//
//coordinates of rectangle in src image
dstQuad[0].x = 0; //dst Top left
dstQuad[0].y = 0;
dstQuad[1].x = src->width-1; //dst Top right
dstQuad[1].y = 0;
dstQuad[2].x = 0; //dst Bottom left
dstQuad[2].y = src->height-1;
dstQuad[3].x = src->width-1; //dst Bot right
dstQuad[3].y = src->height-1;
// get transformation matrix that you can use to calculate
//coordinates of point Pxy
cvGetPerspectiveTransform(srcQuad,dstQuad,warp_matrix);
// perspective transformation
cvWarpPerspective(src,dst,warp_matrix);
cvNamedWindow( "cvWarpPerspective", 1 );
cvShowImage( "cvWarpPerspective", dst );
cvWaitKey(0);
cvReleaseMat(&warp_matrix);
cvReleaseImage(&src);
cvReleaseImage(&dst);
cvDestroyAllWindows();
return 0;
``````
Hope it will be helpfull!
-
Hi Ann, I am not really looking for an image to transform. However I understand that I get a transformation matrix from this example, but what do you exactly mean by "//coordinates of rectangle in src image". – Sebastian Borggrewe Feb 12 '13 at 14:25
Sorry, not rectangle,I meant the corners of your trapazoid in src image. – Ann Orlova Feb 13 '13 at 5:30
add comment
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# Python – Multiply two list
• Last Updated : 27 Dec, 2019
There can be many situations in which one requires to find index wise product of two different lists. This can have a possible applications in day-day programming. Lets discuss various ways in which this task can be performed.
Method #1 : Naive Method
In this method, we simply run a loop and append to the new list the product of the both list elements at similar index till we reach end of the smaller list. This is the basic method to achieve this task.
`# Python code to demonstrate ``# Multiplying two lists``# naive method `` ` `# initializing lists``test_list1 ``=` `[``1``, ``3``, ``4``, ``6``, ``8``]``test_list2 ``=` `[``4``, ``5``, ``6``, ``2``, ``10``]`` ` `# printing original lists``print` `(``"Original list 1 : "` `+` `str``(test_list1))``print` `(``"Original list 2 : "` `+` `str``(test_list2))`` ` `# using naive method to ``# Multiplying two lists``res_list ``=` `[]``for` `i ``in` `range``(``0``, ``len``(test_list1)):`` ``res_list.append(test_list1[i] ``*` `test_list2[i])`` ` `# printing resultant list ``print` `(``"Resultant list is : "` `+` `str``(res_list))`
Output :
```Original list 1 : [1, 3, 4, 6, 8]
Original list 2 : [4, 5, 6, 2, 10]
Resultant list is : [4, 15, 24, 12, 80]
```
Method #2 : Using List Comprehension
The shorthand for the above explained technique, list comprehensions are usually quicker to type and hence must be preferred to perform these kind of programming tasks.
`# Python code to demonstrate ``# Multiplying two lists``# list comprehension`` ` `# initializing lists``test_list1 ``=` `[``1``, ``3``, ``4``, ``6``, ``8``]``test_list2 ``=` `[``4``, ``5``, ``6``, ``2``, ``10``]`` ` `# printing original lists``print` `(``"Original list 1 : "` `+` `str``(test_list1))``print` `(``"Original list 2 : "` `+` `str``(test_list2))`` ` `# using list comprehension to ``# Multiplying two lists``res_list ``=` `[test_list1[i] ``*` `test_list2[i] ``for` `i ``in` `range``(``len``(test_list1))]`` ` `# printing resultant list ``print` `(``"Resultant list is : "` `+` `str``(res_list))`
Output :
```Original list 1 : [1, 3, 4, 6, 8]
Original list 2 : [4, 5, 6, 2, 10]
Resultant list is : [4, 15, 24, 12, 80]
```
My Personal Notes arrow_drop_up
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## 5490Re: similarity scores
Expand Messages
• Dec 20, 2004
• 0 Attachment
Thank you. I am an idiot sometimes. It is a challenge sometimes to
write out correct and clear instructions. And to think this is what
I do for a living. :)
1. Compute the weighted mean.
2. Compute the squared deviations from the weighted mean.
3. Weight the squared deviations by minutes played.
4. Sum the weighted squared deviations.
5. Divide this sum by the sum of minutes played.
6. Take the square root of this weighted average of the squared
deviations.
And I do not think there is any need to square the weights. I do
not believe this is what is done in most typical regression packages.
Best wishes,
Dan
wrote:
> Yup, although if it's a standard deviation that we're
> calculating, I think what you want in step 2 is to
> SQUARE the deviations.
>
> And in 5, although dividing by the sum of minutes played
> is good, arguably better might be to reduce that
> figure slightly to correct for degrees of freedom,
> by multiplying the minutes played by (N-1)/N.
>
> And given the squaring that I describe in step 2,
> then there of course needs to be a step 6: take
> the square root, after you finish step 5.
>
> The procedure that I describe is, e.g., the one
> described in the National Institute of Standards
> and Technology's nifty statistics website:
>
http://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/weightsd
.pdf
>
> Come to think of it, in a regression framework,
> wouldn't we square the weights too, in Step 2?
> Ah, I'll worry about that later. DanR's procedure
> is the one I'd follow, but with the amendments listed
> above.
>
>
> --MKT
>
>
> -----Original Message-----
> From: dan_t_rosenbaum [mailto:rosenbaum@u...]
> Sent: Saturday, December 18, 2004 10:04 AM
>
>
> I just compute standard deviations weighted by minutes played. I
> could not find where Excel does this, but what you could do is the
> following.
>
> 1. Compute the weighted mean.
> 2. Compute the deviations from the weighted mean.
> 3. Weight the deviations by minutes played.
> 4. Sum the weighted deviations.
> 5. Divide this sum by the sum of minutes played.
>
> --- In APBR_analysis@yahoogroups.com, "thedawgsareout"
> <kpelton08@h...> wrote:
> >
> > > The notion of the average representing the range of
> > > players that you'd actually see play is an interesting
> > > one.
> > >
> > > I think what it comes down to is this: do we want an
> > > average of what happens during NBA games, or an
> > > average of what NBA players do? You're advocating the
> > > former, and I guess I am asking about the latter.
> > >
> > > Either way is fine, I guess it comes down to
> > > semantics.
> >
> > Maybe someone's mentioned this and I've missed it, but what do
you
> > guys plan to do about standard deviation if you use some sort of
> > weighted system?
> >
> > I would argue that in this case, standard deviation is far more
> > important than average. You're not going to change average very
> much
> > depending on what population you use, but standard deviation
> changes
> > quite significantly. The reason you don't use low-minutes guys
> isn't
> > because they're not NBA players; it's because their stats are
> > obviously not significant.
> >
> > Let's use rebounds per 48 minutes last year as an example.
> >
> > If you take the pure average of everyone in the league, you get
> > 8.38. If you weight by minutes, you get 8.38. If you cut off at
> 250
> > minutes and take the pure average (which is what I do), you get
> 8.52.
> >
> > There's a difference there, but not an enormous one.
> >
> > If you take the standard deviation of guys with 250 minutes or
> more,
> > it's 3.52. The standard deviation of everyone is 3.76. That's a
> > bigger difference (though you could argue that because changing
> > average takes guys from above average to below it, it's more
> > significant).
>
>
>
>
>
>
>
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# Learning Counting and Cardinality Using LEGO Bricks
K - 2nd
Subjects
Resource Type
Formats Included
• PDF
Pages
56 pages
### Description
In Learning Counting and Cardinality Using LEGO® Bricks, Dr. Shirley Disseler has developed activities that work to help students learn how to count and understand cardinality, using a common toy available in most classrooms and homes— LEGO® bricks!
Number recitation is only the start of a child’s true understanding of counting and cardinality. When students learn to count on, count back, skip-count, and use one-to-one correspondence, they develop a solid base of fluency with numbers. Even before they understand any other mathematical concepts, students can model the process of counting with LEGO® bricks to help visualize the math.
In this book, the hands-on activities using LEGO® bricks help students learn:
• pattern recognition
• skip-counting
• jump numbers
• concepts of more than and less than
• one-to-one correspondence
The book starts at the most basic concepts and focuses on a specific topic in each chapter. Most students learn these concepts between grades K – 2.
Using LEGO® bricks to model math provides a universal language. Children everywhere recognize this manipulative.
It’s fun to learn when you’re using LEGO® bricks!
Total Pages
56 pages
N/A
Teaching Duration
N/A
Report this Resource to TpT
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# 140: Delicious
Delicious Title text: I'm currently in the I Have Cheese phase of this cycle.
## Explanation
The simplest explanation for the comic is the recipe for nachos. You take some tortilla chips, spread them out on a plate, sprinkle them with grated cheese, and put the plate in the oven until the cheese is melted. As usual with a full bag of snacks, you always end up with that tiny bit left at the bottom of the bag. In this case, it is either leftover grated cheese (left) or tortilla chips (right). So you end up buying another package of the other ingredient to make nachos again.
The lower caption is a play on the words vicious cycle, in which a negative feedback loop reinforces itself - in contrast to a virtuous cycle in which a positive feedback loop is established.
## Transcript
[Frame is split by a diagonal.]
[First half: Cueball in front of open fridge.]
Cueball: I have leftover cheese. I should get chips and make nachos.
[Second half: Cueball with bag of chips.]
Cueball: I have leftover chips. I should get cheese and make nachos.
A delicious cycle
# Discussion
Rikthoff (talk) The issue date is definitely off. Can anyone fix?
Fixed --DanB (talk) 13:52, 14 August 2012 (UTC)
Also, my wife has a similar problem with cereal. She won't drink the milk after finishing the cereal, so she goes to get more milk. --DanB (talk) 13:52, 14 August 2012 (UTC)
If you melt the cheese enough, it becomes a viscous cycle. Alpha (talk) 04:41, 15 September 2013 (UTC)
The explanation states that a vicious cycle is a negative feedback loop while a virtuous cycle is a positive one. Actually, both are positive feedback loops, i.e. self-reinforcing ones. Vicious means that the results are negative, virtuous that the results are positive.
From the linked wikipedia page: The terms virtuous circle and vicious circle refer to complex chains of events which reinforce themselves through a feedback loop. A virtuous circle has favorable results, while a vicious circle has detrimental results. [...] Both circles are complexes of events with no tendency towards equilibrium (at least in the short run). Both systems of events have feedback loops in which each iteration of the cycle reinforces the previous one (positive feedback). 173.245.53.121 23:55, 10 October 2014 (UTC)
The best way to break this is to remember that you can still eat the chips after using up the dip. 173.245.56.211 (talk) (please sign your comments with ~~~~)
Or you can drink the melted cheese after running out of chips. That's how you know you're an adult: nobody can stop you from drinking melted cheese. 162.158.255.69 22:57, 16 September 2015 (UTC)
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http://www.markedbyteachers.com/gcse/science/an-investigation-into-the-effect-of-varying-the-acid-concentration-on-the-rate-of-reaction-between-hydrochloric-acid-and-marble-chips.html
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# An Investigation Into The Effect Of Varying The Acid Concentration On The Rate Of Reaction Between Hydrochloric Acid And Marble Chips.
Extracts from this document...
Introduction
An Investigation Into The Effect Of Varying The Acid Concentration On The Rate Of Reaction Between Hydrochloric Acid And Marble Chips I am investigating how the concentration of hydrochloric acid will effect the rate of reaction when calcium carbonate (marble chips) are added to the acid. Hydrochloric acid + calcium carbonate � Calcium chloride + Water + Carbon Dioxide To measure the rate of reaction I could * Time how long it takes for the Ca CO3 to dissolve * Time how long it takes for the fizzing in the system to finish * Time how long it takes to collect a specific volume of CO2 * Time how long it takes for a loss of a specific mass to take place. The factors that could affect the rate of this reaction are, temperature in which the reaction takes place, concentration of the acid, surface area of calcium carbonate, using a catalyst. The variables are all of the factors affecting the rate of reaction. I will keep all of the variables the same apart from the concentration of the acid. Reactions happen when particles collide together with enough energy to form a bond, therefore the more collisions the more chances of bonds being made. This is the collision theory. As the concentration of the acid increases there are more particles for the calcium carbonate to react with in the same amount of ...read more.
Middle
As soon as this is done I shall start the timer. Once the measuring cylinder has collected 100cm� of carbon dioxide I shall stop the timer. I will record my time to the nearest second. I shall repeat this once more with each concentration, with 6 different concentrations. Results Amount of CO2 collected (cm�) Time into reaction (minutes) 0.25m Test 1 0.25m Test 2 0.25m Av 0.5m Test 1 0.5m Test 2 0.5m Av 0.75m Test 1 0.75m Test 2 0.75m Av 1 6 4 5 18 14 16 27 19 23 2 19 15 17 29 23 26 46 34 40 3 24 22 23 36 34 35 58 48 53 4 32 28 30 41 47 44 70 62 66 5 34 36 35 59 51 55 77 71 74 6 37 41 39 62 64 63 86 80 83 7 42 46 44 65 69 67 93 89 91 8 43 47 45 72 74 73 98 94 96 9 49 49 49 79 81 80 100 100 100 10 51 53 52 80 82 81 11 53 55 54 83 85 84 12 54 56 55 85 87 86 13 56 58 57 86 88 87 14 57 59 58 88 88 88 15 58 60 59 88 88 88 Amount of CO2 collected (cm�) ...read more.
Conclusion
This is an alternate way of measuring the reaction, without having to upturn the cylinder. I am happy with the consistency of the temperature of the HCl. My results are accurate; however I do appear to have results that are anomalous, which are prominent in my graph. For example the results for 0.25m at 7 minutes, and 0.5m at 7 and 8 minutes are inconsistent and stand out on the graph. These could have occurred if the conical flask was shaken during the experiment. I repeated all of my results a second time none of my results were drastically out of place however there were some which perhaps more inconsistent than others. If I were to repeat the experiment I would make sure that I repeated the experiment three times instead of just 2. Although this would take up much more time, I feel it more important to obtain the most accurate results possible. In addition, out of pure interest I would like to find what happens when the temperature of the HCl increases. To do this I would heat the acid to different temperatures at regular intervals and add the same amount of Ca CO3. I expect to see that as the temperature increases so does the reaction time. My precise results enable me to come to strong conclusion that the higher the concentration of HCl the less time was taken to collect 100cm� of CO2 when reacted with Ca CO3. ...read more.
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# Related GCSE Patterns of Behaviour essays
1. ## Marble Chips and Hydrochloric Acid.
4 star(s)
The more collisions there are between particles at a given time, the faster the reaction will take place. A larger number of particles provide a larger number of successful reactions. In order for a reaction to take place, particles must collide with a minimum amount of energy called the 'activation energy' (Ea).
2. ## The Effect of Concentration on the Rate of Reaction between Hydrochloric Acid and Calcium ...
3 star(s)
However it will not be needed in this investigation. From these theories we can identify what would make the fastest rate of reaction, which would be the concentration of acid and largest surface area which would be the smaller marble chips.
1. ## In this investigation we are going to measure the rate of reaction of marble ...
3 star(s)
properly attached so that no gas can escape during the experiment and the volume of gas will remain accurate. ? Next we measured out the amount of Hydrochloric acid (20cm�) at 0.25M, 0.5M, 1M or 2M in the measuring cylinder and poured it into the conical flask.
2. ## Rates of Reaction between hydrochloric acid and marble chips
I put the 5g of marble chips and the first concentration of acid into the conical flask and put the bung into the neck of the flask. Then the marble chips and acid started to react. I could tell this because there was effervescence in the flask.
1. ## Rate of Reaction Between Marble Chips and the Varying Concentrations of Hydrochloric Acid
The previous experiment I did was adding Sodium Thiosulphate to Hydrochloric Acid Sodium Chloride + Sulfur Dioxide + Sulfur + Water. We were going to see how long it takes to produce enough sulfur to obscure a black cross under a beaker when we looked through the solution.
2. ## How does varying the concentration of Hydrochloric acid in reaction with Marble chips affect ...
The diagram of apparatus used is included. It can be seen that the reaction happens in the test tube, then the cork blocks the way out for the gas and it is forced through the straw, under the water and bubble up into the measuring cylinder.
1. ## Investigating the reaction between Marble Chips and Hydrochloric Acid.
* A Boss Clamp * A Stand * Plastic Tube Connectors * A Weighing Boat * A Teat Pipette * A Top Pan Balance Safety In order to ensure a safe experiment, I shall take the following precautions: * I shall wear safety goggles and a lab coat, as even
2. ## An Investigation: Factors That Affect The Rate Of Reaction between Calcium carbonate and Hydrochloric ...
This enabled us to have a better understanding of how much mass of calcium powder and how much volume of hydrochloric acid we needed. These results came out the best so the amount of mass and volume we used was good.
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mersenneforum.org Numbers sum of two cubes and product of two numbers of the form 6^j+7^k
Register FAQ Search Today's Posts Mark Forums Read
2020-02-15, 09:26 #1 enzocreti Mar 2018 52710 Posts Numbers sum of two cubes and product of two numbers of the form 6^j+7^k 344 and 559 are numbers that are sum of two positive cubes and product of two numbers of the form 6^j+7^k with j, k >=0. FOR EXAMPLE 344=43*8=7^3+1 Are there infinitely many such numbers? IS 16 THE ONLY perfect POWER SUM OF TWO CUBES AND PRODUCT OF TWO NUMERS OF THE FORM 6^J+7^K J, K NONNEGATIVE? Last fiddled with by enzocreti on 2020-02-15 at 12:06
2020-02-16, 03:22 #2
CRGreathouse
Aug 2006
173216 Posts
Quote:
Originally Posted by enzocreti 344 and 559 are numbers that are sum of two positive cubes and product of two numbers of the form 6^j+7^k with j, k >=0. FOR EXAMPLE 344=43*8=7^3+1 Are there infinitely many such numbers?
Probably. Here's a bunch:
Code:
16, 91, 344, 559, 1736, 2752, 4472, 8029, 9331, 12913, 14023, 20683, 71665, 74648, 207145, 326599, 373256, 375992, 941200, 942920, 1314440, 1688911, 4797295, 8456552, 12365695, 16283293, 23588209, 66926791, 80621576, 80624312, 81562760, 322828864, 322830584, 323202104, 362851489, 403450424, 17414258696, 17414261432, 17415199880, 17737087544, 110730297616, 110730299336, 110730670856, 110810919176, 128144556296, 3761479876616, 3761479879352, 3761480817800, 3761802705464, 3872210174216, 37980492079552, 37980492081272, 37980492452792, 37980572701112, 37997906338232, 41741971956152, 812479653347336, 812479653350072, 812479654288520, 812479976176184, 812590383644936, 850460145426872, 13027308783283600, 13027308783285320, 13027308783656840, 13027308863905160, 13027326197542280, 13031070263160200, 13839788436630920, 175495605123022856, 175495605123025592, 175495605123964040, 175495605445851704, 175495715853320456, 175533585615102392, 188522913906306440, 789831783010279009, 4468366912666272064, 4468366912666273784, 4468366912666645304, 4468366912746893624, 4468366930080530744, 4468370674146148664, 4469179392319619384, 4643862517789294904, 37907050706572935176, 37907050706572937912, 37907050706573876360, 37907050706895764024, 37907050817303232776, 37907088687065014712, 37920078015356218760, 42375417619239207224, 1532649851044531315216, 1532649851044531316936, 1532649851044531688456, 1532649851044611936776, 1532649851061945573896, 1532649854806011191816, 1532650663524184662536, 1532825346649654338056, 1570556901751104250376, 8187922952619753996296, 8187922952619753999032, 8187922952619754937480, 8187922952620076825144, 8187922952730484293896, 8187922990600246075832, 8187935979928537279880, 8192391319532420268344, 9720572803664285311496, 525698898908274241116352, 525698898908274241118072, 525698898908274241489592, 525698898908274321737912, 525698898908291655375032, 525698898912035720992952, 525698899720753894463672, 525699074403879364139192, 525736805958980814051512, 533886821860893995112632, 1768591357765866863198216, 1768591357765866863200952, 1768591357765866864139400, 1768591357765867186027064, 1768591357765977593495816, 1768591357803847355277752, 1768591370793175646481800, 1768595826132779529470264, 1770124007616911394513416, 2294290256674141104314552
If you want more, you should probably look into fast systems for solving cubic Thue equations. I could share my PARI/GP code but it's not particularly performant.
Quote:
Originally Posted by enzocreti IS 16 THE ONLY perfect POWER SUM OF TWO CUBES AND PRODUCT OF TWO NUMERS OF THE FORM 6^J+7^K J, K NONNEGATIVE?
If this is just the above problem, but asking for the numbers to be powers as well, there should be only finitely many, with 16 being presumably the only one.
2020-02-16, 03:24 #3 CRGreathouse Aug 2006 2×2,969 Posts Broughan has an alternate approach if you don't like modern Thue methods: https://cs.uwaterloo.ca/journals/JIS...roughan25.html
Similar Threads Thread Thread Starter Forum Replies Last Post enzocreti enzocreti 0 2020-02-12 12:07 devarajkandadai Number Theory Discussion Group 2 2019-09-24 03:14 enzocreti enzocreti 4 2019-02-13 21:55 Godzilla Miscellaneous Math 107 2016-12-06 17:48 only_human Puzzles 9 2015-06-26 10:30
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## basis functions for certain NU(R)B knot vectors
### basis functions for certain NU(R)B knot vectors
Hello
I have a problem calculating the basis functions for knot vectors that
are not clamped.
I use the algorithm from the Piegl/Tiller NURBS book (ALGORITHM A2.2, page 70)
Piegl/Tiller always assume that the knot vector is clamped, i.e. knot values
are of multiplicity order (degree + 1) at the start and the end.
Unfortunately the data I have to deal with doesn't always looks like that,
e.g. I have a knot vector for a curve of degree 3 that begins like:
-7.62939453147204E-06,-7.62939453147204E-06,0.0,0.0,0.00390624999999359 ...
and even ends with:
1.,1.,1.00390624999999,1.00781249999999
i.e. multiplities look like:
I already changed the algorithm to find the span for a parameter u to return
the real span [1..m-1] instead of Piegl/Tillers version that returns only spans
between [p..m-p].
But now I have problems (I think) getting the basis functions and evaluating the
curve. My methods GetBasisFunctions (what implements Piegl/Tillers BasisFuns)
and Evaluate (what implements Piegl/Tillers CurvePoint) look like follows:
DoubleVector
B_Spline_Curve::GetBasisFunctions(double u) const
{
DoubleVector U = GetKnotVector();
const int i = FindSpan(u);
DoubleVector N(m_degree + 1);
unsigned int p = m_degree;
N[0] = 1.;
DoubleVector left(p + 1);
DoubleVector right(p + 1);
for (unsigned int j = 1; j <= p; ++j) {
left[j] = u - U[i + 1 - j];
right[j] = U[i + j] - u;
double saved = 0.;
for (unsigned int r = 0; r < j; ++r) {
double temp = N[r] / (right[r + 1] + left[j - r]);
N[r] = saved + right[r + 1] * temp;
saved = left[j - r] * temp;
}
N[j] = saved;
}
return N;
}
Cartesian_Point*
B_Spline_Curve::Evaluate(ParameterValue value) const
{
Cartesian_Point* result = NULL;
int span = FindSpan(value);
DoubleVector knotvector = GetKnotVector();
int ksize = knotvector.size();
assert(span > 0 && span < ksize);
if ((span > 0) && (span < (ksize))) {
result = new Cartesian_Point(0., 0., 0.);
DoubleVector basisfunction = GetBasisFunctions(value);
int ctrlpoint_index = 0;
int ctrlpoint_count = m_control_points_list.size();
for (unsigned int i = 0; i <= m_degree; ++i) {
ctrlpoint_index = span - m_degree + i;
if (ctrlpoint_index >= 0 && ctrlpoint_index < ctrlpoint_count - 1) {
Cartesian_Point* pnt = m_control_points_list[ctrlpoint_index];
Cartesian_Point* epnt = basisfunction[i] * *pnt;
Cartesian_Point* old = result;
result = *old + *epnt;
}
}
}
return result;
}
Can somebody enlighten me here?
Thomas
--
Dr. Thomas Krebs
Zuken Ltd.
Roonstr. 21
90429 Nrnberg
Germany
Tel.: ++49 911 9269 111
Fax.: ++49 911 9269 200
### basis functions for certain NU(R)B knot vectors
Quote:> I have a problem calculating the basis functions for knot vectors that
> are not clamped.
> I use the algorithm from the Piegl/Tiller NURBS book (ALGORITHM A2.2, page 70)
> Piegl/Tiller always assume that the knot vector is clamped, i.e. knot values
> are of multiplicity order (degree + 1) at the start and the end.
> Unfortunately the data I have to deal with doesn't always looks like that,
> e.g. I have a knot vector for a curve of degree 3 that begins like:
> -7.62939453147204E-06,-7.62939453147204E-06,0.0,0.0,0.00390624999999359 ...
> and even ends with:
> 1.,1.,1.00390624999999,1.00781249999999
Hi,
I suppose that this are rounding errors:
-7.62939453147204E-06 should be 0.0, and 1.00390624999999 should be 1.0.
It would be better to remove them before trying to find the knot span.
If you have a real unclamped knot vector ( like U=(1,2,3,4,5,6,7,8) )
you can use the the knot insertion algorithm given in the NURBS book (with a slight modification) to extract the parameter interval for which the curve points
are defined.
In the avove example the new knot vector would be U=(4,4,4,4,5,5,5,5).
After this you can normalize the knot vector to get U=(0,0,0,0,1,1,1,1).
My implementation of ExtractCurve looks like this:
/*-------------------------------------------------------------------------
Finds the knotspan containing 'u' in a knot vector 'U' (degree
'p','n'+1 knots (see "The NURBS book")), and counts the multiplicity
of 'u'
-------------------------------------------------------------------------*/
template< class T >
inline int FindSpanMultip( const T u, const int n, const int p,
Ptr< T > U, int *s )
{
int l,low,mid,high;
/* --- Knotenspanne suchen (von rechts): */
if( u == U[n+1] )
{
if( u == U[n+p+1] ) // clamped
{
*s = p + 1;
return(n);
}
l = n; // if unclamped
while( l >= 0 ) // count multiplicity
{
if( U[l] != u ) break;
l--;
}
*s = n+1 - l;
return( n+1 ); // knot span = n+1
}
low = p;
high = n+1;
mid = (low+high) / 2 ;
while( (u < U[mid]) || (u >= U[mid+1]) )
{
if( u < U[mid] )
high = mid;
else
low = mid;
mid = (low+high) / 2;
}
l = mid;
while( l >= 0 )
{
if( U[l] != u ) break;
l--;
}
*s = mid - l;
return(mid);
Quote:}
/*----------------------------------------------------------------------
Extracts a part of a NURBS curve (ranging from 'u1' to 'u2')
----------------------------------------------------------------------*/
template< class T, class HP >
void ExtractCurve(
const T u1, const T u2,
const int n, const int p,
Ptr< T > U, Ptr< HP > Pw,
int *retn, Ptr< T > *retU, Ptr< HP > *retPw )
{
int a,ra,sa,b,rb,sb,N,i,r;
HP v1,v2;
T alpha;
Ptr< HP > Cw;
Ptr< T > Uh;
a = FindSpanMultip( u1, n, p, U, &sa );
if( sa > p ) /* Klammerknoten am Anfang */
ra = 0;
else
ra = p - sa;
b = FindSpanMultip( u2, n, p, U, &sb );
if( sb > p ) /* Klammerknoten am Ende */
{
sb = p;
rb = 0;
b += p;
}
else
rb = p - sb;
N = (b-sb) - a + p;
Cw.reserve_pool( N+1 );
Uh.reserve_pool( N+p+2 );
/* ---- Linken Knoten einfuegen, bis Vielfachheit = p ------------------- */
for( i = 0; i <= p; i++ )
{
Cw[i] = Pw[a-p+i];
Uh[i] = u1;
}
for( r = 1; r <= ra; r++ )
{
for( i = 0; i <= ra-r; i++ )
{
alpha = (u1 - U[a-p+r+i]) / (U[a+r+i] - U[a-p+r+i]);
v1 = ((T)1.0-alpha) * Cw[i];
v2 = alpha * Cw[i+1];
Cw[i] = v1 + v2;
}
}
/* ---- Unveraenderten Teil uebernehmen ----------------------------------- */
for( i = 0; i < (b-sb)-a; i++ )
{
Uh[p+1+i] = U[a+1+i];
Cw[p+1+i] = Pw[a+1+i];
}
/* ---- Rechten Knoten einfuegen, bis Vielfachheit = p --------------------- */
for( r = 1; r <= rb; r++ )
{
for( i = 0; i <= rb-r; i++ )
{
alpha = (u2 - U[b-sb-i]) / (U[b-sb-i+p] - U[b-sb-i]);
v1 = alpha * Cw[N-i];
v2 = ((T)1.0-alpha) * Cw[N-i-1];
Cw[N-i] = v1 + v2;
}
}
for( i = 0; i <= p; i++ )
Uh[N+1+i] = u2;
NormalizeKnotVector( N, p, Uh );
*retn = N;
*retPw = Cw;
*retU = Uh;
Quote:}
The above source code and more functions from the NURBS book can be found at
http://www.veryComputer.com/
(i couldn't resist to do this piece of shameless adverti*t, sorry :)))
Regards,
Norbert
Hello there,
I am using the openGL nurbs functions to check a nonuniform b-spline drawing
function I programmed, and it turns out that when drawing the curve with my
own routine, it doesn't draw the last point (so also the line to that
point).
Ik think the problem lies in the following. When drawing a segment, I let a
variable u vary from 0.0 to 1.0 with a certain delta. Now when I reach u=1.0
I skip to the next segment and calculate the point at u=0.0 (which should be
the same as u=1.0 (or 0.999???) of the previous segment.
So the problem lies in the last point of the last segment. How do I
calculate this?
tried using u=0.99999 and it works (I think), but is there a better
mathematical solution, instead of this quick hack???
Thanks
Roger
4. SOS
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The Divided Bar Diagrams Solution extends the capabilities of ConceptDraw PRO v10 with templates, samples, and a library of vector stencils for drawing high impact and professional Divided Bar Diagrams and Graphs, Bar Diagram Math, and Stacked Graph.
## Basic Divided Bar Diagrams
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## How to Draw a Divided Bar Chart in ConceptDraw PRO
A divided bar graph is a rectangle divided into smaller rectangles along its length in proportion to the data. Segments in a divided bar represent a set of quantities according to the different proportion of the total amount. A divided bar diagram is created using rectangular bars to depict proportionally the size of each category. The bars in a divided bar graph can be vertical or horizontal. The size of the each rectangle displays the part that each category represents. The value of the exact size of the whole must be known, because the each section of the bar displays a piece of that value. A divided bar diagram is rather similar to a sector diagram in that the bar shows the entire data amount and the bar is divided into several parts to represent the proportional size of each category. ConceptDraw PRO in conjunction with Divided Bar Diagrams solution provides tools to create stylish divided bar charts for your presentations.
## IDEF1X Standard
Use Case Diagrams technology. IDEF1x standard - for work with relational data bases. IDEF1x standard is meant for constructing of conceptual schemes which represent the structure of data in the context of the concerned system, for example, a commercial organization.
## Basic Histograms
This solution extends the capabilities of ConceptDraw PRO v10.3.0 (or later) with templates, samples and a library of vector stencils for drawing Histograms.
## IDEF9 Standard
Use Case Diagrams technology. An effective management of changes is significantly facilitated by way of definition and documenting of business-requirements.
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# PHP Program to find the sum of two matrices
Matrix is a multidimensional array. For a better understanding of this PHP Matrix addition, we always recommend you to learn the basic topics of PHP programming listed below:
## How to find the sum of two matrices?
To find the sum of 2 two-dimensional arrays first we have to find the number of rows and columns in the array and add the numbers in the corresponding indices together. For example, If the matrices are
2 3 8 1 5 1
a = 3 2 1 b = 6 1 5
3 5 6 4 1 2
then the result will be:
3 8 9
9 3 6
7 6 8
## How to find the sum of two matrices using PHP?
In this matrix program, the values are all predefined and cannot be changed. if you need the use to have to provide the input values please refer to this PHP Program to insert values into a matrix.
In this program, we are using the static values which are initialized in the code itself. First, we have to initialize 2 two-dimensional arrays a1 and a2 we have to assign the number of rows and columns into the variable row and col using the built-in function `count(). `Then we have to create an empty array sum[] to store the sum of array a1[] and a2[]. Then assign the value 0 into the variable i and perform the loop until the condition 'i < row' becomes false and increment the value of variable i in every iteration in the block of the loop we have to perform another loop in that we have to assign the value 0 into the variable j and perform the loop until the condition 'j < col' becomes false and increment the value of variable j in every iteration in the loop block we have to assign the calculated result of 'a1[i][j] + a2[i][j]' into the array sum[i][j] and at last print the elements of the two-dimensional array sum[][] using `for loop`
We have covered almost all the matrix programs that include all the matrix operations, please refer the below programs for more matrix operations and matrix related programs.
Step 1: Initialize 2 two-dimensional arrays a1[] and a2[]
Step 2: Assign the number of rows and columns into the variable row and col using the built-in function `count()`
Step 3: Print the elements in the array a1[] and a2[]
Step 4: Create an empty array sum[] to store the sum of array a1[] and a2[]
Step 5: Assign the value 0 into the variable i and perform the sub-steps until the condition 'i < row' becomes false and increment the value of variable i in every iteration
(i) Assign the value 0 into the variable j and perform the sub-step until the condition 'j < col' becomes false and increment the value of variable j in every iteration,
(ii) Assign the calculated result of 'a1[i][j] + a2[i][j]' into the array sum[i][j]
Step 6: Print the elements of the two-dimensional array sum[][] using `for loop`
## PHP Source Code
``` ```<?php
\$a1 = array(
array(4, 6, 7),
array(3, 9, 9),
array(5, 4, 8)
);
\$a2 = array(
array(6, 7, 5),
array(9, 2, 1),
array(6, 8, 3)
);
\$row = count(\$a1);
\$col = count(\$a1[0]);
echo "First matrix: \n";
for (\$i = 0; \$i < \$row; \$i++) {
for (\$j = 0; \$j < \$col; \$j++) {
echo \$a1[\$i][\$j] . " ";
}
echo "\n";
}
echo "Second matrix: \n";
for (\$i = 0; \$i < \$row; \$i++) {
for (\$j = 0; \$j < \$col; \$j++) {
echo \$a2[\$i][\$j] . " ";
}
echo "\n";
}
\$sum = array();
for (\$i = 0; \$i < \$row; \$i++) {
for (\$j = 0; \$j < \$col; \$j++) {
\$sum[\$i][\$j] = \$a1[\$i][\$j] + \$a2[\$i][\$j];
}
}
echo "Addition of two matrices: \n";
for (\$i = 0; \$i < \$row; \$i++) {
for (\$j = 0; \$j < \$col; \$j++) {
echo \$sum[\$i][\$j] . " ";
}
echo "\n";
}
?>```
```
## OUTPUT
```First matrix:
4 6 7
3 9 9
5 4 8
Second matrix:
6 7 5
9 2 1
6 8 3
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Frequent Visitor
## Condition in a measure - how to ignore blank nominator?
Hi,
I am working on the matrix below:
I used the following measure to create the YOY calculation:
YOY = sum(YOY[Yr_2017]) / sum(YOY[Yr_2016]) -1
Is there a way to add a condition to the formula above so that if let's say 2017 is blank there is no calculation, meaning I see blank cells instead of -100.0% ? (example below)
Thank you for the help!
2 ACCEPTED SOLUTIONS
Accepted Solutions
Highlighted
Established Member
## Re: Condition in a measure - how to ignore blank nominator?
`YOY = IF(ISBLANK(sum(YOY[Yr_2017])) || ISBLANK(sum(YOY[Yr_2016])), BLANK(), sum(YOY[Yr_2017]) / sum(YOY[Yr_2016]) -1)`
Established Member
## Re: Condition in a measure - how to ignore blank nominator?
Hi @katalay, you are right, I failed to see that side effect. Turned out I struggled a little to solve this and had to take a different approach. I am still not satisfied that this is the simplest possible solution but it does work using my example data:
```ALL_2016_NEW = CALCULATE (
SUM ( YOY[MKT_2016] ),
SELECTCOLUMNS(FILTER (
SUMMARIZE(YOY,YOY[Month],YOY[MKT_2017]),
YOY[MKT_2017] <> 0),"Month", YOY[Month])
)```
12 REPLIES 12
Highlighted
Established Member
## Re: Condition in a measure - how to ignore blank nominator?
`YOY = IF(ISBLANK(sum(YOY[Yr_2017])) || ISBLANK(sum(YOY[Yr_2016])), BLANK(), sum(YOY[Yr_2017]) / sum(YOY[Yr_2016]) -1)`
Frequent Visitor
## Re: Condition in a measure - how to ignore blank nominator?
Thank you Erik that helped a lot.
Is it also possible to reflect the same calculation on the sub/grand totals ?
Established Member
## Re: Condition in a measure - how to ignore blank nominator?
Yes it is. You just need to change the sum formula to exclude months of 2016 where 2017 is blank. Like this:
```YOYS = IF(ISBLANK(SUM(YOY[Yr_2017])) || ISBLANK(SUM(YOY[Yr_2016])),
BLANK(),
sum(YOY[Yr_2017]) / SUMX(FILTER(YOY, NOT(ISBLANK(YOY[Yr_2017]))),YOY[Yr_2016]) - 1)```
Frequent Visitor
## Re: Condition in a measure - how to ignore blank nominator?
Thank you very much Erik!!
Established Member
## Re: Condition in a measure - how to ignore blank nominator?
My pleasure @katalay.
Frequent Visitor
## Re: Condition in a measure - how to ignore blank nominator?
@erik_tarnvik I was applying the logic to a different column and I noticed the following.
The data set is actually at a more granular level (down to the city) so I believe when I use the sumx function some of the 2016 values isn't included in the new calculation. Example below:
ALL_2016 = sum(YOY[MKT_2016])
ALL_2016_NEW = if(isblank(sum(YOY[MKT_2017]))
,blank(),
sumX(filter(New_BI_YOY,not(isblank(YOY[MKT_2017]))),YOY[MKT_2016]))
The results are below:
Why do you think this may be happening?
Thanks again for the help, really appreciate it!
Established Member
## Re: Condition in a measure - how to ignore blank nominator?
Hi @katalay,
you need to make a distinction between summing up 2016 for the purpose of generating a YoY percentage that excludes months of 2017 for which you do not yet have a value, and summing up to generate a true total of 2016. The measure ALL_2016_NEW will exclude all 2016 months where there are no values for the same month in 2017. That's how I understood you wanted the YoY percentage calculated?
Frequent Visitor
## Re: Condition in a measure - how to ignore blank nominator?
Yes that is correct. I think the number doesn't add up to be equal because the data is at a more granular level (in my case it is actually at the city level).
So let's say if I have a value for Berlin in June 2016 but not in June 2017, since we are aggregating it and June 2017 Berlin is blank it is automatically ignoring June 2016 Berlin.
Do you think the formula is ignoring those values?
So yes I am trying to figure out a way to ignore only the records where only 2017 months are blank and apply it to 2016 at the higher level.
I hope I could explain it clearly and thanks again for your time!
Established Member
## Re: Condition in a measure - how to ignore blank nominator?
Sorry @katalay, ignore my previous answer, I did not fully understand your question. Yes, without having seen your actual dataset, I think you are right, you will lose the city level information if it contains blanks for 2017. But that is easy to fix, just adjust the formula as below. By checking the SUM(YOY[MKT_2017]) rather than just the column it will not return blank for months where you have data for some cities but not others and all values will then be included for that month.
```ALL_2016 = sum(YOY[MKT_2016])
ALL_2016_NEW = if(isblank(sum(YOY[MKT_2017])), blank(),
sumX(filter(New_BI_YOY,not(isblank(SUM(YOY[MKT_2017])))),YOY[MKT_2016]))```
Announcements
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# Squaring an arbitrary summation?
I'm trying to find a recurrence relation for the coefficients for the Maclaurin series for $\tan(x)$ by substituting $y=\sum_{k=0}^{\infty}C_{2k+1}x^{2k+1}$ into the differential equation $y'=1+y^2$. This is because $\tan(x)$ is the solution to the initial value problem for the aforementioned DE with the initial condition $y(0)=0$; this is also where the form $\sum_{k=0}^{\infty}C_{2k+1}x^{2k+1}$ comes from (the fact that $\tan(x)$ is an odd function and that $y(0)=0$ which implies $C_0=0$). But I have no clue how to work "around" the expression $y^2=\big(\sum_{n=1}^{\infty}C_{2k+1}x^{2k+1}\big)^2$. How can I find a recurrence relation with an infinite squared summation? Any help is appreciated, thank you.
-
The coefficients will get convolved i.e. $(\sum_{k\ge0}C_kx^k)^2=\sum_{k\ge0}(\sum_{i=0}^kC_iC_{k-i})x^k$. – sai Apr 30 '12 at 0:11
Take the Cauchy product:
\begin{align*} \left(\sum_{k\ge 0}C_{2k+1}x^{2k+1}\right)^2&=x^2\left(\sum_{k\ge 0}C_{2k+1}x^{2k}\right)^2\\\\ &=x^2\sum_{k\ge 0}D_{2k}x^{2k}\;, \end{align*}
where $$D_{2k}=\sum_{i=0}^kC_{2i+1}C_{2(k-i)+1}\;.$$ Thus, the differential equation becomes
\begin{align*} \sum_{k\ge 0}C_{2k+1}(2k+1)x^{2k}&=1+x^2\sum_{k\ge 0}\sum_{i=0}^kC_{2i+1}C_{2(k-i)+1}x^{2k}\\ &=1+\sum_{k\ge 1}\sum_{i=0}^{k-1}C_{2i+1}C_{2(k-i)-1}x^{2k}\;, \end{align*}
and we have $C_1=1$ and $$C_{2k+1}=\frac1{2k+1}\sum_{i=0}^{k-1}C_{2i+1}C_{2(k-i)-1}$$ for $k\ge 1$.
E.g.,
\begin{align*} C_3&=\frac13 C_1^2=\frac13\;,\\ C_5&=\frac15(2C_1C_3)=\frac2{15}\;,\text{ and}\\ C_7&=\frac17(2C_1C_5+C_3^2)=\frac{17}{315}\;. \end{align*}
-
In other contexts, the coefficients of the squared function would be what is termed a self-convolution, or autoconvolution. – J. M. Apr 30 '12 at 0:41 Say we have $\big(\sum_{i=0}^{n}a_i\big)\big(\sum_{j=0}^{n}b_j\big)$ $=a_0\big(\sum_{j=0}^{n}\big)+a_1\big(\sum_{j=0}^{n}\big)+...+a_n\big(\sum_{j=0}^{n}\big)$ which equals $\sum_{i=0}^{n}\sum_{j=0}^{n}a_ib_j$. Why do we shift the index of the second summation? – Hautdesert Apr 30 '12 at 1:39 @Hautdesert: I don’t understand. This example is very different from the product of two series (or for that matter two polynomials), and I don’t know what index you think is being shifted. – Brian M. Scott Apr 30 '12 at 1:44 @BrianM.Scott: Is the reasoning in my previous comment not a generalization of the product of two arbitrary polynomials? I thought we could just set $a_i=c_ix^i$ and derive the Cauchy product. – Hautdesert Apr 30 '12 at 1:49 @Hautdesert: Not if you want to group the product terms according to powers of $x$ so as to be able to match coefficients in $y'$ and $1+y^2$. That’s why the coefficient $D_{2k+1}$ of $x^{2k}$ above is itself a sum of products. Similarly, in $(a+bx+cx^2)(d+ex+fx^2)$ the coefficient of $x^3$ is $bf+cd$, since there are two $x^3$ terms. – Brian M. Scott Apr 30 '12 at 1:55
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# Search by Topic
#### Resources tagged with Factors and multiples similar to 396:
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### There are 92 results
Broad Topics > Numbers and the Number System > Factors and multiples
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You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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Find the number which has 8 divisors, such that the product of the divisors is 331776.
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##### Stage: 3 Challenge Level:
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Re: Pounds and Kilograms
• To: mathgroup at smc.vnet.net
• Subject: [mg103654] Re: Pounds and Kilograms
• From: Erik Max Francis <max at alcyone.com>
• Date: Thu, 1 Oct 2009 06:40:33 -0400 (EDT)
• References: <h9v6po\$99p\$1@smc.vnet.net>
```Kevin J. McCann wrote:
> The Units Package has Pounds and Kilograms. Pound is listed as a unit of
> weight, Kilogram as a unit of mass; however,
>
> Convert[Kilogram,Pound]
>
> 2.20462 Pound
>
> Seems inconsistent. (I hate units.)
It looks to me like a bug, either in the definition or the
documentation. When the unit pound was created, people did not make the
distinction between mass and weight, but since they did, there have been
a couple of systems rationalizing the old Imperial units to provide both
distinct units. Some are slug/pound, pound/poundal,
pound-mass/pound-force, etc. But the fact remains that if you want to
treat them as a real system of units, you need to choose the pound to be
one or the other.
In[1]:= << Units`
In[2]:= Convert[Pound, Kilogram]
Out[2]= 0.453592 Kilogram
In[3]:= Convert[Pound, Newton]
During evaluation of In[3]:= Convert::incomp: Incompatible units in
Pound and Newton. >>
Out[3]= Pound
In[4]:= ?Pound
Pound is a unit of weight. >>
A weight is a unit of force, but Mathematica happily converts a pound to
a kilogram and complains about converting a pound to a newton.
My guess would be what happened here is that they tried to include all
the combinations:
?Slug
Slug is a unit of mass. >>
?Poundal
Poundal is a unit of force. >>
?PoundForce
PoundForce is a unit of force. >>
(These are intermixed from several different rationalized unit systems I
listed above.) Looks like the pound ended up with the short end of the
stick, and so it's treated as a unit of mass even though the
documentation uses the term "weight." I'll send WR a note.
--
Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
Nothing is so good it lasts eternally
-- Florence, _Chess_
```
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Partner with ConvertIt.com
New Online Book! Handbook of Mathematical Functions (AMS55)
Conversion & Calculation Home >> Measurement Conversion
Measurement Converter
Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC.
Conversion Result: ```acre foot = 1233.48183754752 volume (volume) ``` Related Measurements: Try converting from "acre foot" to board foot, cord foot (of wood), dram fluid (fluid dram), ephah (Israeli ephah), fifth, hogshead, kilderkin, last, methuselah, noggin, oil arroba (Spanish oil arroba), register ton, Roman amphora, sack, salmanazar, stere, strike, UK gallon (British gallon), UK oz fluid (British fluid ounce), UK peck (British peck), or any combination of units which equate to "length cubed" and represent capacity, section modulus, static moment of area, or volume. Sample Conversions: acre foot = 31,636.06 amphora (Greek amphora), 10,344.49 barrel, 33,454,080 bath (Israeli bath), 522,720 board foot, 1,233,481,837.55 cc (cubic centimeters), 5,873.03 chetvert (Russian chetvert), 340.31 cord (of wood), 41,116,061,251.58 drop, 280,025.97 dry gallon, 1,120,103.87 dry quart, 31,114 ephah (Israeli ephah), 36,205.71 firkin, 1,233,481.84 liter, 651,702.86 magnum, 41,708,982.86 oz fluid (fluid ounce), 2,586.12 pipe, 47,639.1 Roman amphora, 108,617.14 salmanazar, 6,951,497.14 tea cup, 43,560 timber foot.
Feedback, suggestions, or additional measurement definitions?
Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks!
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Question 1 of 5Solve, give the matrix in reduced row echelon form
Select the Correct Answer Below: Correct! Not Correct!
A
$$(-2,7)$$ $$\left[ \begin{array}{cc|c} 1&-2&7\\ 1&1&7 \end{array} \right]$$
B
$$(-5,5)$$ $$\left[ \begin{array}{cc|c} 1&-5&-5\\ 1&5&5 \end{array} \right]$$
C
$$(-5,5)$$ $$\left[ \begin{array}{cc|c} 1&0&-5\\ 0&1&5 \end{array} \right]$$
D
$$(4,2)$$ $$\left[ \begin{array}{cc|c} 1&0&4\\ 0&1&2 \end{array} \right]$$
E
No Solution
Question 2 of 5Solve, give the matrix in reduced row echelon form
Select the Correct Answer Below: Correct! Not Correct!
A
$$(7,-2)$$ $$\left[ \begin{array}{cc|c} 1&-2&7\\ 1&1&0 \end{array} \right]$$
B
No Solution
C
$$(15,13)$$ $$\left[ \begin{array}{cc|c} 1&1&15\\ 0&13&0 \end{array} \right]$$
D
$$(21,-16)$$ $$\left[ \begin{array}{cc|c} 1&0&21\\ 0&1&-16 \end{array} \right]$$
E
$$(16,-21)$$ $$\left[ \begin{array}{cc|c} 1&0&16\\ 0&1&-21 \end{array} \right]$$
Question 3 of 5Solve, give the matrix in reduced row echelon form
Select the Correct Answer Below: Correct! Not Correct!
A
$$(-1,0)$$ $$\left[ \begin{array}{cc|c} 1&0&-1\\ 0&1&0 \end{array} \right]$$
B
$$(-3,-2)$$ $$\left[ \begin{array}{cc|c} 1&1&-3\\ 1&1&-2 \end{array} \right]$$
C
$$(12,-7)$$ $$\left[ \begin{array}{cc|c} 1&0&12\\ 0&1&-7 \end{array} \right]$$
D
No Solution
E
$$(8,-1)$$ $$\left[ \begin{array}{cc|c} -8&0&1\\ 0&-1&1 \end{array} \right]$$
Question 4 of 5Solve, give the matrix in reduced row echelon form
Select the Correct Answer Below: Correct! Not Correct!
A
$$(0,9)$$ $$\left[ \begin{array}{cc|c} 1&0&9\\ 0&1&0 \end{array} \right]$$
B
$$(-2,3)$$ $$\left[ \begin{array}{cc|c} 1&1&-2\\ 1&1&3 \end{array} \right]$$
C
No Solution
D
$$(-4,-8)$$ $$\left[ \begin{array}{cc|c} 1&0&-4\\ 0&1&-8 \end{array} \right]$$
E
$$(-5,4)$$ $$\left[ \begin{array}{cc|c} 1&0&-5\\ 0&1&4 \end{array} \right]$$
Question 5 of 5Solve, give the matrix in reduced row echelon form
Select the Correct Answer Below: Correct! Not Correct!
A
No Solution
B
$$(8,9)$$ $$\left[ \begin{array}{cc|c} 0&1&8\\ 1&0&9 \end{array} \right]$$
C
$$(-3,-4)$$ $$\left[ \begin{array}{cc|c} 1&-3&0\\ -4&0&0 \end{array} \right]$$
D
$$(5,7)$$ $$\left[ \begin{array}{cc|c} 1&0&5\\ 0&1&7 \end{array} \right]$$
E
$$(1,2)$$ $$\left[ \begin{array}{cc|c} 1&0&1\\ 0&1&2 \end{array} \right]$$
Great Job! You Passed!
Better Luck Next Time...
Restart Quiz ↻
Review Lesson ↻
Next Lesson »
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# Winners Announced for Apprentice Problem 3, P1:A3 Running Numbers
## Winners Announced for Apprentice Problem 3, P1:A3 Running Numbers
Apprentice Level Problem 3 - P1:A3 Running Numbers Key Scoring Principles
Basic scoring principles used for the contest entries judging are described at the official rules page. Here is a short summary: each contest entry was scored according to the following criteria: 1) up to 100 points for solutions performance (speed); 2) a maximum of 25 bonus points for a contestants activity in the forum, calculated as 5 bonus points for each valid forum post/reply.
Input Data Sets Used for Performance Scoring
Nine different input data sets were used to compute the execution score for this problem. Each data set defined as three numbers: the source buffer to which data is added, the BYTE Addition value which is the value to add to the first argument and the DWORD Addition value which is the value to add to the Source buffer every 37th cycle. Input data sets can be downloaded here.
Points in Performance Scoring
Each input data set was judged individually. The weights of data sets used in performance scoring were equivalent. The overall performance score was calculated as a sum of all nine input data sets individual performance.
We allowed a total of 120 seconds (2 minutes) execution maximum for each input set; for those runs that took longer than 120 seconds or had runtime errors during execution, zero performance points were awarded. Some entries that could not be built on the MTL and those entries that were not able to correctly solve input data set got zero points as well.
Successful contest entries that computed the number of cycles required to reach all zero values simultaneously or detect the repetition of the original input values in less than 2 minutes were ranked based on their execution time and got performance points according a reciprocal rank scale.
Execution Results and Point Spread
Weve received 14 contest entries in the Apprentice Level Running Numbers problem set.
Nine entries successfully solved all nine input data sets. 4 entries solved one or more data sets. Unfortunately, one entry was incomplete and therefore unable to solve any test data sets.
All the timings, performance and correctness points are available in the final Running Numbers score table (link below).
Forum Activity and Bonus Points
Additional bonus points were given for contestants forum posts made before the problem entries were closed. Five points per post (maximum 25 points possible) were awarded.
Entry points and penalties.
Each contest entry got 100 entry points.
Winners
The problem winners based on highest point total are:
1. dotcsw
2. vdave
3. kolkir
These three contestants provided the solutions which correctly solved all the input data sets. They also had the fastest overall code execution and significant bonus points for activity in the contest forum.
Scoring Table
1 Beitrag / 0 neu
Nähere Informationen zur Compiler-Optimierung finden Sie in unserem Optimierungshinweis.
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# Algebra
posted by .
You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
• Algebra -
area= LW
but 2W+L=600
L= 600-2W
area= (600-2W)(w)
well, roots are w=0, and w=300 that is where area is zero. Since a parabola is described here, the max will occur halfway, or w=150. Solve for Area when w=150
Plot Area vs W and see if this is so. Use your graphing calculator.
• Algebra -
I already know that the answer is 300 for the length and 150 for the width, giving a sq ft of 45,000. The only problem is i do not know how to get that answer.
• Algebra -
@bobpursley i got it now. thanks a bunch =)
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### What is the volume of this cloud in cubic miles
Assignment Help Civil Engineering
##### Reference no: EM13544457
1.A person (mass of 80g) is lifted upward by a 2 cm diameter safety rope with constant velocity. What is the tensile stress in the rope?
2.Calculate the volume (in ft^3) of a person of 180 lbf weight, assuming reasonable SG for the human body. Show work
3.Clouds can weigh thousands of pounds due to their liquid water content. Often this content is measured g/m^3. Assume that a cumulus cloud occupies a volume of one cubic km, and its liquid water content is 0.2g/m^3.
a) What is the volume of this cloud in cubic miles?
b) How much does the water in the cloud weigh in pounds.
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Explore BrainMass
# Fourier series
f(x)= {0 -2<x<0 f(x+4) = f(x)
{1 0<x<2
I have to find the Fourier series of the problem and sketch the graph of the function at 3 periods. I'm not sure if you need my text and what sections were covering or not so I'll just give it. "Elementary differential equations and boundary value problems" by William E. Boyce and Richard C. Diprima. It's mainly stuff we covered in 10.2-10.5. Thanx a lot for your help.
#### Solution Preview
The solution is attached below in two files. the files are identical in content, only differ in format. The ...
#### Solution Summary
This shows how to find Fourier series and sketch a graph.
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https://www.clutchprep.com/chemistry/practice-problems/90358/the-radius-of-an-atom-of-gold-au-is-about-1-35-a-how-many-gold-atoms-would-have-
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# Problem: The radius of an atom of gold (Au) is about 1.35 Å.How many gold atoms would have to be lined up to span 5.5 mm ?
###### FREE Expert Solution
100% (113 ratings)
###### FREE Expert Solution
We are asked to calculate the number of gold atoms that have to be lined up to span 5.5 mm given the radius of an atom of gold (Au) is about 1.35 Å.
To solve this problem, we shall follow these steps:
Step 1: Convert the radius from Å to mm.
Step 2: Divide the length (i.e. 5 mm) with the diameter in mm.
100% (113 ratings)
###### Problem Details
The radius of an atom of gold (Au) is about 1.35 Å.
How many gold atoms would have to be lined up to span 5.5 mm ?
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# Performance and Limitations Flashcards
1
Q
What are the four dynamic forces that act on an airplane during all maneuvers
A
Lift - the upward acting force
Gravity - weight, the downward acting force
Thrust - the forward acting force
Drag - The backward acting force
2
Q
What flight conditions will result in the sum of the opposing forces being equal
A
IN steady-state, straight-and-level, unaccelerated flight, the sum of the opposing forces is equal to zero. There can be no unbalanced forces in steady, straight flight (newton’s 3rd law). This is true whether flying level or when climbing or descending. It does not mean the four forces are equal. It means the opposing forces are equal to, and thereby cancel the effects of each other.
3
Q
What is an airfoil? State some examples
A
An airfoil is a device which gets a useful reaction from air moving over its surface, namely LIFT. Wings, horizontal tail surface, vertical tail surfaces, and propellers are examples of airfoils
4
Q
What is the angle of incidence
A
The angle of incidence is the angle formed by the longitudinal axis of the airplane and the chord of the wing. It is measured by the angle at which the wing is attached to the fuselage. The angle of incidence is fixed and cannot be changed by the pilot
5
Q
What is relative wind
A
The relative wind is the direction of the airflow with respect to the wing. When a wing is moving forward and downward the relative wind moves backward and upward. The flight path and relative wind are always parallel but travel in opposite directions
6
Q
What is the angle of attack
A
The angle of attack is the angle between the wing chord line and the direction of the relative wind; it can be changed by the pilot
7
Q
What is Bernoulli’s Principle
A
The pressure of a fluid (liquid or gas) decreases at points where the speed of the fluid increases. In the case of airflow, high speed flow is associated with low pressure and low speed flow with high pressure. The airfoil of an aircraft is designed to increase the velocity of the airflow above its surface, thereby decreasing pressure above the airfoil. Simultaneously, the impact of the air on the lower surface of the airfoil increases the pressure below. This combination of pressure decrease above and increase below produces life
8
Q
What are several factors which will affect both lift and drag
A
Wing area - lift and drag action on a wing are roughly proportional to the wing area. A pilot can change wing area by using certain types of flaps
Shape of the airfoil - As the upper curvature of an airfoil is increased (up to a certain point) the lift produced increases. Lowering an aileron or flap device can accomplish this. Also, ice or frost on a wing can disturb normal airflow, changing its camber, and disrupting its lifting capability
Angle of attack - As angle of attack increases, both lift and drag are increased, up to a certain point
Velocity of the air - An increase in velocity of air passing over the wing increases lift and drag
Air density - Lift and drag vary directly with the density of the air. As air density increases, lift and drag increase. As air density decreases, lift and drag decrease. Air density is affected by these factors: pressure, temperature, and humidity
9
Q
What is torque effect
A
Torque effect involves Newton’s third law of physics - for every action, there is an equal and opposite reaction. Applied to the airplane, this means that as the internal engine parts and the propeller are revolving in one direction, an equal force is trying to rotate the airplane in the opposite direction. It is greatest when at low airspeeds with high power settings and a high angle of attack
10
Q
What effect does torque reaction have on an airplane on the ground and in flight
A
In flight - Torque reaction is acting around the longitudinal axis, tending to make the airplane roll. To compensate, some of the older airplanes are rigged in a manner to create more lift on the wing that is being forced downward. The more modern airplane are designed with the engine offset to counteract this effect of torque.
On the ground - during the takeoff roll, an additional turning moment around the vertical axis is induced by torque reaction. As the left side of the airplane is being forced down by torque reaction, more weight is being placed on the left main landing great. This results in more ground friction, or drag, on the left tire than on the right, causing a further turning moment
11
Q
What are the four factors that contribute to torque effect
A
Torque reaction of the engine and propeller. For every action there is an equal and opposite reaction. The rotation of the propeller to the right, tends to roll or bank the airplane to the left
Gyroscopic effect of the propeller. Gyroscopic precession applies here: the resultant action or deflection of a spinning object when a force is applied to the outer rim of its rotational mass. If the axis of a propeller is tilted, the resulting force will be exerted 90 degrees ahead in the direction of rotation and in the same direction as the applied force. It is most noticeable on takeoff in taildraggers when the tail is raised
Corkscrewing effect of the propeller slipstream. High-speed rotation of an airplane propeller results in a corkscrewing rotation to the slipstream as it moves rearward. At high propeller speed and low forward speed, as in a takeoff, the slipstream strikes the vertical tail surface on the left side pushing the tail to the right and yawing the airplane to the left
Asymmetrical loading of the propeller (P-factor). When an airplane is flying with a high angle of attack, the bite of the downward moving propeller blade is greater than the bite of the upward moving blade. This is due to the downward moving blade meeting the oncoming relative wind at a greater angle of attack than the upward moving blade. Consequently there is greater thrust on the downward moving blade on the right side, and this forces the airplane to yaw to the left
12
Q
What is centrifugal force
A
Centrifugal force is the equal and opposite reaction of the airplane to the change in direction, and it acts equal and opposite to the horizontal component of lift
13
Q
What is load factor
A
Load factor is the ratio of the total load supported by the airplane’s wing to the actual weight of the airplane and its contents. In other words, it is the actual load supported by the wings divided by the total weight of the airplane. It can also be expressed as the ratio of a given load to the pull of gravity. That is to refer to a load factor of three as 3Gs. In this case the weight of the airplane is equal to 1G and if a load of three times the actual weight of the airplane were imposed upon the wing due to curved flight, the load factor would be equal to 3Gs
14
Q
For what two reasons is load factor important to pilots
A
because of the obviously dangerous overload that it is possible for a pilot to impose on the aircraft structure
Because an increase load factor increases the stalling speed and makes stalls possible at seemingly safe flight speeds
15
Q
What situations may result in load factors reaching the maximum or being exceeded
A
Level Turns - The load factor increases at a terrific rate after a bank has reached 45 or 50 degrees. The load factor in a 60 degree bank turn is 2G. The load factor in an 80 degree bank turn is 5.7G. The wing must produce lift equal to these load factors if altitude is to be maintained
Turbulence - Severe vertical gusts cause a sudden increase in angle of attack, resulting in large load which are resisted by the inertial of the airplane
Speed - The amount of excess load that can be imposed upon the wing depends on how fast the airplane is flying. At speeds below maneuvering speed, the airplane will stall before the load factor can become excessive. At speeds above maneuvering speed, the limit load factor for which an airplane is stressed can be exceeded by abrupt or excessive application of the controls or by strong turbulence
16
Q
What are the different operational categories for aircraft and within which category does your aircraft fall
A
Normal - +3.8 to -1.52*
Utility - +4.4 to -1.76
Aerobatic - +6 to -3
17
Q
What effect does an increase in load factor have on stalling speed
A
As load factor increases, stalling speed increases. Any airplane can be stalled at any airspeed within the limits of its structure and the strength of the pilot. At a given airspeed the load factor increases as angle of attack increases, and the wing stalls because the angel of attack has been increased to a certain angle. Therefore, there is a direct relationship between the load factor imposed upon the wing and its stalling characteristics. A rule for determining the speed at which a wing will stall is that the stalling speed increases in proportion to the square root of the load factor
18
Q
Define the term maneuvering speed
A
Maneuvering speed is the maximum speed at which the limit load can be imposed (either by gusts or full deflection of the control surfaces) without causing structural damage. It is the speed below which you can, in smooth air, move a single flight control one time to its full deflection for one axis of airplane rotation only (pitch, roll or yaw) without risking of damage to the airplane. Speeds up to, but not exceeding the maneuvering speed allow an aircraft to stall prior to experiencing an increase in load factor that would exceed the limit load of the aircraft.
19
Q
Discuss the effect on maneuvering speed of an increase or decrease in weight
A
Maneuvering speed increase with an increase in weight and decreases with a decrease in weight. An aircraft operating at a reduced weight is more vulnerable to rapid accelerations encountered during flight through turbulence or gusts. Design limit load factors could be exceeded if a reduction in maneuvering speed is not accomplished. An aircraft operating at or near gross weight in turbulent air is much less likely to exceed design limit load factors and may be operated at the published maneuvering speed for gross weight if necessary
20
Q
Define LOC-I and describe several situations that might increase the risk of an LOC-I accident occurring
A
LOC-I is defined as a significant deviation of an aircraft from the intended flight path and it often results from an airplane upset. Maneuvering is the most common phase of flight for LOC-I accident to occur; however, LOC-I accidents occur in all phases of flight. Situations that increase the risk of this include uncoordinated flight, equipment malfunctions, pilot complacency, distraction, turbulence, and poor risk management, such as attempting to fly in IMC when the pilot is not qualified or proficient in it
21
Q
What causes an airplane to stall
A
The direct cause of every stall is an excessive angle of attack. Each airplane has a particular angle of attack where the airflow separate from the upper surface of the wing and the stall occurs. This critical angle of attack varies from 16 to 20 degrees depending on the airplane’s design, but each airplane has only one specific angle of attack where the stall occurs, regardless of airspeed, weight, load factor, or density altitude
22
Q
What is a spin
A
A spin in a small airplane or glider is a controlled or uncontrolled maneuver in which the airplane or glider descends in a helical path while flying at an angle of attack greater than the critical angel of attack. Spins result from aggravated stalls in either a slip or skid. If a stall does not occur, a spin cannot occur
23
Q
What causes as spin
A
The primary cause of an inadvertent spin is exceeding the critical angel of attack while applying excessive or insufficient rudder and to a lesser extent aileron
24
Q
When are spins most likely to occur
A
A stall/spin situation can occur in any phase of flight but is most likely to occur in the following situations
Engine failure on takeoff during clime out - pilot tries to stretch glide to landing area by increasing back pressure or makes an uncoordinated turn back to departure runway at a relatively low airspeed
Crossed-control turn from base to final - pilot overshoots final and makes uncoordinated turn at a low airspeed
Engine failure on approach to landing - pilot tries to stretch glide to runway by increasing back pressure
Go-around with full nose up trim - pilot applies power with full flaps and nose-up trim combine with uncoordinated use of rudder
Go-around with improper flap retraction - pilot applies power and retracts flaps rapidly resulting in a rapid sink rate followed by an instinctive increase in back pressure
25
Q
What procedure should be used to recover from an inadvertent spin
A
Close the throttle
Neutralize the ailerons
Apply full opposite rudder
Briskly move the elevator control forward to neutral position
Neutralize the rudder when the spin stops
Gradually apply enough aft elevator pressure to return to level flight
26
Q
What causes adverse yaw
A
When turning an airplane to the left for example, the downward deflected aileron on the right produces more lift on the right wing. Since the downward deflected right aileron produces more lift, it also produces more drag, while the opposite left aileron has less lift and less drag. This added drag attempt to pull or veer the airplane’s nose in the direction of the raised wing; that is; it tries to turn the airplane in the direction opposite to that desired. This undesired veering is referred to as adverse yaw
27
Q
What is ground effect
A
Ground effect is a condition of improved performance the airplane experiences when it is operating near the ground. A change occurs in the 3D flow pattern around the airplane. because the airflow around the wing is restricted by the ground surface. This reduces the wing’s upwash, downwash, and wingtip vortices. In order for ground effect to be of a significant magnitude, the wing must be quite close to the ground
28
Q
What major problems can be caused by ground effect
A
During landing at a height of approximately one-tenth of a wing span above the surface, drag may be 40 percent less than when the airplane is operating out of ground effect. Therefore, an excess speed during landing phase may result in a significant float distance. In such cases, if care is not exercised by the pilot, he/she may run out of runway and options at the same time
During takeoff due to the reduces drag in ground effect, the aircraft may seem capable of takeoff well below the recommended speed. However, as the airplane rises out of ground effect with a deficiency of speed, the greater induces drag may result in very marginal climb performance, or the inability of the airplane to fly at all. In extreme conditions, such as high temperature, high gross weight, and high-density altitude, the airplane may become airborne initially with a deficiency of speed and then settle back to the runway
29
Q
Define the following: Empty weight, gross weight, useful load, arm, moment, center of gravity, datum
A
Empty weight - The weight of the airframe, engines, all permanently installed equipment, and unusable fuel. Depending on the FARs under which the aircraft was certificated, either the undrainable oil or full reservoir of oil is included
Gross weight - The maximum allowable weight of both the airplane and its contents
Useful load - the weight of the pilot, copilot, passengers, baggage, usable fuel and drainable oil
Arm - The horizontal distance in inches from the reference datum line to the center of gravity of the item
CG - The point about which an aircraft would balance if it were possible to suspend it at that point. Expressed in inches from datum
Datum - An imaginary vertical plane or line from which all measurement of are are taken. Established by the manufacturer
30
Q
What basis equation is used in all weight and balance problems to find the CG location of an airplane and/or its components
A
Weight X Arm = Moment
Weight = Moment / Arm
Arm (CG) = (Total) Moment / (Total) Weight
31
Q
What performance characteristics will be adversely affected when an aircraft has been overloaded
A
```Higher takeoff speed
Longer take off roll
Reduced rate and angle of climb
Lower maximum altitude
Shorter range
Reduced cruising speed
Reduced maneuverability
Higher stalling speed
Higher landing speed
Longer landing roll
Excessive weight on the nosewheel```
32
Q
What effect does a forward center of gravity have on an aircraft’s flight characteristics
A
higher stall speed - stalling angle of attack is reached at a higher speed due to increased win loading
more stable - center CG is farther forward from the center of pressure which increases longitudinal stability
Greater back elevator pressure required - longer takeoff roll; higher approach speeds and problems with landing flare
33
Q
What effect does a rearward center of gravity have on an aircraft’s flight characteristics
A
Lower stall speed - less wing loading
Higher cruise speed - reduced drag; smaller angle of attack is required to maintain altitude
Less table - stall and spin recovery more difficult; the center of gravity is closer to the center of pressure, causing longitudinal instability
34
Q
What are standard weight assumed for the following when calculating weight and balance problems
A
Crew and passengers 190lb each
Gasoline 6lb/gal
Oil 7.5 lb /gal
Water 8.35 lb/gal
35
Q
What are some of the main elements of aircraft performance
A
```Takeoff and landing distance
rate of climb
ceiling
payload
range
speed
fuel economy
maneuverability
stability```
36
Q
What factors affect the performance of an aircraft during takeoffs and landings
A
```Air density
Surface wind
Runway surface
Upslope or downslope of runway
Weight```
37
Q
What effect does wind have on aircraft performance
A
Landing - The effect of win on landing distance is identical to its effect on takeoff distance. A headwind will lower ground speed and increase airplane performance by steepening the approach angle and reducing the landing distance. A tailwind will increase ground speed and decrease performance, by decreasing the approach angle and increasing the landing speed
Cruise flight - Winds aloft have somewhat an opposite effect on airplane performance. A headwind will decrease performance by reducing groundspeed, which in turn increase the fuel required for the flight. A tailwind will increase performance by increasing the ground speed, which in turn reduces the fuel requirement for the flight
38
Q
How does weight affect takeoff and landing performance
A
Increased gross weight can have a significant effect on takeoff performance
Higher liftoff speed
greater mass to accelerate / slow acceleration
Increased retarding force (drag and ground friction)
Longer takeoff distance
The effect of gross weight on landing distance is that the airplane will require a greater speed to support the airplane at the landing angel of attack and lift coefficient resulting in an increased landing distance
39
Q
What effect does an increase in density altitude have on takeoff an landing performance
A
An increase in density altitude results in
increased takeoff distance
reduced rate of climb
increased true airspeed on approach and landing
increased landing roll distance
40
Q
Define the term density altitude
A
Density altitude is pressure altitude corrected for nonstandard temperature. Under standard atmospheric condition, air at each level of the atmosphere has a specific density, and under standard conditions, pressure altitude and density altitude identify the same level. Therefore, density altitude is the vertical distance above sea level in the standard atmosphere at which a given density is found
41
Q
How does air density affect aircraft performance
A
```The density of the air has a direct effect on
lift produced by the wings
power output of the engine
propeller efficiency
drage force```
42
Q
What factors affect air density
A
Altitude - the higher the altitude, the less dense the air
Temperature - the warmer the air, the less dense it is
Humidity - more humid air is less dense
43
Q
How does temperature, altitude, and humidity affect density altitude
A
Density altitude will increase (low air density) when on or more of the following occurs
Higher air temp
High altitude
High humidity
Density altitude will decrease (high air density) when one or more of the following occurs
low air temp
low altitude
low humidity
44
Q
Vso
A
Stall speed in landing configuration
45
Q
Vs1
A
Stall speed clean configuration
46
Q
Vy
A
Best rate-of-climb max alt. per unit of time
47
Q
Vx
A
Best angle-of-climb highest alt. in given horizontal distance
48
Q
Vle
A
Max landing great extend speed
49
Q
Vlo
A
Max landing great operating speed
50
Q
Vfe
A
Max flap extend speed
51
Q
Va
A
Maneuvering speed
52
Q
Vno
A
Normal operating speed
53
Q
Vne
A
Never exceed speed
54
Q
What information can you obtain from the following charts
A
Takeoff charts - These allow you to compute the takeoff distance of the airplane with no flaps or with a specific flap configuration. You can also compute distance for a no flap takeoff over a 50” obstacle. The takeoff distance chart provides for various airplane weights, altitudes, temp. winds, and obstacle heights
Fuel, time, and distance-to-climb chart - This chart will give the fuel amount used during the climb, the time it will take to accomplish the climb, and the ground distance that will be covered during the climb. To use this chart obtain the information for the departing airport and for the cruise altitude
Cruise and range performance chart - This is designed to give true airspeed, fuel consumption, endurance in hours, and range in miles at specific cruise configurations
Crosswind and headwind component chart - This allows for figuring the headwind and crosswind component for any given wind direction and velocity
Landing charts - Provide normal landing distance as well as landing distance over 50” obstacle
Stall speed performance charts - These are designed to give an understanding of the speed at which the airplane will stall in a given configuration. Will typically take into account the angle of bank, the position of the gear and flaps and the throttle position
55
Q
Define the term pressure altitude and state why it is important
A
Pressure altitude - the altitude indicated when the altimeter setting window is adjusted to 29.92. This is the altitude above the standard datum plane, a theoretical plane where air pressure at 15 degrees C equals 29.92’ Hg. Pressure altitude is used to compute density altitude, true altitude, true airspeed, and other performance data
56
Q
What is the normal climb-out speed
A
76kts
57
Q
What is the best rate-of-climb Vy
A
76
58
Q
What is the best angel of climb Vx
A
64
59
Q
What is the maximum flap extension speed Vfe
A
102
60
Q
What is the stall speed in the normal configuration Vso
A
45
61
Q
What is the stall speed in the clean configuration
A
50
62
Q
What is the normal approach-to-land speed
A
66
63
Q
What is maneuvering speed
A
89-113
64
Q
What is red-line speed
A
154
65
Q
What engine-out glide speed will give you max rnage
A
76
66
Q
What is the make and horsepower of the engine
A
Lycoming 180 BHP
67
Q
How many usable gallons of fuel can you carry
A
48
68
Q
Where are the fuel tanks located, and what are their capacities
A
wings 24 US gal each of usable fuel
69
Q
Where are the fuel vents for your aircraft
A
Fuel vents are on top of the wing
70
Q
What is the octane rating of the fuel used by your aircraft
A
100LL
71
Q
Where are the fuel sumps located on your aircraft? When should you drain them?
A
One under each wing tank and 1 behind the firewall in the engine.
They should be drained for the first flight of the day and after each refueling
72
Q
What are the minimum and max oil capacities
A
min 2 max 8 qt
73
Q
What wight of oil is being used
A
40
74
Q
What is the maximum oil temp and pressure
A
245F
115 PSI
75
Q
What are the nose wheel turning limitations
A
30 degrees
76
Q
What is the x/w comp
A
17 kt
77
Q
How many people will this aircraft cary safely with a full fuel load
A
2
78
Q
What is the max weight the A/C can carry with baggage
A
2550 (2350 with 200lb of bags)
79
Q
Takeoff distance at sea-level
A
2,000 feet
80
Q
What is your max allowable useful load
A
860.63
81
Q
How much fuel can be carried
A
48 gal 300/lb
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Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.
# Re: st: RE: Percentiles with basic statistics
From Maarten Buis <[email protected]> To [email protected] Subject Re: st: RE: Percentiles with basic statistics Date Thu, 18 Aug 2011 16:41:06 +0200
```On Thu, Aug 18, 2011 at 4:11 PM, Ozgur Ozdemir wrote:
> I have a list of 20 variables in an excel and would like to get the mean, standard dev etc of all variables after eliminating the1% and 99% percentiles. is there any easy way of doing it rather than doing it one by one. thanks
I have a number of comments:
1) We can only help you with Stata, not with excel (whatever that may be).
2) Do you want this variable by variable, or remove all observations
where at least one variable satisfies your criterion? If you want to
use these variables later together in an estimation command you will
have to use the latter option and live with the fact that you will
loose more than 2% of your observations.
3) This is a very bad idea. Outliers are the most informative
observations, blindly throwing those away should (IMHO) be a crime!
See: http://www.stata.com/statalist/archive/2011-08/msg00398.html
Anyhow, below is an example that shows how to do this over all
variables and variable by variable:
*------------------------ begin example ---------------------
sysuse auto, clear
// store a list of all variables excluding foreign and make in
// a local macro `varl'
ds foreign make, not
local varl `"`r(varlist)'"'
// remove if at least one variable contains "outlier"
gen byte touse = 1
foreach var of local varl {
qui sum `var', detail
replace touse = 0 if `var' <= r(p1) | ( `var' >= r(p99) & `var' < .)
}
// get the means and standard deviations
sum `varl' if touse == 1
// remove "outlier" variable by variable
foreach var of local varl {
qui sum `var', detail
sum `var' if `var' > r(p1) & `var' < r(p99)
}
*---------------- end example -----------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )
--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany
http://www.maartenbuis.nl
--------------------------
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
```
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# Teaching and learning Maths: learning sequence catering for diversity
This post is addressing the Year 6 content strand ‘measurement and geometry’, substrand ‘using units of measurement’ and content descriptor ACMMG137solve problems involving the comparison of lengths and areas using appropriate units” (ACARA, 2017), which were discussed in the previous posts on Maths unit and lesson planning process, rubric construction, multiple representation of mathematical concepts, and using Math apps. The achievement standards are mapped to the proficiency strands and include:
• students are to understand and describe properties of surface area and length,
• develop fluency in measuring using metric units,
• solve authentic problems, and
• be able to explain shape transformations
### A short learning sequence of comparison of lengths and areas – major steps
Booker et al. detail the conceptual and procedural steps required to master length and area (2015). Applied toACMMG137, these include three major steps:
1. Perceiving and identifying the attributes ‘area’ and ‘length’
2. Comparing and ordering areas and lengths (non-standard units => standard units)
3. Measuring areas and lengths (non-standard units => standard units), including covering surfaces without leaving gaps
This sequence is introduced using multiple representations, progressing from hands-on experiences with manipulatives towards abstract logical thinking and transformation tasks (see examples).
### Activities to aid the learning sequence
The steps are mapped to a range activities that cater for diverse classrooms in alignment with the framework of Universal Design of Learning (UDL) (Fuchs & Fuchs, 2001):
• Students cut their own tangram puzzle (with or without template) and explore how small shapes can create larger shapes
• Students order tangram shapes by area and perimeter and establish base units: smallest shape (small triangle) as area unit, side of small square and hypotenuse of small triangle as length units
• Students colour tangram pieces and puzzle range of objects (with and without colour, line clues), exploring how larger geometric shapes can be covered by smaller and making statistical observations on the number of units within each shape and corresponding perimeter. Non-standard units are measured and used for calculations.
(The activities are detailed with examples in the post on multiple representations of mathematical concepts)
### Adjustments for a child with learning difficulties
Student with very limited English knowledge (e.g. EAL/D beginning phase). ACARA provides detailed annotated content descriptors (ACARA, 2014). The language and cultural considerations are specifically addressed by keeping discussion relevant to the tasks, offering alternatives to ‘word problems’ in both activities and assessment (as highlighted in the rubric design). Teaching strategy considerations are followed by explicitly teaching the vocabulary, making explicit links between terminology, symbols and visual representations (e.g. by pausing explanatory movie and writing out and illustrating on the whiteboard using colours (e.g. area = blue, equal sides = green, hypotenuse = red, labelling the count of units). The EAL/D student is provided with opportunities to develop cognitive academic language proficiency through mixed-ability group work. All content knowledge can be demonstrated by the student using physical manipulatives, charts and algorithms.
### Adjustments for a child with advanced abilities
Children with advanced abilities can only develop their potential if provisions are made to deliver a challenging, enriched and differentiated curriculum, and a supportive learning environment
(Gagné, 2015). Maker’s updated recommendations on the four dimensions of curriculum modifications (2005) are applied as follows:
• Content – content is framed in an interdisciplinary way, using tangram that connects to Japanese culture and art
• Process – design emphasises self-directed learning, choice, variety and discovery of underlying patterns by offering a range of tangram puzzle options at multiple levels of difficulty to be explored in abstract terms (i.e. sorting by ratio of area to perimeter)
• Product – high-ability students are encouraged to work on expert puzzles and transform learned concept knowledge by designing their own tangrams with constraints (e.g. tangrams with identical perimeter, sequence reduced by one length unit, …) and present their products to the class
• Environment -high-ability students are provided access to spreadsheet software (e.g. for statistical observations, to graph relationships between area and perimeter) and allowed time to work independently
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Brian Bi
$\DeclareMathOperator{\End}{End} \DeclareMathOperator{\char}{char} \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\ker}{ker} \DeclareMathOperator{\im}{im} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\Hom}{Hom} \DeclareMathOperator{\span}{span} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\Id}{Id} \DeclareMathOperator{\ad}{ad} \newcommand\d{\mathrm{d}} \newcommand\pref[1]{(\ref{#1})}$
Section 3.3. Representations of direct sums of matrix algebras
Problem 3.3.3
1. We will prove the following:
Lemma: If $$V$$ is a representation of $$A$$, where $$A = \bigoplus_{i=1}^n A_n$$, then $$V$$ can be written as the direct sum of representations $$V = \bigoplus_{i=1}^n 1_i V$$.
Proof: Suppose $$v \in V$$ is given. Since $$1 = \sum_{i=1}^n 1_i$$, it follows that $$v = \sum_{i=1}^n 1_i v$$. Also, suppose $$v = \sum_{i=1}^n v_i$$ where $$v_i \in 1_i V$$ for all $$i$$. Then, let $$j \in \{1, 2, \ldots, n\}$$; left-multiplying by $$1_j$$ yields $$1_j v = \sum_{i=1}^n 1_j v_i = \sum_{i=1}^n 1_j 1_i v_i = v_i$$. Therefore, $$V$$ is the direct sum of the $$1_i V$$'s as vector spaces. But each $$1_i V$$ is also a subrepresentation of the full $$A$$ (where the $$A_j$$ components act as zero for all $$j \neq i$$), which proves the desired result.
Corollary: $$V$$ is irreducible if and only if there is exactly one $$i$$ for which $$1_i V$$ is nonzero, and that $$1_i V$$ is an irrep of $$A_i$$.
Proof of corollary: Write $$V = \bigoplus_{i=1}^n 1_i V$$. If there is a unique $$i$$ with $$1_i V$$ nonzero, then $$V = 1_i V$$. Since $$A$$ acts on $$1_i V$$ exactly as its $$A_i$$ component does, it follows that $$V$$ is an irrep of $$A$$ iff $$1_i V$$ is an irrep of $$A_i$$. If, on the other hand, there are multiple $$i$$'s with $$1_i V$$ nonzero, then $$V$$ is not irreducible, since a nonzero proper subrepresentation is constructed by removing one $$1_i V$$ component from the direct sum.
Therefore, we can find all irreps of $$A$$ by considering each $$i$$ in turn as the $$i$$ for which $$1_i V \neq \{0\}$$. For each such pair $$(i, V)$$ where $$V$$ is an irrep of $$A_i$$, $$V$$ is also an irrep of $$A$$ with $$(a_1, \ldots, a_n)v = a_i v$$; and all irreps of $$A$$ are of this form.
2. Following the Hint, for every $$(i, j) \in \{1, 2, \ldots, d\}^2$$, let $$E_{ij} \in \mathrm{Mat}_d(k)$$ be the matrix with 1 in the $$i$$th row of the $$j$$th column and 0's everywhere else. Let $$V$$ be a finite-dimensional representation of $$\mathrm{Mat}_d(k)$$, and let $$v \in V$$. Now since $$E_{11} + \ldots + E_{dd}$$ is the identity, it follows that $$v = E_{11}v + \ldots + E_{dd}v$$. So each $$v \in V$$ can be written as $$v = \sum_{i=1}^d v_i$$ where $$v_i \in E_{ii}V$$ for every $$i$$. Furthermore, this decomposition is unique since left-multiplying by $$E_{jj}$$ yields $$E_{jj} v = v_j$$ for each $$j$$. We conclude that $$V = \bigoplus_{i=1}^d E_{ii}V \label{eqn:matdirectsum}$$
Also, for every $$v \in E_{11}V$$, and for every $$i \in \{1, 2, \ldots, d\}$$, we have $$E_{ii}E_{i1}v = E_{i1}v$$, so $$E_{i1}v \in E_{ii}V$$. Let $$\Phi_i: E_{11}V \to E_{ii}V$$ be defined by $$\Phi_i(v) = E_{i1}v$$. Observe that if $$w \in E_{ii}V$$, then the equation $$w = E_{i1}v$$ has exactly one solution: left-multiplying by $$E_{1i}$$ yields $$v = E_{1i}w$$, and indeed $$E_{i1}(E_{1i}w) = E_{ii}w = w$$. Therefore $$\Phi_i$$ is one-to-one and onto.
Fix $$v \in E_{11}V \setminus \{0\}$$, and let $$S(v) = \langle E_{11}v, E_{21}v, \ldots, E_{d1}v\rangle$$. Since each $$\Phi_i$$ is one-to-one, it follows that none of the $$E_{i1}v$$'s vanish, and since each lies in $$E_{ii}V$$, it follows from $$(\ref{eqn:matdirectsum})$$ that they are all linearly independent. So $$S(v)$$ has dimension $$d$$, and can be put into isomorphism with $$k^d$$ (with standard basis $$\{e_1, \ldots, e_d\}$$), with the mapping given by $$E_{i1}v \mapsto e_i$$. If $$a \in \mathrm{Mat}_d(k)$$, write $$a = \sum_{j,k} c_{jk} E_{jk}$$; then for each $$i$$, $$a E_{i1} v = \sum_{j,k} c_{jk} E_{jk} E_{i1}v = \sum_j c_{ji} E_{j1}v \in S(v)$$, so $$S(v)$$ is a subrepresentation of $$V$$; also, since $$a e_i = \sum_{j,k} c_{jk} E_{jk} e_i = \sum_j c_{ji} e_j$$, it follows that $$S(v)$$ and $$k^d$$ are in fact isomorphic as representations. So $$V$$ is irreducible iff $$V$$ is isomorphic to $$k^d$$ as a representation of $$\mathrm{Mat}_d(k)$$. (Since $$\mathrm{Mat}_d(k)$$ is finite-dimensional, it cannot, of course, have any infinite-dimensional irreps either.)
Fix a basis $$\{v_1, v_2, \ldots, v_k\}$$ of $$E_{11}V$$. Suppose $$v \in V$$ is given. Using $$(\ref{eqn:matdirectsum})$$ and the fact that each $$\Phi_i$$ is an isomorphism, we see that there is a unique set of coefficients $$c_{ij}$$ such that $$v = \sum_{j=1}^k \sum_{i=1}^d c_{ij} E_{i1} v_j$$. Therefore $$V = S(v_1) \oplus S(v_2) \oplus \ldots \oplus S(v_k)$$ as vector spaces. And since each $$S(v_j)$$ is a subrepresentation of $$V$$, we conclude that $$V = S(v_1) \oplus \ldots \oplus S(v_k)$$ as representations.
3. Let $$A = \bigoplus_{i=1}^r A_i$$ where $$A_i = \mathrm{Mat}_{d_i}(k)$$. By part (a), every irrep of $$A$$ is obtained as an irrep of one of the $$A_i$$'s. By part (b), the only irrep of $$A_i$$ is $$k^i$$. Therefore all irreps of $$A$$ are given by $$V_1 = k^{d_1}, V_2 = k^{d_2}, \ldots, V_r = k^{d_r}$$. If $$V$$ is a general finite-dimensional representation of $$A$$, then by the Lemma proven in part (a), we can write $$V = \oplus_{i=1}^r 1_i V$$. Each $$1_i V$$ is a representation of $$A_i$$ so by part (b), it decomposes as a direct sum of $$k^{d_i}$$'s, and we are done.
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CHAP 26 Questions
# CHAP 26 Questions - Chapter 26 1 A gambler goes to the...
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Chapter 26 1. A gambler goes to the local casino and observes the action at the craps table for 100 throws of the dice. He notices that 21 of the throws come up 7. State the null and alternative hypotheses, and find the P -value of his observations. Is this a statistically significant result? 2. Suppose you want to determine if a coin is biased to land tails more often than heads. You flip the coin 125 times and find that you got 53 heads. State the null and alternative hypotheses, and find the P -value of your observations. Is this a statistically significant result? 3. Of 12 people on a jury Denver, 8 of them are men. The prosecutor argues that the jury is not a fair representation of Denver’s population (In 2004, Denver had 50.7% men). A statistician is called to verify this. a) Should the statistician use a z -test or a t -test? b) Find the test statistic for the percentage of men in the jury. Does the prosecutor have a valid argument? 4. In many cities, chlorine is added to drinking water to remove microbes.
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# Geometrical Proof
1. Jan 5, 2015
### franceboy
1. The problem statement, all variables and given/known data
Consider an triangle ABC with M as the middle point of the side AB.
On the straight line through AB you put the angle ∠ ACM at A and the angle ∠ MCB at B. Now you have two new lines. The new lines should be on the same side of AB as C.
Proof that the intersection point of the two new lines is located on the line through CM.
2. Relevant equations
3. The attempt at a solution
I wanted to use Ceva`s Theorem but I could not use it :(
I hope you can give me some advice.
2. Jan 5, 2015
### Joffan
You've generated some similar triangles there which should help, if you work out the scaling. Note that |AM| = |BM|
3. Jan 5, 2015
### Staff: Mentor
I don't understand. From your explanation you would have two new angles. In my drawing below I have labelled ∠ ACM as a and ∠ MCB as b.
???
What is Ceva's Theorem?
4. Jan 5, 2015
### Joffan
Hi Mark, this is the construction as I understand it:
5. Jan 5, 2015
### Staff: Mentor
OK, that makes sense.
6. Jan 5, 2015
### franceboy
Sorry thai i did not add a sketch but a GeoGebra sketch was not accepted as file.
Joffan your sketch is correct. I used the symmetry so that I " only" need to proof
BX / XC * CY / YA = 1
I determined all the angles and I found some similarities but they did not help to solve the problem.
Is Ceva' s theorem the right idea to solve the problem?
7. Jan 5, 2015
### Joffan
Maybe you could use Ceva's theorem - it seems a little overpowered.
I would proceed by marking X as the intersection of the new line from A with CM and Y as the intersection of the new line from B with CM. Then show that |MX| = |MY| and thus that X == Y
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1. ## critical value
for normal hypothesis testing
1% level 1-tailed critical value of z = 2.326
2.531 > 2.236 so significant
i dont understand how they got 2.326
2. ## Re: critical value
we need more information than that to reprodruce the 2.326. Post the entire question and the working (if known) to get the answer.
3. ## Re: critical value
The farmer also grows onions. The weight in kilograms of the onions is Normally distributed
with mean 0.155 and variance 0.005. He is trying out a new variety, which he hopes will yield
a higher mean weight. In order to test this, he takes a random sample of 25 onions of the new
variety and finds that their total weight is 4.77 kg. You should assume that the weight in kilograms
of the new variety is Normally distributed with variance 0.005.
Carry out the test at the 1% level.
Mean weight = 4.77/25 = 0.1908
test statistic= (0.1908-0.155)/sqrt(0.005)*sqrt(25)=2.531
1% level 1-tailed critical value of z = 2.326
2.531 > 2.236 so significant.
There is sufficient evidence to reject H0
4. ## Re: critical value
Are you allowed to use a calculator(Ti-83?)? With 1-PropZtest you can compare the given p-value with the significance level (1%).
5. ## Re: critical value
The farmer also grows onions. The weight in kilograms of the onions is Normally distributed
with mean 0.155 and variance 0.005. He is trying out a new variety, which he hopes will yield
a higher mean weight. In order to test this, he takes a random sample of 25 onions of the new
variety and finds that their total weight is 4.77 kg. You should assume that the weight in kilograms
of the new variety is Normally distributed with variance 0.005.
Carry out the test at the 1% level.
Mean weight = 4.77/25 = 0.1908
test statistic= (0.1908-0.155)/sqrt(0.005)*sqrt(25)=2.531
1% level 1-tailed critical value of z = 2.326
2.531 > 2.236 so significant.
There is sufficient evidence to reject H0
sorry, i misread your first post. The 2.326 is the upper 99% point on the normal distribution. You are doing a 1-tailed 1% test so you should look at the 99% point.
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# Solution of Chapter 12. Circles (RS Aggarwal - Mathematics Book)
## Exercise 12A
1
Find the length of tangent drawn to a circle with radius 8 cm from a point 17 cm away from the center of the circle.
2
A point P is 25 cm away from the center of a circle and the length of tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
3
Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle.
4
In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, find the lengths of AD, BE and CF.
5
In the given figure, PA and PB are the tangent segments to a circle with center 0. Show that the points A, O, B and P are concyclic.
6
In the given figure, the chord AB of the larger of the two concentric circles, with center O, touches the smaller circle at C. Prove that AC = CB.
7
From an external point P, tangents PA and PB are drawn to a circle with center O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of PCD.
8
A circle is inscribed in a LABC touching AB, BC and AC at P, Q and R respectively. If AB = 10 cm, AR = 7 cm and CR = 5 cm, find the length of BC.
9
In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.
10
In the given figure, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.
11
In the given figure, O is the center of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.
12
In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 6 cm and 9 cm respectively. If the area of ABC = 54 cm2 then find the lengths of sides AB and AC.
13
PQ is a chord of length 4.8 cm of a circle of radius 3 cm. The tangents at P and Q intersect at a point T as shown in the figure. Find the length of TP.
14
Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its center.
15
In the given figure, a circle with center O, is inscribed in a quadrilateral ABCD such that it touches the side BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, LB = 90° and DS = 5 cm then find the radius of the circle.
16
In the given figure, O is the center of the circle and TP is the tangent to the circle from an external point T. If PBT = 30°, prove that BA : AT = 2 : 1.
## Exercise 12B
1
In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of side AD.
2
In the given figure, PA and PB are two tangents to the circle with center O. If APB = 50° then what is the measure of OAB.
3
In the given figure, O is the center of a circle. PT and PQ are tangents to the circle from an external point P. If TPQ = 70°, find TRQ.
4
In the given figure, common tangents AB and CD to the two circles with centers O1 and O2 intersect at E. Prove that AB = CD.
5
If PT is a tangent to a circle with center O and PQ is a chord of the circle such that QPT = 70°, then find the measure of POQ.
6
In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4 cm and 3 cm respectively. If the area of ΔABC = 21 cm2 then find the lengths of sides AB and AC.
7
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle (in cm) which touches the smaller circle.
8
Prove that the perpendicular at the point of contact of the tangent to a circle passes through the center.
9
In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with center 0. If PRQ = 120°, then prove that OR = PR + RQ.
10
In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.
11
In the given figure, 0 is the center of the circle. PA and PB are tangents. Show that AOBP is a cyclic quadrilateral.
12
In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then find the radius of the smaller circle.
13
In the given figure, PQ is a chord of a circle with center 0 and PT is a tangent. If QPT = 60°, find P
14
In the given figure, PA and PB are two tangents to the circle with center O. If APB = 60° then find the measure of OAB.
## Multiple Choice Questions (MCQ)
1
The number of tangents that can be drawn from an external point to a circle is
2
In the given figure, RQ is a tangent to the circle with center O. If SQ = 6 cm and QR = 4 cm, then OR is equal to
3
In a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If O is the center of the circle, then length OP = ?
4
Which of the following pairs of lines in a circle cannot be parallel?
5
The chord of a circle of radius 10 cm subtends a right angle at its center. The length of the chord (in cm) is
6
In the given figure, PT is a tangent to the circle with center O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is
7
In the given figure, point P is 26 cm away from the center 0 of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then, the radius of the circle is
8
PQ is a tangent to a circle with center O at the point P. If ΔOPQ is an isosceles triangle, then OQP is equal to
9
In the given figure, AB and AC are tangents to the circle with center O such that BAC = 40°. Then, BOC is equal to
10
If a chord AB subtends an angle of 60° at the center of a circle, then the angle between the tangents to the circle drawn from A and B is
11
In the given figure, O is the center of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of chord AB is
12
In the given figure, AB and AC are tangents to a circle with center 0 and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is
13
In the given figure, 0 is the center of a circle, AOC is its diameter such that ACB = 50°. If AT is the tangent to the circle at the point A then BAT = ?
14
In the given figure, O is the center of a circle, PQ is a chord and PT is the tangent at P. If POQ = 70°, then TPQ is equal to
15
In the given figure, AT is a tangent to the circle with center O such that OT = 4 cm and OTA = 30°. Then, AT = ?
16
If PA and PB are two tangents to a circle with center O such that AOB = 110° then APB is equal to
17
In the given figure, the length of BC is
18
In the given figure, if AOD = 135° then BOC is equal to
19
In the given figure, 0 is the center of a circle and PT is the tangent to the circle. If PQ is a chord such that QPT = 50° then POQ = ?
20
In the given figure, PA and PB are two tangents to the circle with center O. If APB = 60° then OAB is
21
If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm then the length of each tangent is
22
In the given figure, PQ and PR are tangents to a circle with center A. If QPA = 27° then QAR equals
23
In the given figure, PA and PB are two tangents drawn from an external point P to a circle with center C and radius 4 cm. If PA PB, then the length of each tangent is
24
If PA and PB are two tangents to a circle with center O such that APB = 80°. Then, AOP = ?
25
In the given figure, O is the center of the circle. AB is the tangent to the circle at the point P. If APQ = 58° then the measure of PQB is
26
In the given figure, O is the center of the circle. AB is the tangent to the circle at the point P. If PAO = 30° then CPB + ACP is equal to
27
In the given figure, PQ is a tangent to a circle with center O. A is the point of contact. If PAB = 67°, then the measure of AQB is
28
In the given figure, two circles touch each other at C and AB is a tangent to both the circles. The measure of ACB is
29
O is the center of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to P the circle. Then, the area of quad. PQOR is
30
In the given figure, PQR is a tangent to the circle at Q, whose center is O and AB is a chord parallel to PR such that BQR = 70°. Then, AQB =?
31
The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the center of the circle is
32
In the given figure, 0 is the center of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If PBO = 30° then PTA = ?
33
In the given figure, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the perimeter of ΔEDF is
34
To draw a pair of tangents to a circle, which is inclined to each other at an angle of 45°, we have to draw tangents at the end points of those two radii, the angle between which is
35
In the given figure, O is the center of a circle; PQL and PRM are the tangents at the points Q and R respectively and S is a point on the circle such that SQL = 50° and SRM = 60°. Then, QSR = ?
36
In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are of lengths 12 cm and 9 cm respectively. If the area of ΔPQR = 189 cm2 then the length of side PQ is
37
In the given figure, QR is a common tangent to the given circles, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm then the length of QR is
38
In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7 cm and CS = 3 cm. Then, the length AB = ?
39
In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 6 cm, BP = 5 cm, CQ = 3 cm and DR = 4 cm then perimeter of quad. ABCD is
40
In the given figure, O is the center of a circle, AB is a chord and AT is the tangent at A. If AOB = 100° then BAT is equal to
41
In a right triangle ABC, right - angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle is
42
In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. lithe radius of the circle is 10 cm, BC = 38 cm, PB = 27 cm and AD CD then the length of CD is
43
In the given figure, LABC is right - angled at B such that BC = 6 cm and AB = 8 cm. A circle with center O has been inscribed inside the triangle. OP AB, OQ BC and OR AC. If OP = OQ = OR = x cm then x = ?
44
Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm then the length of AD is
45
In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and APB = 60°. The length of chord AB is
46
In the given figure, DE and DF are tangents from an external point D to a circle with center A. If DE = 5 cm and DE DF then the radius of the circle is
47
In the given figure, three circles with centers A, B, C respectively touch each other externally.
If AB = 5 cm, BC = 7 cm and CA = 6 cm then the radius of the circle with center A is
48
In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm then the length of AP is
49
In the given figure, O is the center of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to
50
Which of the following statements is not true?
51
Which of the following statements is not true?
52
Which of the following statements is not true?
53
Assertion - and - Reason Type
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
54
Assertion - and - Reason Type
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code
55
Assertion - and - Reason Type
Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
## Formative Assessment (Unit Test)
1
In the given figure, O is the center of a circle, PQ is a chord and the tangent PT at P makes an angle of 50° with PQ. Then, POQ = ?
2
If the angle between two radii of a circle is 130° then the angle between the tangents at the ends of the radii is
3
If tangents PA and PB from a point P to a circle with center O are drawn so that APB = 80° then POA = ?
4
In the given figure, AD and AE are the tangents to a circle with center O and BC touches the circle at F. If AE = 5 cm then perimeter of ΔABC is
5
In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively.
If AB = x cm, BC = 7 cm, CR = 3 cm and
AS = 5 cm, find x.
6
In the given figure, PA and PB are the tangents to a circle with center O. Show that the points A, 0, B, P are concyclic.
7
In the given figure, PA and PB are two tangents from an external point P to a circle with center O. If PBA = 65°, find OAB and APB.
8
Two tangent segments BC and BD are drawn to a circle with center O such that CBD = 120°. Prove that OB = 2BC.
9
Fill in the blanks.
(i) A line intersecting a circle in two distinct points is called a ……..
(ii) A circle can have ………..parallel tangents at the most.
(iii) The common point of a tangent to a circle and the circle is called the ………..
(iv) A circle can have ………..tangents.
10
Prove that the lengths of two tangents drawn from an external point to a circle are equal.
11
Prove that the tangents drawn at the ends of the diameter of a circle are parallel.
12
In the given figure, if AB = AC, prove that BE = CE.
13
If two tangents are drawn to a circle from an external point, show that they subtend equal angles at the center.
14
Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.
15
Prove that the parallelogram circumscribing a circle, is a rhombus.
16
Two concentric circles are of radii 5 cm and 3 cm respectively. Find the length of the chord of the larger circle which touches the smaller circle.
17
A quadrilateral is drawn to circumscribe a circle. Prove that the sums of opposite sides are equal.
18
Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.
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# Python Tutorial: An Introduction to Scipy Minimize Examples
Posted on
Are you looking for an introduction to scipy minimize examples? Python is an extremely powerful language and its applications in data science have made it one of the most popular languages in the industry. Scipy minimize is a useful tool that can help you optimize your code and achieve better results. In this Python tutorial, we will explore the basics of scipy minimize and provide some examples of how to use it. So if you’re ready to take your Python coding to the next level, read on!
Scipy minimize allows you to minimize a given set of parameters to a single value. For example, you could use scipy minimize to minimize the cost of a product or to minimize the amount of time it takes to complete a task. Scipy minimize can also be used for optimization of complex functions. It can be used for solving complex equations or for finding the optimal solution to a problem. In this tutorial, we will provide some examples of how to use scipy minimize.
The first example is a simple linear equation. We will use scipy minimize to find the minimum value of the equation given three parameters. The equation is y = ax + b. The parameters are a, b, and c. We will use scipy minimize to find the minimum value of the equation given the three parameters. We will use the same equation for our second example, but this time we will use scipy minimize to find the maximum value of the equation given the three parameters.
The third example is a bit more complex. We will use scipy minimize to find the minimum value of a given function given four parameters. The function is f(x,y,z) = x^2 + y^2 + z^2. The parameters are x, y, and z. We will use scipy minimize to find the minimum value of the function given the four parameters. In this example, we will also use the same function for our fourth example, but this time we will use scipy minimize to find the maximum value of the function given the four parameters.
This tutorial is just an introduction to scipy minimize examples. There are many more applications of scipy minimize and many more examples that can be explored. If you are interested in learning more about scipy minimize and its applications in data science, we invite you to read our full Python tutorial. With our tutorial, you will be able to take your Python coding to the next level and unlock the power of scipy minimize.
# Python Tutorial: An to Scipy Minimize Examples
## Introduction to Scipy Minimize
Scipy minimize is a powerful tool for optimizing and minimizing problems. It is widely used in scientific computing, data analysis, and machine learning. It is part of the SciPy library, which is a collection of mathematical algorithms and functions for Python. The minimize function is used to find the minimum or maximum of an objective function, subject to a set of constraints. This tutorial will cover the basics of how to use Scipy minimize, and will explain some of the more advanced features of the library.
## Getting Started with Scipy Minimize
The first step to using Scipy minimize is to import the minimize module. This can be done with the following command:
import scipy.optimize as optimize
Once the module is imported, the minimize function can be used. The syntax for the minimize function is as follows:
optimize.minimize(func, x0, args=(), method=None, jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None)
## Understanding the Arguments of Scipy Minimize
The first argument of the minimize function is the objective function. This is the function that needs to be minimized or maximized. The objective function must be written as a Python function. The second argument is the initial guess of the solution. This is the starting point of the minimization process. The third argument is the additional arguments to the objective function. If the objective function requires additional parameters, they must be passed as a tuple.
The fourth argument is the method to use for the minimization. This can be one of several different algorithms. The fifth argument is the Jacobian of the objective function. This is a matrix of partial derivatives of the objective function with respect to the parameters. The sixth argument is the Hessian of the objective function. This is a matrix of second order partial derivatives of the objective function with respect to the parameters. The seventh argument is the Hessian of the objective function with respect to the parameters. This is a matrix of third order partial derivatives of the objective function with respect to the parameters.
## Using Scipy Minimize for Optimization
The minimize function can be used to optimize an objective function. This is done by supplying the minimize function with the objective function, the initial guess of the solution, and the additional arguments. The minimize function will then find the minimum or maximum of the objective function, subject to the constraints. The minimize function can also be used to solve equations, find roots, and perform other types of optimization.
## Example of Scipy Minimize
To demonstrate how to use Scipy minimize, we will use a simple example. Consider the objective function f(x) = x2. The goal is to find the minimum of this function. To do this, we will use the minimize function. The code is as follows:
import scipy.optimize as optimize
def f(x):
return x**2
res = optimize.minimize(f, [2])
print(res.x)
The output of this code is [0.0]. This means that the minimum of the function is 0.0, which can be verified by plotting the function.
## Limitations of Scipy Minimize
Scipy minimize is a powerful tool for optimization, but it has some limitations. Firstly, the minimize function is limited to finding solutions to unconstrained problems. If the problem has constraints, then a different approach must be taken. Secondly, the minimize function is not suitable for problems with noisy or discontinuous functions. In these cases, a different approach must be taken as well. Finally, the minimize function is not suitable for very large problems, as it will take a long time to find the solution.
## Using Scipy Minimize with a Constraint
Scipy minimize can also be used with constraints. Consider the objective function f(x) = x2 + y2, where x and y are variables. The goal is to find the minimum of this function, subject to the constraint x + y = 1. To do this, we need to use the minimize function with a constraint. The code is as follows:
import scipy.optimize as optimize
def f(x):
return x[0]**2 + x[1]**2
res = optimize.minimize(f, [0.5, 0.5], constraints={‘type’: ‘eq’, ‘fun’: lambda x: x[0] + x[1] – 1})
print(res.x)
The output of this code is [0.5, 0.5]. This means that the minimum of the function is 0, which can be verified by plotting the function.
## Tips to Improve Coding Skill Relate to Python Tutorial: An Introduction to Scipy Minimize Examples
### 1. Understand the Algorithms
The first step to improving your coding skills is to understand the algorithms used in Python. This includes understanding the syntax of the language, as well as the libraries and modules that are available. It is also important to understand how the algorithms work, so that you can use them effectively in your code.
### 2. Practice, Practice, Practice
The best way to improve your coding skills is to practice. The more you practice, the better you will become. It is also important to review the code that you have written, and to think critically about the problems that you have solved.
### 3. Read Tutorials and Examples
Reading tutorials and examples can be a great way to learn about coding and Python. Reading tutorials and examples can provide you with valuable insight into the language, as well as help you to understand the syntax and structure of the language.
### 4. Ask Questions
If you are struggling with a particular problem, don’t be afraid to ask questions. There are many online forums and communities where you can get help with coding problems. Asking questions can also help to broaden your understanding of the language and help you to become a better programmer.
### 5. Take Online Courses
Taking online courses is a great way to learn more about Python and coding. There are many free and paid courses available online. Taking a course can help to give you a better understanding of the language and can help to improve your coding skills.
Scipy minimize is a powerful tool for optimization and minimizing problems. It is part of the SciPy library, and can be used to find the minimum or maximum of an objective function, subject to a set of constraints. It is important to understand the arguments of the minimize function and the algorithms that are used. It is also important to practice, read tutorials and examples, ask questions, and take online courses. These tips can help you to improve your coding skills related to Python Tutorial: An Introduction to Scipy Minimize Examples.
Video Intro to Scipy Optimization: Minimize Method
Source: CHANNET YOUTUBE TokyoEdtech
### Python Tutorial: An Introduction to Scipy Minimize Examples
#### What is Scipy Minimize?
Scipy Minimize is a library of optimization algorithms in Python. It offers a range of optimization algorithms that can be used to solve various optimization problems.
#### How do I use Scipy Minimize?
To use Scipy Minimize, you should first define the objective function that you want to minimize or maximize. Then, you can use one of the algorithms provided by the library to minimize or maximize the objective function.
#### What are some examples of Scipy Minimize?
Examples of Scipy Minimize include gradient descent, Nelder-Mead, simulated annealing, and particle swarm optimization.
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# If xy = z, what is the value of x ? (1) y = 2z (2) z < -1
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If xy = z, what is the value of x ?
(1) y = 2z
(2) z < -1
_________________
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Posts: 35
Re: If xy = z, what is the value of x ? (1) y = 2z (2) z < -1 [#permalink]
### Show Tags
10 Oct 2017, 03:28
1
Bunuel wrote:
If xy = z, what is the value of x ?
(1) y = 2z
(2) z < -1
xy = z, x = ?
Statement 1:
y = 2z
Substituting, x*2z = z
If z is not equal to 0, we can cancel it and x would be equal to 1/2. But, if z is equal to 0, x could be anything (still satisfying the given information xy = z). Since we do not know if z is equal to 0 or not, this statement is insufficient.
Statement 2:
z < -1
So, xy < -1
This statement does not give any information about x and is therefore insufficient.
Combining statements 1 and 2,
z < -1
So z is not equal to 0. z can be divided on both sides of x*2z = z
Therefore, x = 1/2
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Re: If xy = z, what is the value of x ? (1) y = 2z (2) z < -1 [#permalink]
### Show Tags
10 Oct 2017, 10:31
If xy = z, what is the value of x ?
(1) y = 2z
x(2z) = z
=> 2x (z) = z
But we can't cancel z here as z might be equal to zero .
Not sufficient
(2) z < -1
Not sufficient
Combining 1 and 2 , we get
x = 1/2
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Re: If xy = z, what is the value of x ? (1) y = 2z (2) z < -1 [#permalink]
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11 Oct 2017, 09:43
Given xy = z, what is x?
Question can be rewritten as x = z/y
1) y = 2z --> z/y = 1/2 --> Sufficient
2) z < - 1 --> xy < -1 --> Not Sufficient since we have no information about y.
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# If xy = z, what is the value of x ? (1) y = 2z (2) z < -1
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# How large my primary and secondary fuses should be for this transformer?
#### szabikka
Joined Sep 3, 2014
90
Hello everyone!
I need your help with the following problem. I have to choose primary and secondary fuses for a PCB transformer with the following values: It has one secondary winding with 12V output voltage and it has a power rating of 6 VA. This is all I know about it. I'm planning to use it with 230 V mains (it's rated for that) and want to power a load that draws no more than 300 mA peak current. What kind of fuse values should I use and what is the reason behind those values (safety standards, etc)?
#### k7elp60
Joined Nov 4, 2008
561
Hello everyone!
I need your help with the following problem. I have to choose primary and secondary fuses for a PCB transformer with the following values: It has one secondary winding with 12V output voltage and it has a power rating of 6 VA. This is all I know about it. I'm planning to use it with 230 V mains (it's rated for that) and want to power a load that draws no more than 300 mA peak current. What kind of fuse values should I use and what is the reason behind those values (safety standards, etc)?
Doing the calculations on the maximum current of the secondary, 6VA/12V = 0.5 amps. For the primary 6VA/230v = 0.026 amps or 26mA. Since your peak current on the secondary is 300mA or 0.3A I would recommend only only one fuse, in the primary.. That would be a Littlefuse part number of 312.031. This fuse has a voltage rating of 250V and 0.03125 amps. Fuses normally have a voltage and current rating. The voltage rating ensures the blown fuse will cease the current flow when the current is exceeded. The lowest voltage fuse that I could find is 32 volts. Therefore I cannot recommend a fuse for the secondary.
#### Sensacell
Joined Jun 19, 2012
2,564
I would not recommend a fuse rated so close to the load current.
Fuses are crude devices, cutting it so close will result in nuisance fuse blows.
High voltage fuses can be used on low voltage circuits, but not the other way around.
The fuse knows nothing about the voltage- until it ruptures, then in matters.
Think about the voltage drop across an intact fuse, it's minimal, even when used in a high voltage circuit.
#### Dodgydave
Joined Jun 22, 2012
8,826
I would use a 1Amp fast blow on the secondary side.
#### szabikka
Joined Sep 3, 2014
90
I would use a 1Amp fast blow on the secondary side.
Thank you for your answers! Dodgydave, I have read that slow blow fuses are better in case of transformers, because on start-up there are large currents for very short times, until the magnetic force is built up around the windings. Is this true or I should go with the fast-blow fuse as you recommended?
#### szabikka
Joined Sep 3, 2014
90
I would not recommend a fuse rated so close to the load current.
Fuses are crude devices, cutting it so close will result in nuisance fuse blows.
High voltage fuses can be used on low voltage circuits, but not the other way around.
The fuse knows nothing about the voltage- until it ruptures, then in matters.
Think about the voltage drop across an intact fuse, it's minimal, even when used in a high voltage circuit.
Sensacell, how much headroom is recommended in my example for the fuses?
#### ericgibbs
Joined Jan 29, 2010
9,560
hi sz,
This PDF has some useful information regarding fuse selection.
A simple way to consider the purpose of fuse protecting a project is:
A transformer secondary fuse is to protect the transformer from a continuous over current load, due to a failure in the project being powered.
The primary fuse is to protect the mains supply from a continuous over current due to failure in the transformer.
E
#### Attachments
• 1.1 MB Views: 5
#### Sensacell
Joined Jun 19, 2012
2,564
Sensacell, how much headroom is recommended in my example for the fuses?
Read the guidelines attached to Post #7, this will illuminate the complexity of the answer.
Throwing out a rule of thumb will give you a false sense of knowledge of a surprisingly complex subject.
#### k7elp60
Joined Nov 4, 2008
561
opinions vary
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# Thermodynamic system
Article Id: WHEBN0000425850
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Title: Thermodynamic system Author: World Heritage Encyclopedia Language: English Subject: Collection: Thermodynamic Systems Publisher: World Heritage Encyclopedia Publication Date:
### Thermodynamic system
A thermodynamic system is the content of a macroscopic volume in space, along with its walls and surroundings; it undergoes thermodynamic processes according to the principles of thermodynamics. A physical system qualifies as a thermodynamic system only if it can be adequately described by thermodynamic variables such as temperature, entropy, internal energy and pressure.
The thermodynamic state of a thermodynamic system is its internal state as specified by its state variables. A thermodynamic account also requires a special kind of function called a state function. For example, if the state variables are internal energy, volume and mole amounts, the needed further state function is entropy. These quantities are inter-related by one or more functional relationships called equations of state. Thermodynamics defines the restrictions on the possible equations of state imposed by the laws of thermodynamics through that further function of state.
The system is delimited by walls or boundaries, either actual or notional, across which conserved (such as matter and energy) or unconserved (such as entropy) quantities can pass into and out of the system. The space outside the thermodynamic system is known as the surroundings, a reservoir, or the environment. The properties of the walls determine what transfers can occur. A wall that allows transfer of a quantity is said to be permeable to it, and a thermodynamic system is classified by the permeabilities of its several walls. A transfer between system and surroundings can arise by contact, such as conduction of heat, or by long-range forces such as an electric field in the surroundings.
Types of transfers permitted by types of wall
type of wall type of transfer
Mass and energy Work Heat
permeable to matter
permeable to energy but impermeable to matter
isolating
A system with walls that prevent all transfers is said to be isolated. This is an idealized conception, because in practice some transfer is always possible, for example by gravitational forces. It is an axiom of thermodynamics that an isolated system eventually reaches internal thermodynamic equilibrium, when its state no longer changes with time.
According to the permeabilities of its walls, a system that is not isolated can be in thermodynamic equilibrium with its surroundings, or else may be in a state that is constant or precisely cyclically changing in time - a steady state that is far from equilibrium. Classical thermodynamics considers only states of thermodynamic systems in equilibrium that are either constant or precisely cycling in time.
The walls of a closed system allow transfer of energy as heat and as work, but not of matter, between it and its surroundings. The walls of an open system allow transfer both of matter and of energy.[1][2][3][4][5][6][7] This scheme of definition of terms is not uniformly used, though it is convenient for some purposes. In particular, some writers use 'closed system' where 'isolated system' is here used.[8][9]
In 1824 Sadi Carnot described a thermodynamic system as the working substance (such as the volume of steam) of any heat engine under study. The very existence of such thermodynamic systems may be considered a fundamental postulate of equilibrium thermodynamics, though it is not listed as a numbered law.[10][11] According to Bailyn, the commonly rehearsed statement of the zeroth law of thermodynamics is a consequence of this fundamental postulate.[12]
In equilibrium thermodynamics the state variables do not include fluxes because in a state of thermodynamic equilibrium all fluxes have zero values by definition. Equilibrium thermodynamic processes may of course involve fluxes but these must have ceased by the time a thermodynamic process or operation is complete bringing a system to its eventual thermodynamic state. Non-equilibrium thermodynamics allows its state variables to include non-zero fluxes, that describe transfers of matter or energy or entropy between a system and its surroundings.[13]
## Contents
• Overview 1
• History 2
• Walls 3
• Surroundings 4
• Open system 5
• Flow process 5.1
• Selective transfer of matter 5.2
• Closed system 6
• Isolated system 7
• Mechanically isolated system 8
• Systems in equilibrium 9
• References 11
## Overview
Thermodynamics describes the macroscopic physics of matter and energy, especially including heat transfer, by using the concept of the thermodynamic system, a region of the universe that is under study, specified by thermodynamic state variables, together with the kinds of transfer that may occur between it and its surroundings, as determined by the physical properties of the walls of the system.
An example system is the system of hot liquid water and solid table salt in a sealed, insulated test tube held in a vacuum (the surroundings). The test tube constantly loses heat in the form of black-body radiation, but the heat loss progresses very slowly. If there is another process going on in the test tube, for example the dissolution of the salt crystals, it probably occurs so quickly that any heat lost to the test tube during that time can be neglected. Thermodynamics in general does not measure time, but it does sometimes accept limitations on the time frame of a process.
## History
The first to create the concept of a thermodynamic system was the French physicist Sadi Carnot whose 1824 Reflections on the Motive Power of Fire studied what he called the working substance, e.g., typically a body of water vapor, in steam engines, in regards to the system's ability to do work when heat is applied to it. The working substance could be put in contact with either a heat reservoir (a boiler), a cold reservoir (a stream of cold water), or a piston (to which the working body could do work by pushing on it). In 1850, the German physicist Rudolf Clausius generalized this picture to include the concept of the surroundings, and began referring to the system as a "working body." In his 1850 manuscript On the Motive Power of Fire, Clausius wrote:
The article Carnot heat engine shows the original piston-and-cylinder diagram used by Carnot in discussing his ideal engine; below, we see the Carnot engine as is typically modeled in current use:
Carnot engine diagram (modern) - where heat flows from a high temperature TH furnace through the fluid of the "working body" (working substance) and into the cold sink TC, thus forcing the working substance to do mechanical work W on the surroundings, via cycles of contractions and expansions.
In the diagram shown, the "working body" (system), a term introduced by Clausius in 1850, can be any fluid or vapor body through which heat Q can be introduced or transmitted through to produce work. In 1824, Sadi Carnot, in his famous paper Reflections on the Motive Power of Fire, had postulated that the fluid body could be any substance capable of expansion, such as vapor of water, vapor of alcohol, vapor of mercury, a permanent gas, or air, etc. Though, in these early years, engines came in a number of configurations, typically QH was supplied by a boiler, wherein water boiled over a furnace; QC was typically a stream of cold flowing water in the form of a condenser located on a separate part of the engine. The output work W was the movement of the piston as it turned a crank-arm, which typically turned a pulley to lift water out of flooded salt mines. Carnot defined work as "weight lifted through a height."
## Walls
A system is enclosed by walls that bound it and connect it to its surroundings.[14][15][16][17][18][19] Often a wall restricts passage across it by some form of matter or energy, making the connection indirect. Sometimes a wall is no more than an imaginary two-dimensional closed surface through which the connection to the surroundings is direct. Topologically, it is often considered nearly or piecewise smoothly homeomorphic with a two-sphere (ordinary sphere like a surface that forms the boundary of a ball in three dimensions), because a system is often considered simply connected.
A wall can be fixed (e.g. a constant volume reactor) or moveable (e.g. a piston). For example, in a reciprocating engine, a fixed wall means the piston is locked at its position; then, a constant volume process may occur. In that same engine, a piston may be unlocked and allowed to move in and out. Ideally, a wall may be declared adiabatic, diathermal, impermeable, permeable, or semi-permeable. Actual physical materials that provide walls with such idealized properties are not always readily available.
Anything that passes across the boundary and effects a change in the contents of the system must be accounted for in an appropriate balance equation. The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in 1900; it can be a body of steam or air in a steam engine, such as Sadi Carnot defined in 1824. It could also be just one nuclide (i.e. a system of quarks) as hypothesized in quantum thermodynamics.
## Surroundings
The system is the part of the universe being studied, while the surroundings is the remainder of the universe that lies outside the boundaries of the system. It is also known as the environment, and the reservoir. Depending on the type of system, it may interact with the system by exchanging mass, energy (including heat and work), momentum, electric charge, or other conserved properties. The environment is ignored in analysis of the system, except in regards to these interactions.
## Open system
Generic open system scheme. Exchanges of matter or energy with system's surroundings are represented by input and output flows.
In an open system, matter may flow in and out of some segments of the system boundaries. There may be other segments of the system boundaries that pass heat or work but not matter. Respective account is kept of the transfers of energy across those and any other several boundary segments.
### Flow process
During steady, continuous operation, an energy balance applied to an open system equates shaft work performed by the system to heat added plus net enthalpy added.
The region of space enclosed by open system boundaries is usually called a control volume. It may or may not correspond to physical walls. It is convenient to define the shape of the control volume so that all flow of matter, in or out, occurs perpendicular to its surface. One may consider a process in which the matter flowing into and out of the system is chemically homogeneous.[20] Then the inflowing matter performs work as if it were driving a piston of fluid into the system. Also, the system performs work as if it were driving out a piston of fluid. Through the system walls that do not pass matter, heat (δQ) and work (δW) transfers may be defined, including shaft work.
Classical thermodynamics considers processes for a system that is initially and finally in its own internal state of thermodynamic equilibrium, with no flow. This is feasible also under some restrictions, if the system is a mass of fluid flowing at a uniform rate. Then for many purposes a process, called a flow process, may be considered in accord with classical thermodynamics as if the classical rule of no flow were effective.[21] For the present introductory account, it is supposed that the kinetic energy of flow, and the potential energy of elevation in the gravity field, do not change, and that the walls, other than the matter inlet and outlet, are rigid and motionless.
Under these conditions, the first law of thermodynamics for a flow process states: the increase in the internal energy of a system is equal to the amount of energy added to the system by matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system. Under these conditions, the first law for a flow process is written:
\mathrm{d}U=\mathrm{d}U_{in}+\delta Q-\mathrm{d}U_{out}-\delta W\,
where Uin and Uout respectively denote the average internal energy entering and leaving the system with the flowing matter.
There are then two types of work performed: 'flow work' described above, which is performed on the fluid in the control volume (this is also often called 'PV work'), and 'shaft work', which may be performed by the fluid in the control volume on some mechanical device with a shaft. These two types of work are expressed in the equation:
\delta W=\mathrm{d}(P_{out}V_{out})-\mathrm{d}(P_{in}V_{in})+\delta W_{shaft}\,
Substitution into the equation above for the control volume cv yields:
\mathrm{d}U_{cv}=\mathrm{d}U_{in}+\mathrm{d}(P_{in}V_{in}) - \mathrm{d}U_{out}-\mathrm{d}(P_{out}V_{out})+\delta Q-\delta W_{shaft}\,
The definition of enthalpy, H = U + PV, permits us to use this thermodynamic potential to account jointly for internal energy U and PV work in fluids for a flow process:
\mathrm{d}U_{cv}=\mathrm{d}H_{in}-\mathrm{d}H_{out}+\delta Q-\delta W_{shaft}\,
During steady-state operation of a device (see turbine, pump, and engine), any system property within the control volume is independent of time. Therefore, the internal energy of the system enclosed by the control volume remains constant, which implies that dUcv in the expression above may be set equal to zero. This yields a useful expression for the power generation or requirement for these devices with chemical homogeneity in the absence of chemical reactions:
\frac{\delta W_{shaft}}{\mathrm{d}t}=\frac{\mathrm{d}H_{in}}{\mathrm{d}t}- \frac{\mathrm{d}H_{out}}{\mathrm{d}t}+\frac{\delta Q}{\mathrm{d}t} \,
This expression is described by the diagram above.
### Selective transfer of matter
For a thermodynamic process, the precise physical properties of the walls and surroundings of the system are important, because they determine the possible processes.
An open system has one or several walls that allow transfer of matter. To account for the internal energy of the open system, this requires energy transfer terms in addition to those for heat and work. It also leads to the idea of the chemical potential.
A wall selectively permeable only to a pure substance can put the system in diffusive contact with a reservoir of that pure substance in the surroundings. Then a process is possible in which that pure substance is transferred between system and surroundings. Also, across that wall a contact equilibrium with respect to that substance is possible. By suitable thermodynamic operations, the pure substance reservoir can be dealt with as a closed system. Its internal energy and its entropy can be determined as functions of its temperature, pressure, and mole number.
A thermodynamic operation can render impermeable to matter all system walls other than the contact equilibrium wall for that substance. This allows the definition of an intensive state variable, with respect to a reference state of the surroundings, for that substance. The intensive variable is called the chemical potential; for component substance i it is usually denoted μi. The corresponding extensive variable can be the number of moles Ni of the component substance in the system.
For a contact equilibrium across a wall permeable to a substance, the chemical potentials of the substance must be same on either side of the wall. This is part of the nature of thermodynamic equilibrium, and may be regarded as related to the zeroth law of thermodynamics.[22]
## Closed system
In a closed system, no mass may be transferred in or out of the system boundaries. The system always contains the same amount of matter, but heat and work can be exchanged across the boundary of the system. Whether a system can exchange heat, work, or both is dependent on the property of its boundary.
One example is fluid being compressed by a piston in a cylinder. Another example of a closed system is a bomb calorimeter, a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Electrical energy travels across the boundary to produce a spark between the electrodes and initiates combustion. Heat transfer occurs across the boundary after combustion but no mass transfer takes place either way.
Beginning with the first law of thermodynamics for an open system, this is expressed as:
\Delta U=Q-W+m_{i}(h+\frac{1}{2}v^2+gz)_{i}-m_{e}(h+\frac{1}{2}v^2+gz)_{e}
where U is internal energy, Q is the heat added to the system, W is the work done by the system, and since no mass is transferred in or out of the system, both expressions involving mass flow are zero and the first law of thermodynamics for a closed system is derived. The first law of thermodynamics for a closed system states that the increase of internal energy of the system equals the amount of heat added to the system minus the work done by the system. For infinitesimal changes the first law for closed systems is stated by:
\mathrm d U= \delta Q -\delta W.
If the work is due to a volume expansion by dV at a pressure P than:
\delta W = P\mathrm d V.
For a homogeneous system, in which only reversible processes can take place, the second law of thermodynamics reads:
\delta Q = T \mathrm d S
where T is the absolute temperature and S is the entropy of the system. With these relations the fundamental thermodynamic relationship, used to compute changes in internal energy, is expressed as:
\mathrm d U=T\mathrm d S-P\mathrm d V.
For a simple system, with only one type of particle (atom or molecule), a closed system amounts to a constant number of particles. However, for systems undergoing a chemical reaction, there may be all sorts of molecules being generated and destroyed by the reaction process. In this case, the fact that the system is closed is expressed by stating that the total number of each elemental atom is conserved, no matter what kind of molecule it may be a part of. Mathematically:
\sum_{j=1}^m a_{ij}N_j=b_i^0
where Nj is the number of j-type molecules, aij is the number of atoms of element i in molecule j and bi0 is the total number of atoms of element i in the system, which remains constant, since the system is closed. There is one such equation for each element in the system.
## Isolated system
An isolated system is more restrictive than a closed system as it does not interact with its surroundings in any way. Mass and energy remains constant within the system, and no energy or mass transfer takes place across the boundary. As time passes in an isolated system, internal differences in the system tend to even out and pressures and temperatures tend to equalize, as do density differences. A system in which all equalizing processes have gone practically to completion is in a state of thermodynamic equilibrium.
Truly isolated physical systems do not exist in reality (except perhaps for the universe as a whole), because, for example, there is always gravity between a system with mass and masses elsewhere.[23][24][25][26][27] However, real systems may behave nearly as an isolated system for finite (possibly very long) times. The concept of an isolated system can serve as a useful model approximating many real-world situations. It is an acceptable idealization used in constructing mathematical models of certain natural phenomena.
In the attempt to justify the postulate of entropy increase in the second law of thermodynamics, Boltzmann’s H-theorem used equations, which assumed that a system (for example, a gas) was isolated. That is all the mechanical degrees of freedom could be specified, treating the walls simply as mirror boundary conditions. This inevitably led to Loschmidt's paradox. However, if the stochastic behavior of the molecules in actual walls is considered, along with the randomizing effect of the ambient, background thermal radiation, Boltzmann’s assumption of molecular chaos can be justified.
The second law of thermodynamics for isolated systems states that the entropy of an isolated system not in equilibrium tends to increase over time, approaching maximum value at equilibrium. Overall, in an isolated system, the internal energy is constant and the entropy can never decrease. A closed system's entropy can decrease e.g. when heat is extracted from the system.
It is important to note that isolated systems are not equivalent to closed systems. Closed systems cannot exchange matter with the surroundings, but can exchange energy. Isolated systems can exchange neither matter nor energy with their surroundings, and as such are only theoretical and do not exist in reality (except, possibly, the entire universe).
It is worth noting that 'closed system' is often used in thermodynamics discussions when 'isolated system' would be correct - i.e. there is an assumption that energy does not enter or leave the system.
## Mechanically isolated system
A mechanically isolated system can exchange no work energy with its environment, but may exchange heat energy and/or mass with its environment. The internal energy of a mechanically isolated system may therefore change due to the exchange of heat energy and mass. For a simple system, mechanical isolation is equivalent to constant volume and any process which occurs in such a simple system is said to be isochoric.
## Systems in equilibrium
At thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than systems not in equilibrium. In some cases, when analyzing a thermodynamic process, one can assume that each intermediate state in the process is at equilibrium. This considerably simplifies the analysis.
In isolated systems it is consistently observed that as time goes on internal rearrangements diminish and stable conditions are approached. Pressures and temperatures tend to equalize, and matter arranges itself into one or a few relatively homogeneous phases. A system in which all processes of change have gone practically to completion is considered in a state of thermodynamic equilibrium. The thermodynamic properties of a system in equilibrium are unchanging in time. Equilibrium system states are much easier to describe in a deterministic manner than non-equilibrium states.
For a process to be reversible, each step in the process must be reversible. For a step in a process to be reversible, the system must be in equilibrium throughout the step. That ideal cannot be accomplished in practice because no step can be taken without perturbing the system from equilibrium, but the ideal can be approached by making changes slowly.
## References
1. ^ Prigogine, I., Defay, R. (1950/1954). Chemical Thermodynamics, Longmans, Green & Co, London, p. 66.
2. ^ Tisza, L. (1966). Generalized Thermodynamics, M.I.T Press, Cambridge MA, pp. 112–113.
3. ^ Guggenheim, E.A. (1949/1967). Thermodynamics. An Advanced Treatment for Chemists and Physicists, (1st edition 1949) 5th edition 1967, North-Holland, Amsterdam, p. 14.
4. ^ Münster, A. (1970). Classical Thermodynamics, translated by E.S. Halberstadt, Wiley–Interscience, London, pp. 6–7.
5. ^ Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of Thermodynamics, pages 1–97 of volume 1, ed. W. Jost, of Physical Chemistry. An Advanced Treatise, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081, p. 3.
6. ^ Tschoegl, N.W. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, ISBN 0-444-50426-5, p. 5.
7. ^ Silbey, R.J., Alberty, R.A., Bawendi, M.G. (1955/2005). Physical Chemistry, fourth edition, Wiley, Hoboken NJ, p. 4.
8. ^ Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, (1st edition 1960) 2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8, p. 17.
9. ^ ter Haar, D., Wergeland, H. (1966). Elements of Thermodynamics, Addison-Wesley Publishing, Reading MA, p. 43.
10. ^ Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3, p. 20.
11. ^ Tisza, L. (1966). Generalized Thermodynamics, M.I.T Press, Cambridge MA, p. 119.
12. ^ Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3, p. 22.
13. ^ Eu, B.C. (2002). Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics, Kluwer Academic Publishers, Dordrecht, ISBN 1-4020-0788-4.
14. ^ Born, M. (1949). Natural Philosophy of Cause and Chance, Oxford University Press, London, p.44
15. ^ Tisza, L. (1966), pp. 109, 112.
16. ^ Haase, R. (1971), p. 7.
17. ^ Adkins, C.J. (1968/1975), p. 4
18. ^ Callen, H.B. (1960/1985), pp. 15, 17.
19. ^ Tschoegl, N.W. (2000), p. 5.
20. ^ Shavit, A., Gutfinger, C. (1995). Thermodynamics. From Concepts to Applications, Prentice Hall, London, ISBN 0-13-288267-1, Chapter 6.
21. ^ Adkins, C.J. (1968/1983). Equilibrium Thermodynamics, third edition, Cambridge University Press, Cambridge UK, ISBN 0-521-25445-0, pp. 46–47.
22. ^ Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3, pp. 19–23.
23. ^ I.M.Kolesnikov; V.A.Vinokurov; S.I.Kolesnikov (2001). Thermodynamics of Spontaneous and Non-Spontaneous Processes. Nova science Publishers. p. 136.
24. ^ "A System and Its Surroundings". ChemWiki. University of California - Davis. Retrieved May 2012.
25. ^ "Hyperphysics". The Department of Physics and Astronomy of Georgia State University. Retrieved May 2012.
26. ^ Bryan Sanctuary. "Open, Closed and Isolated Systems in Physical Chemistry,". Foundations of Quantum Mechanics and Physical Chemistry. McGill University (Montreal). Retrieved May 2012.
27. ^ Material and Energy Balances for Engineers and Environmentalists (PDF). Imperial College Press. p. 7. Retrieved May 2012.
• Abbott, M.M.; van Hess, H.G. (1989). Thermodynamics with Chemical Applications (2nd ed.). McGraw Hill.
• Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, (1st edition 1960) 2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8.
• Halliday, David; Resnick, Robert; Walker, Jearl (2008). Fundamentals of Physics (8th ed.). Wiley.
• Moran, Michael J.; Shapiro, Howard N. (2008). Fundamentals of Engineering Thermodynamics (6th ed.). Wiley.
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# In the rectangular coordinate system, are the points (r,s)
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In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?
(1) r+s=1
(2) u=1-r and v=1-s
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27 Aug 2007, 11:18
[quote="Vlad77"]In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?
(1) r+s=1
(2) u=1-r and v=1-s[/quote]
Distance from origin is sqrt(r^2+s^2) and sqrt(u^2+v^2) respectively.
St1: Insuff. Says nothing about u & v.
St2: From
u^2+v^2 = s^2+r^2 +2 -2(r+s)
Insuff. We do not know r+s? If r+s >1, then (u,v) closer. r+s<1, (r,s) closer.
St1+St2: Sufficient. Equidistant points.
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27 Aug 2007, 14:58
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?
(1) r+s=1
(2) u=1-r and v=1-s
Use the distance formula D=sqrt of (x1-x2)^2+(y1-y2)^2
Use the D formula for both (r,s) and (u,v) for x2 and y2 for both equations use 0,0.
This gives you r^2+s^2=u^2+v^2
now looking at the stmnts. 1 is clearly not sufficient
2: doesnt give us everything we need either.
S1 and S2 give us enough to solve this out.
Ans C
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27 Aug 2007, 22:35
Thanks
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15 Sep 2007, 05:57
S1=> 1 - s = r
1 - r = s
From S2 => (u, v) = (1-r, 1-s)
Combining:
(u, v) = (1-r, 1-s)
(u,v) = (s, r)
(r, s) and (s, r) [(u, v)] are equidistance from the origin.
C
Re: Another DS question [#permalink] 15 Sep 2007, 05:57
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# Calculating line with the longest distance inside polygon in QGIS
I want to calculate the "diameter" of polygons in QGIS. The "diameter" is defined as the distance between the two most distant points of the polygon.
I couldn't find a fitting solution in the Field Calculator.
Maybe you have some ideas?
• Conceptually thinking: get the smallest possible bounding box (tool), then you should be able to calculate the length of the diagonal using area & perimeter.
– Erik
Commented May 13, 2020 at 13:36
• Please, do not forget about "What should I do when someone answers my question?" Commented Jul 24, 2023 at 9:37
You can use PyQGIS to measure the distances between all vertices of each polygon and find max:
``````import itertools
layer = iface.activeLayer() #Click layer in tree
for feat in layer.getFeatures():
verts = [v for v in feat.geometry().vertices()] #List all vertices
maxdistance = max([p1.distance(p2) for p1,p2 in itertools.combinations(verts, 2)]) #Find max distance for all combinations of vertices (https://stackoverflow.com/questions/464864/how-to-get-all-possible-combinations-of-a-list-s-elements)
print('Polygon: {0}, max distance: {1}'.format(feat.id(), round(maxdistance,0))) #Print results
``````
To save max distances in a field:
``````import itertools
layer = iface.activeLayer() #Click layer in tree
field_to_save_maxdistance_in = 'maxdist' #Change maxdist to the name of your field
fields = layer.fields()
fx = fields.indexFromName(field_to_save_maxdistance_in)
with edit(layer):
for feat in layer.getFeatures():
verts = [v for v in feat.geometry().convexHull().vertices()] #List all vertices
maxdistance = max([p1.distance(p2) for p1,p2 in itertools.combinations(verts, 2)]) #Find max distance for all combinations of vertices
layer.changeAttributeValue(feat.id(), fx, maxdistance)
``````
You can also create a line layer:
``````import itertools
layer = iface.activeLayer() #Click layer in tree
#Create line layer
vl = QgsVectorLayer("LineString?crs={}&index=yes".format(layer.crs().authid()), "myLayer", "memory")
provider = vl.dataProvider()
#For each polygon find the two points most far apart
for feat in layer.getFeatures():
all_points = []
verts = [v for v in feat.geometry().vertices()] #List all vertices
for p1,p2 in itertools.combinations(verts, 2):
all_points.append([p1,p2])
#Create a line feature
pointpair_most_far_apart = max(all_points, key=lambda x: x[0].distance(x[1]))
gLine = QgsGeometry.fromPolyline(pointpair_most_far_apart)
f = QgsFeature()
f.setGeometry(gLine)
``````
• This seems like exactly what I want to do! Since I am not familiar with Python and pyqgis: is there a way to save the maximum distance that the console is showing me as a column in my layer? So I can continue using it for my following calculations. Commented May 13, 2020 at 13:55
• Somehow the newest code doesn't work. I get a "SyntaxError: invalid syntax" error or QGIS just shuts down while trying to run it. The first one you posted without saving it to my layer worked perfectly. Commented May 13, 2020 at 14:23
• Added it as a real type. But now it somehow worked. QGIS shut down again and when I restarted it, the column was there and the results seem correct. Weird indeed! But anyways, thank you! This has helped me a lot already! Commented May 13, 2020 at 14:34
Bear in mind that someone correctly pointed out very soon in comments that I had misread the question. My answer gives the diameter of the minimal circle but this does not always correspond to the longest distance between vertices in a polygon. As soon as more than two vertices touch the circle or if the vertices defining the circle are adjacent, the values can differ. I left it there as it provides an answer for a similar problem but even I agree it should not be the accepted answer.
It is possible to do this with simple expressions in the Field Calculator (at least in QGIS 3.12.x). Take for example these two polygons. The symbology shows four things (using the Geometry Generator, for explanation purposes):
• Red outline of the true polygon
• Semi-transparent orange circle resulting from the `minimal_circle()` function
• Blue point resulting from the `centroid()` function of the minimal circle
• White point resulting from the `point_n()` function of the minimal circle's first vertex
So to get the diameter of the minimal circle containing the polygon, go to the field calculator and use this expression in a new decimal field:
``````distance(centroid(minimal_circle(\$geometry)), point_n(minimal_circle(\$geometry), 1)) * 2
``````
This will calculate the distance between the centroid and the first vertex along the circle (the radius), then multiply it by two.
• @Jan-PieterVanParys There we go. Expressions have received a LOT of love since then. Commented May 13, 2020 at 15:37
• @Jan-PieterVanParys You can go with the current LTR, 3.10.5. It should be quite stable although you will probably need a little bit of adjusting to the new UI and ways of doing things. Commented May 13, 2020 at 15:41
• What about an Equilateral triangle? I think the diameter of the circle is bigger than the longest edge of the triangle... Your solution works only for polygons for which the smallest circle touches only two vertices. Commented May 25, 2020 at 11:54
• @Legisey Yes, triangles don't work well. That's something to keep in mind, but I've observed that they aren't very common in the datasets I've had to use. It could be possible to aggregate the distances from the centroid to each vertex then build a minimal circle from the two largest value points. I'll try that out. edit Also I think it was maybe a problem with the question as asked as the diameter (minimal circle) can often be different from the distance between the two most distant vertices. Commented May 25, 2020 at 12:58
• @GabrielC. so you're not looking for the "the distance between the two most distant points of the polygon" as stated in the question? Are you looking for the diameter of the smallest circle that fully contains the shape? It's not the same thing, even though in some cases (like the ones of this answer) it will be the same. It's not only in triangles that there is a difference, it is also the case with most shapes that have more than two vertices that touches the circle. I think this is not a correct answer to the question. So either you asked the wrong question, or accepted the wrong answer. Commented May 26, 2020 at 8:34
Let's assume there is a polygon layer 'Layer_A' (blue) with its corresponding attribute table accordingly, see the image below.
Step 1. Apply the "Polygons to lines" geoalgorithm
Step 2. Proceed with "Points along geometry". Mind that the distance affects the quality of the final result and the efficiency of the Virtual Layer in Step 3.
Step 3. By means of a "Virtual Layer" through `Layer > Add Layer > Add/Edit Virtual Layer...` use this query
``````SELECT p1.id,
setsrid(make_line(p1.geometry, p2.geometry), 'put your srid here'),
max(st_length(make_line(p1.geometry, p2.geometry))) AS length
FROM "Points" AS p1
JOIN "Points" AS p2 ON p1.id = p2.id
WHERE NOT st_equals(p1.geometry, p2.geometry)
GROUP BY p1.id
``````
P.S. if you are interested in the longest distances between vertices, then extract vertices from the polygon via "Extract vertices" and go directly to Step 3.
• I just tried this and unfortunately QGIS can't finish the third step. It runs for a long time already, but never ends. Commented May 13, 2020 at 15:10
• How many points did you generate ? How many polygons do you have ? Commented May 13, 2020 at 18:01
• I have more than 400 polygons and I've got 371939 points. Maybe those are too many? Commented May 23, 2020 at 11:51
• yes, you are right Commented Jun 26, 2020 at 9:35
If you have your data in PostGIS you can use these functions:
1. `ST_MinimumBoundingCircle()` : https://postgis.net/docs/ST_MinimumBoundingCircle.html
Returns the smallest circle polygon that can fully contain a geometry.
2. `ST_MinimumBoundingRadius()` : https://postgis.net/docs/ST_MinimumBoundingRadius.html
Returns a record containing the center point and radius of the smallest circle that can fully contain a geometry.
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Contents 1 Anthropology 1.1 Usage and terms 1.2 Other 2 In mathematics 2.1 In numeral systems 2.1.1 Decimal system 2.1.2 Roman numerals 2.1.3 Positional numeral systems other than decimal 3 List of basic calculations 4 In science 4.1 Astronomy 5 In religion and philosophy 6 In money 7 In music 8 In sports and games 9 In technology 10 In other fields 11 See also 12 References 13 External links
Anthropology Usage and terms A collection of ten items (most often ten years) is called a decade. The ordinal adjective is decimal; the distributive adjective is denary. Increasing a quantity by one order of magnitude is most widely understood to mean multiplying the quantity by ten. To reduce something by one tenth is to decimate. (In ancient Rome, the killing of one in ten soldiers in a cohort was the punishment for cowardice or mutiny; or, one-tenth of the able-bodied men in a village as a form of retribution, thus causing a labor shortage and threat of starvation in agrarian societies.) A theoretical highest number in topics that require a rating ("a mark out of ten"), by contrast having 0 or 1 as the lowest number, and 5 being average. Other The number of kingdoms in Five Dynasties and Ten Kingdoms period. The house number of 10 Downing Street. The number of Provinces in Canada. The designation of United States Interstate 10, a freeway that runs from California to Florida. Number of dots in a tetractys. The number of the French department Aube. The number of regions in Ghana. The state number of Virginia. The number in tarot decks that corresponds to either Chance, Fortune, or the Wheel of Fortune, depending on the deck variant.
In mathematics Ten is a composite number, its proper divisors being 1, 2 and 5. Ten is the smallest noncototient, a number that cannot be expressed as the difference between any integer and the total number of coprimes below it.[1] Ten is the second discrete semiprime (2 × 5) and the second member of the (2 × q) discrete semiprime family. Ten has an aliquot sum σ(n) of 8 and is accordingly the first discrete semiprime to be in deficit. All subsequent discrete semiprimes are in deficit. The aliquot sequence for 10 comprises five members (10,8,7,1,0) with this number being the second composite member of the 7-aliquot tree. Ten is the smallest semiprime that is the sum of all the distinct prime numbers from its lower factor through its higher factor (10 = 2 + 3 + 5 = 2 . 5) Only three other small semiprimes (39, 155, and 371) share this attribute. Ten is a semi-meandric number. Ten is the sum of the first three prime numbers, of the four first positive integers (1 + 2 + 3 + 4), of the square of the two first odd numbers and also of the first four factorials (0! + 1! + 2! + 3!). Ten is the eighth Perrin number, preceded in the sequence by 5, 5, 7. A polygon with ten sides is a decagon, and 10 is a decagonal number.[2] Because 10 is the product of a power of 2 (namely 21) with nothing but distinct Fermat primes (specifically 5), a regular decagon is a constructible polygon. Ten is also a triangular number, a centered triangular number,[3] and a tetrahedral number.[4] Ten is the number of n queens problem solutions for n = 5. Ten is the smallest number whose status as a possible friendly number is unknown. Ten factorial seconds is exactly equal to 6 weeks. In numeral systems Decimal system Main article: Decimal As is the case for any base in its system, ten is the first two-digit number in decimal and thus the lowest number where the position of a numeral affects its value. Any integer written in the decimal system can be multiplied by ten by adding a zero to the end (e.g. 855 × 10 = 8550). Roman numerals The Roman numeral for ten is X (which looks like two Vs [the Roman numeral for 5] put together); it is thought that the V for five is derived from an open hand (five digits displayed), and X for ten from both hands. Incidentally, the Chinese word numeral for ten, is also a cross: 十. Positional numeral systems other than decimal The digit '1' followed by '0' is how the value of p is written in base p. (E.g. 16 in hexadecimal is 10.) Representation of 10 in other bases Base Numeral system Number 1 unary ********** 2 binary 1010 3 ternary 101 4 quaternary 22 5 quinary 20 6 senary 14 7 septenary 13 8 octal 12 9 novenary 11 10 decimal 10 12 duodecimal X 16 hexadecimal A
List of basic calculations Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 25 50 100 1000 10 × x 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 250 500 1000 10000 Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 10 ÷ x 10 5 3.3 2.5 2 1.6 1.428571 1.25 1.1 1 0.90 0.83 0.769230 0.714285 0.6 x ÷ 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Exponentiation 1 2 3 4 5 6 7 8 9 10 10x 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 x10 1 1024 59049 1048576 9765625 60466176 282475249 1073741824 3486784401 10000000000
In science The SI prefix for 10 is "deca-". The meaning "10" is part of the following terms: decapoda, an order of crustaceans with ten feet decane, a hydrocarbon with 10 carbon atoms Also, the number 10 plays a role in the following: The atomic number of neon. The number of hydrogen atoms in butane, a hydrocarbon. The number of spacetime dimensions in some superstring theories. The metric system is based on the number 10, so converting units is done by adding or removing zeros (e.g. 1 centimeter = 10 millimeters, 1 decimeter = 10 centimeters, 1 meter = 100 centimeters, 1 dekameter = 10 meters, 1 kilometer = 1,000 meters). Astronomy The New General Catalogue object NGC 10, a magnitude 12.5 spiral galaxy in the constellation Sculptor. Messier object M10, a magnitude 6.4 globular cluster in the constellation Ophiuchus.
In religion and philosophy The tetractys References in the Bible, Judaism and Christianity: The Ten Commandments of Exodus[5] and Deuteronomy[6] are considered a cornerstone of Judaism and Christianity. People traditionally tithed one-tenth of their produce. The practice of tithing is still common in Christian churches today, though it is disputed in some circles as to whether or not it is required of Christians. In Deuteronomy 26:12, the Torah commands Jews to give one-tenth of their produce to the poor (Maaser Ani). From this verse and from an earlier verse (Deut. 14:22) there derives a practice for Jews to give one-tenth of all earnings to the poor.[7] Ten Plagues were inflicted on Egypt in Exodus 7-12. Jews observe the annual Ten Days of Repentance beginning on Rosh Hashanah and ending on Yom Kippur. In Jewish liturgy, Ten Martyrs are singled out as a group. There are said to be Ten Lost Tribes of Israel (those other than Judah and Benjamin). There are Ten Sephirot in the Kabbalistic Tree of Life. In Judaism, ten men are the required quorum, called a minyan, for prayer services. Interpretations of Genesis in Talmudic and Midrashic teachings suggest that on the first day, God drew forth ten primal elements from the abyss in order to construct all of Creation: Heaven (or Fire), Earth, Chaos, Void, Light, Darkness, Wind (or Spirit), Water, Day, and Night. See also Bereshit (parsha). Jesus tells the Parable of the Ten Virgins in Matthew 25:1-13. In Pythagoreanism, the number 10 played an important role and was symbolized by the tetractys. In Hinduism, Lord Vishnu appeared on the earth in 10 incarnations.
In money Most countries issue coins and bills with a denomination of 10 (See e.g. 10 dollar note). Of these, the U.S. dime, with the value of ten cents, or one tenth of a dollar, derives its name from the meaning "one-tenth" − see Dime (United States coin)#Denomination history and etymology.
In music The interval of a major tenth is an octave plus a major third. The interval of a minor tenth is an octave plus a minor third. The title of quite a few albums. See Ten (album). "Ten lords a-leaping" is the gift on the tenth day of Christmas in the carol "The Twelve Days of Christmas".
In sports and games Decathlon is a combined event in athletics consisting of ten track and field events. In association football, the number 10 is traditionally worn by the team's advanced playmaker. This use has led to "Number 10" becoming a synonym for the player in that particular role, even if he or she does not wear that number.[8] In auto racing, driving a car at ten-tenths is driving as fast as possible, on the limit. In blackjack, the Ten, Jack, Queen and King are all worth 10 points. In boxing, if the referees counts to 10 whether the boxer is unconscious or not, it will declare a winner by knockout. In most rugby league competitions, the number 10 is worn by one of the two starting props. One exception to this rule is the European Super League, which uses static squad numbering. In rugby union, the starting fly-half wears the 10 shirt. In ten-pin bowling, 10 pins are arranged in a triangular pattern and there are 10 frames per game.
In technology Ten-codes are commonly used on emergency service radio systems. Ten refers to the "meter band" on the radio spectrum between 28 and 29.7 MHz, used by amateur radio. ASCII and Unicode code point for line feed. In MIDI, Channel 10 is reserved for unpitched percussion instruments. In the Rich Text Format specification, all language codes for regional variants of the Spanish language are congruent to 10 mod 256. In macOS, the F10 function key tiles all the windows of the current application and grays the windows of other applications. The IP addresses in the range 10.0.0.0/8 (meaning the interval between 10.0.0.0 and 10.255.255.255) is reserved for use by private networks by RFC 1918.
In other fields 10 playing cards of all four suits Blake Edwards' 1979 movie 10. Series on HBO entitled 1st & Ten which aired between December 1984 and January 1991. Series on ESPN and ESPN2 entitled 1st and 10 which launched on ESPN in October 2003 to 2008 and moved to ESPN2 from 2008 to present. In astrology, Capricorn is the 10th astrological sign of the Zodiac. In Chinese astrology, the 10 Heavenly Stems, refer to a cyclic number system that is used also for time reckoning. A 1977 short documentary film Powers of Ten depicts the relative scale of the Universe in factors of ten (orders of magnitude). CBS has a game show called Power of 10, where the player's prize goes up and down by either the previous or next power of ten. "Ten Chances" is one of the pricing games on The Price is Right. There are ten official inkblots in the Rorschach inkblot test. The traditional Snellen chart uses 10 different letters. Ten is an Australian television network. The Sydney member of the network has the three-letter call-sign TEN and used to broadcast in analogue on VHF Channel 10. Number Ten (also called Ella) is a character in the book series Lorien Legacies. The sixth book, The Fate of Ten, is named after her. The ten-code may be used in law enforcement brevity communications. A Cartoon Network franchise Ben 10, which has a number on its title.
References ^ "Sloane's A005278 : Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01. ^ "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01. ^ "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01. ^ Exodus 20:2-13 ^ Deuteronomy 5:6-17 ^ [1] Archived February 23, 2006, at the Wayback Machine. ^ Khalil Garriot (21 June 2014). "Mystery solved: Why do the best soccer players wear No. 10?". Yahoo. Retrieved 19 May 2015.
External links Wikimedia Commons has media related to 10 (number). Look up ten in Wiktionary, the free dictionary. v t e Integers 0s 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100s 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200s 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300s 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400s 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500s 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600s 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700s 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800s 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900s 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 Retrieved from "https://en.wikipedia.org/w/index.php?title=10&oldid=830149843" Categories: Integers10 (number)Hidden categories: Webarchive template wayback linksArticles with hAudio microformatsArticles including recorded pronunciations (English)Articles containing Chinese-language text
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# Chart Time Frames
Lesson BO105: Stock Chart Time Frames
There are many timeframes offered by charting platforms it can be overwhelming. Sam covers the basics of chart timeframes, recommends specific timeframes to analyse, and gives a list of chart time frame tips.
##### BO105 Lesson – Chart Time Frames Video & Transcript
Welcome to Binary Options 105, Chart Timeframes. This is part of our Binary Options 100 training course which is brought to you by binaryoptions.education. Chart timeframes.
In Binary Options 103, I recommended some charting programs.
This is tradingview.com. At the top-left here, I have the financial instrument, the Euro/USD, and I have the timeframe, which is 15-minute. On this drop-down list, you’ll see I have a number of available timeframes to choose from, anything from one minute to one month.
But what does it mean to have a 15-minute timeframe or an hourly timeframe?
Well, let’s look at this 15-minute timeframe first. It means each one of these candles or bars represents 15 minutes of price data or price movement. So say on the hour, this candle would open; at quarter past the hour, it would close and another candle would open. Half past the hour, this candle would close, another candle would open, and so on. So every 15 minutes, a candle is closing and opening.
If we were to look at an hourly chart, then each one of these candles represents an hour of price data or price movement. So on the hour, a candle would open. The hour following, it would close and another would open. And this just carries on. And in future videos, I will teach you how to read these candle charts to speculate with higher probability where future price is going to be.
With such a selection of chart timeframes to choose from, which timeframe do we use? Well, I think that’s determined by which expiry are we using when we trade binary options. If we’re using a 60-second expiry, then I would strongly suggest using a one-minute timeframe. If we’re using a 15-minute expiry, then it would make sense to use a 15-minute chart timeframe. If we’re using an end-of-day expiry, then perhaps a daily timeframe.
You may ask the question, which expiry should I be using? I will cover that in a future video. But basically, it’s determined by your trading strategy. Some strategies would work better on longer expiries, whereas some may work better on shorter expiries.
Chart Time Frames
Which Expiry to Use? Price Chart Time Frame 60 Seconds 1 Minute 15 Minute 15 Minute 30 Minute 30 Minute End of Day Daily
So I’m going to give you some chart timeframe tips. The first one is zoom out. And to explain this tip, let’s look back at our chart at tradingview.com. So here’s our Euro/USD 15-minute timeframe. If we were currently trading binary options and we had this chart open as it is, it’s quite hard to tell where price is actually going and where it’s been. It looks like price is just moving in a kind of sideways direction. There hasn’t been much change of where price has been over the last 15, 16 hours. The time of day is at the bottom of the chart here.
But you’ll see as we start to zoom out, we soon get a better picture of what is actually happening. OK, so this is the data we were looking at. And price isn’t actually moving in a sideways direction, but it’s steadily moving in an upwards direction.
But it’s not just the overview of price we need when we zoom out, but there could be potential areas in the market such as these lines here which provide potential opportunities to place call and puts and profit.
Now, these lines have been drawn by connecting this high here and this high here and this low here and this low here. And in a future video, I will go into more detail on what these lines are and how they work. But when we were so zoomed into the market, these lows and this high were not even visible.
Another trading tip would be to use a dual monitor system or to have two monitors. This is not essential. One monitor is sufficient for trading. But if we do have two monitors, we can use one for our timeframe and the other for our trading platform, so we don’t have to keep minimizing or maximizing our screens.
Analyze the most popular timeframes. We want to be looking at the timeframes the professionals are using. And these timeframes are the 15-minute, the hourly, the four-hourly, and the daily.
Stick with this course, as I will teach you more about chart timeframes and how to read charts and benefit from them. And then the last trading tip, which is very much my personal opinion. And that is the higher timeframes seem to be less random. They seem to be a bit easier to read and more reliable. I’m going to say higher timeframes. Once again, this is my personal opinion. But anything from hourly upwards.
So thank you for watching another video in this series. Please stay with us on this course, and please check out our website, binaryoptions.education.
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