Answer:
Below...
Explanation:
To find the critical points, we need to find where the gradient of f(x,y) is equal to zero.
∇f(x,y) = (-sin x, sin y)
Setting each component of the gradient equal to zero, we get
-sin x = 0 and sin y = 0
This gives us critical points at (nπ, mπ) for any integers n and m.
Next, we need to find the second partial derivatives of f(x,y) at each critical point.
f_xx = -cos x
f_yy = cos y
f_xy = 0
At a critical point (nπ, mπ), we have f_xx = (-1)^n and f_yy = (-1)^m.
If f_xx and f_yy have the same sign, then the critical point is a local extremum. If they have opposite signs, then the critical point is a saddle point.
Thus, we have the following cases:
(nπ, mπ) is a local minimum if n and m are both even.
(nπ, mπ) is a local maximum if n and m are both odd.
(nπ, mπ) is a saddle point if n and m have different parities.
To find the level curves for z = 0, we set f(x,y) = 0:
cos y - cos x = 0
cos y = cos x
y = ±x + 2πk, where k is an integer
Thus, the level curves for z = 0 are given by the planes y = x + 2πk and y = -x + 2πk for integer values of k.
What are 3 mechanisms of evolution and how do they work?
Three mechanisms of evolution are Natural Selection , Genetic Drift and Mutation
How do they work :
1. Natural Selection: This is the process by which organisms that are better adapted to their environment tend to survive and reproduce more successfully than those that are less adapted. This process results in the gradual evolution of the species over time.
2. Genetic Drift: This is the process by which the gene frequencies of a population can change randomly over time due to chance events. This can lead to the emergence of new traits and the disappearance of existing traits within the population.
3. Mutation: This is the process by which new genetic information is added to the gene pool of a population. This can result in the emergence of new traits or the alteration of existing traits.
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Suppose yougot a new job and each day your boss (Mrs. Gallas) draws a slip of paper from a bag to determine your wage for the day. Let the random variable X= daily wage ($ per hour).
The wage distribution in Factory A is more erratic. The standard deviation calculates the wage variability or dispersion. The tabular data in this situation show that Factory A has 500 > 400 standard deviation. As a result, there is more variation in the wage distribution in this factory.
What are the different way to calculate wages?By dividing the total number of earnings in a data collection by the number of wages, the mean wage is determined.
It is usually overestimated or underestimated since there are extremes in the data, despite the fact that it is frequently regarded as the “average” wage.
Therefore, Your daily pay is drawn from a slip of paper that is placed in a bag.
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What were the political, economic, and religious causes of European exploration?
Answer:
God, gold, and glory
Explanation:
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gmc automobiles come in the following colors and are manufactured in these percentages (white=0.46, black=0.22, red=0.09, grey=0.11, blue=0.12) if choose a car at random the probability that i do not choose a white or black car is
If an automobile is chosen at random, there is a 0.32 percent chance that I won't select a white or black car.
How does probability work?
The part of mathematics that deals with probability is called probability theory. Probability is a concept that can be interpreted in a variety of ways, but probability theory tackles the idea in a rigorous mathematical way by articulating it through a series of axioms. Typically, such axioms define chance in terms of a sample space, which links a collection of outcomes known as the sample space to a measure having values ranging from 0 and 1.
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What is the standard deviation for the normal curve provided?
0 10
015
034
50
68
The supplied normal curve has a standard deviation of 0.34.
What is deviation ?
Deviation is a mathematical and statistical measure of the difference between the measured parameter and another value, frequently the mean of that variable. The deviation's sign indicates the difference's orientation (the deviation is positive when the observed value exceeds the reference value). The size of the difference is indicated by the value's size. A deviation is a mistake where there is a discrepancy between the actual value and the actual value of a quantity of interest (where the true value represents the Expected Value, like the population mean). A deviation is the variance between an estimation of the true value and the observed value.
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Even today, some believe that certain occurrences have supernatural causes. Think of an event, recent or historical, for which others have provided the supernatural explanation
Because it will contain clear assumptions about the best way to investigate the condition, its origin, and what kinds of therapies or treatments are most effective, the perspective used to describe a psychiatric disorder is crucial.
What are the main reason of supernatural causes?Witchcraft was frequently thought to include putting a spell on food, drink, or other items that the victim would come in close contact with. A list of ailments brought on by magic or other unnatural sources.
Therefore, The two supernatural causes that were most frequently cited were being possessed by evil spirits and various forms of witchcraft.
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