Tutor profile: Austin P.
How does paleomagnetism, more specifically, magnetic reversals prove sea floor spreading?
Magnetic reversals surveys done near an oceanic spreading ridge show a pattern of alternating patterns of magnetic normal polarity and reversed polarity that parallel the spreading ridge (this may be confusing in words, so here is a link to an awesome animation that shows this: http://earthguide.ucsd.edu/eoc/teachers/t_tectonics/p_paleomag.html). If you watch the animation and click the button at the top right to switch the polarity of the earth's magnetic field , you can see that magma in a certain polarity comes up, it is together, and then splits and travels at constant rates on each side of the ridge and parallels the ridge. Essentially, the only way to explain these alternating patterns of polarity is the seafloor is spreading!
True or False-- The value of arccos (1.01) exists.
Firstly, it is important to understand what arccos is. Assuming you already understand cosine is, arccos (sometimes denoted as cos^-1) is the inverse function of cosine. So, because the cosine function has a domain of all real numbers, and it's range is [-1,1], then arccos (the inverse of cosine) has a domain and range that is opposite of cosine, however there is one stipulation to that. If you look at a full graph of cosine, it does not pass the horizontal line test, and therefore can not have an inverse, so we have to restrict it's domain in order for it to have a one-to-one function. Mathematicians picked to restrict the domain from [0, pi]. So, finally, the domain of arccos is [-1,1] and the range is [0, pi]. Because in the question I gave the value of 1.01 for the input, which is outside of the domain of the function for arccos, the value does not exist.
Determine whether the following is a heterogenous mixture, homogenous mixture, or pure substance: - One substance present, three phases present
To understand this problem, you must first be able to differentiate between a heterogenous mixtuture, homogenous mixture, and a pure substance. Definitions: Pure substance- Substances that are made only of a single atom or a molecule (example: H20) Heterogenous mix- A combination (mix) of two or more pure substances that are NOT the same throughout (example: Chicken noodle soup) Homogenous mix- A combination (mix) of two or more pure substances that ARE the same throughout (Example: Salt water) - *Essentially, anything that is a pure liquid is going to be a homogenous mix* Now, since we now understand the difference between a homogenous mixture, heterogenous mixture, and a pure substance, we can finally address the question. The way I tackle these kind of problems is I "dissect" each phrase, and worry about them individually. So, regarding the first phrase of "one substance present," going off of our given definitions, it has to be a pure substance! This is because it only has ONE substance. Now, we move on to the next phrase, which is "three phases present." In a basic sense, this just simply means that this one substance can occur in three different phases (gas, liquid, or solid), but does that really matter? No, because if there is only one substance present, it does not matter if it can occur in three phases or one, because it is only one substance.
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