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  1. H

    Did the South have a chance to win the Civil War?

    Thought I'd ask for information here. I have read (but no longer remember where) that the reason Jefferson Davis, Robert E. Lee, and other Confederate leaders were never tried for treason was that such a case would clearly have wound up in the Supreme Court and people were concerned that there...
  2. H

    Did the South have a chance to win the Civil War?

    I'm inclined to agree that the south "never had a chance to win the war" but it was not clear at the time! What chance the south had to win did not depend upon its resources but on the will of the northern people. There were plenty of people in the north who were willing to "sweep the problem...
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    B Mathematical Name of this Space

    Frankly, your question makes no sense! You say "I am surrounded by Space" and since your are a physical object, you are talking about physical space! No, that space is NOT given any name by a Mathematician. Physics is not Mathematics! With apologies to Math_QED physical space is NOT...
  4. H

    I How does one solve Uxx+Uyy+Uzz=C when C is non-zero?

    This is a linear non-homogeneous equation so that you can first find the general solution to the associated homogeneous equation, U_{xx}+ U_{yy}+ U_{zz}= 0, then add any one solution, such as U= \frac{C}{2}x^2, to the entire equation to get the general solution to the entire equat0ion.
  5. H

    Did the South have a chance to win the Civil War?

    One problem the North had was that the onus of the offensive lay on the North and bad weather tends to hurt the offense more than the defense. Also the new rifled muskets, not to mention rifled cannon, tended to give the defensive the edge. Lee's two attempts to invade the north, which led to...
  6. H

    Did the South have a chance to win the Civil War?

    What one would have done if one had lived during the civil war is interesting to speculate on and impossible to say with any certainty! I was born in Georgia of a family that had lived in Georgia for many years (since 1790- before that they lived in Virginia). I am now convinced that the...
  7. H

    At what point(s) on the given curve is the tangent line horizontal?

    You should have more confidence in your own "brilliance".
  8. H

    Solving for f',f'',f''' and determining a general formula

    I'm a bit surprised you did not do what you were asked to do! The problem specifically asked you to "find f'(x), f''(x), f'''(x), and f^{IV}(x) then the nth derivative but you have only found f'(x) and f''(x) before jumping to the nth derivative. Other than the fact that you do not have...
  9. H

    At what point(s) on the given curve is the tangent line horizontal?

    Yes, of course it is! You have posted several questions in which you have given detailed solutions. Wonderful! My only question is why you would feel the need to ask!
  10. H

    Did the South have a chance to win the Civil War?

    Yes, both the South and the Nortn made strategic errors in the civil war. But the most crucial matter was the will of the union citizens. It was a pretty close matter though probably not as close as many in both union and confederate governments thought. The Democratic party made ending the...
  11. H

    Did the South have a chance to win the Civil War?

    And, in case no one else realized it, the reference to the Republican party nominating a "real estate developer" was a reference to Donald Trump, not George McClellan!
  12. H

    I Is this a Linear subspace?

    No, it is very easy to answer the questions I asked before and that is sufficient to answer the question.
  13. H

    Determining whether a set is a vector space

    As much as I hate to- I will have to agree with you! But I will still disagree with Perok, to whom I was originally responding, when he said that the given definition of matrix addition was "wrong"!
  14. H

    Determining whether a set is a vector space

    No, a "two by two array of numbers" is just that, it is NOT by itself a "matrix". A matrix is a an array of numbers together with a standard definition for multiplying and adding those arrays. Here we are given a two by two array of numbers with a definition of "multiplication" that is...
  15. H

    Determining whether a set is a vector space

    You are misreading the problem. It doesn't say anything about matrices! It talks about the set of arrays with the given definition if addition.
  16. H

    I Is this a Linear subspace?

    A subspace of a vector space has two properties: It is "closed under scalar multiplication" and "closed under vector addition". Here the subset is the set of all functions, f, such that f(0)= 2f(1). "Closed under scalar multiplication". If a is any number then does af satisfy af(0)=...
  17. H

    Differentiate 𝑦 = (2𝑥^3 − 5𝑥 + 1)^20(3𝑥 − 5)^10

    Well, the quicker you try to do it, the more likely you are to make mistakes so perhaps you should check my calculations!
  18. H

    Differentiate 𝑦 = (2𝑥^3 − 5𝑥 + 1)^20(3𝑥 − 5)^10

    I don't see any reason to use "logarithmic integration". Just the "product rule" and "chain rule" are sufficient. y= (2𝑥^3 − 5𝑥 + 1)^{20}(3𝑥 − 5)^{10} y'= 20(2x^3- 5x+ 1)^{19}(6x^2- 5)(3x- 5)^{10}+ (2x^3- 5x+ 1)^{20}(10(3x- 5)^{10}(3)).
  19. H

    The work done by gravity on a ball thrown vertically upward

    I'm not sure what you are trying to say. There is "positive" work done on the ball by whatever causes it to go upward to begin with. There is "negative" work done on the ball, as it is going first up and then down, by gravity and air resistance.
  20. H

    Isosceles triangle

    The line of symmetry of an isosceles triangle is always perpendicular to the base. Find the line through (4, 37) and perpendicular to 3y= 2x+ 12.
  21. H

    I Area and Volume Naming Conventions

    More generally, "hyper-volume".
  22. H

    I Average value of a function

    If a function is periodic then it makes sense to refer to the average over one period as the average of the function.
  23. H

    Determining whether a set is a vector space

    Was the "solution" you looked up the solution to this specific question? That is, was the solution set written for this book? Matrices with the standard matrix addition and scalar multiplication do form a vector space but this is NOT "standard" matrix multiplication. It may be that this...
  24. H

    Spring Pushing an Object

    When the object leaves the spring, the energy that was stored in the spring is converted into the kinetic energy of the object. So you can calculate the speed of the object at the time when it first leaves the spring. You are told that "After the object is released from the spring, the force...
  25. H

    Calculate the total area of this rectangle

    The only error I can find is that you have misspelled "height"!
  26. H

    B At what range does a conservative force contribute to the thermal U?

    There is NO such line. The affect of force gets smaller with distance (typically as 1/r^2) but there is no point where it is 0. You will have to decide when you want to declare that the force is "negligible" yourself.
  27. H

    B Is it possible to sit on a chair and self propel oneself back while still sitting on it?

    It's a matter of the friction on the soles of ones feet and the friction on the feet (or casters) on the chair. And that, of course, also depends on the floor surface.
  28. H

    B Is it possible to sit on a chair and self propel oneself back while still sitting on it?

    I'm not sure what you mean by "propel oneself back by using ones legs". Certainly, you can push yourself back by pressing your feet against the floor! If you mean that you sit in the chair and, without making contact with the floor or other "external" structure but just "waving" you legs and...
  29. H

    I Partial Derivative Question

    To take a partial derivative with respect to x you treat y as a constant. So \frac{\partial}{\partial x}x cos(xy)- 2x is the same as \frac{d}{dx} xcos(ax)- 2x= cos(ax)- axsin(x)- 2 where, since I replaced "y" with the constant "a" we need to replace back- \frac{\partial^2V}{\partial xy}=...