Recent content by slider142

Hi, For problem 5, y²(x² - 9) = 2x, we can note the following: Domain: Unless otherwise mentioned, in elementary mathematics, y would be the range variable and x would be the domain variable. The domain of this equation would thus be the set of all x values in the solution set of the equation...

Hi, Note that this method of assigning angle measures to the circle is not the only common one. Bearing degree measure, often used in navigation and the compass rose, assigns the 0° mark to the positive y-axis and increases angular magnitude clockwise from there. Left is a standard compass...

I would first simplify the circuit by reducing any distributed nodes to single nodes, as we did in the previous circuit, then by writing the batteries with internal resistance as equivalent branches: a battery with 0 internal resistance connected in series with a resistor of the requisite...

Q1: What battery does current flow from? In the solution, all branch currents have positive values, which means the directions of the branch currents match the directions of the actual currents in the circuit. The directions of the branch currents were chosen (as shown in the diagram) to align...

Hi, One way to calculate the theoretical readings of ideal ammeters placed at those locations is to apply Kirchhoff's laws to the nodes and loops of the given circuit. In analyzing the circuit using Kirchhoff's Current Law, we would write down the sum of all incoming and outgoing branch currents...

Hi, Different textbooks have different ways of defining increasing or decreasing on an interval. The most common calculus textbook currently used in US universities is James Stewart's "Calculus: Early Transcendentals" (9th Edition). In this particular textbook, a function is defined to be...

Hi, There are several methods of factoring polynomials. Here is the way that I personally tend to do it: (1) Factor out any obvious factors (what is obvious will be different for different people). If you like, this could mean factoring out any common constant factors. This step also covers...

Hi, F₁ and F₃ do not intersect; (-2, 1) is the intersection point of the lines of action of F₁ and F₃. In the previous comment, we derived the fact that the line of action of F₁ has the equation y - 2 = ⅓(x - 1), and the line of action of F₃ has the equation y + 1 = -⅖(x - 3). To find the...

Hi, It is unusual that the problem states the condition "if the group is equivalent to a couple...", since we can add the forces F₁, F₂, and F₃, as given, and readily see that the resultant is 0, and thus the only possible result is a couple resultant. In addition, every system of forces is...

Hi, To find limits for multivariable integrals, you will almost always have to draw a sketch of the curves that form the boundaries of the region you are integrating over. This is because it will often not be enough to merely know at what points the curves intersect, but you will also have to...