An equation is meant to be solved, that is, there are some unknowns. A formula is meant to be evaluated, that is, you replace all variables in it with values and get the value of the formula. Your example is a formula for mpg. But it can become an equation if mpg and one of the other value is given and the remaining value is sought.
The confusion here seems to be about how translation and other transformations apply to the equation of a circle, which is not a function in the sense of passing the vertical line test but rather an implicit relation. Let's clear up the confusion: Translation: For the circle's equation $ (x - x_1)^2 + (y - y_1)^2 = r^2 $, the $ x_1 $ and $ y_1 $ terms represent the coordinates of the center of ...
I love your answer for a line equation in the form of z = f (x, y)... Unfortunately calculating square roots can be impractical from the calculational standpoint and hence I really doubt any plotting software will be able to graph it correctly.
The equation of an object is a way of telling whether a point is part of an object -- if you substitute the coordinates of the point into the equation and the equation is true, then the point is on the object; if the equation is not true for that point, then the point is not on the object.
I found this question in a differential equation textbook as a question The equation $$ \frac {dy} {dx} =A (x)y^2 + B (x)y +C (x) $$ is called Riccati's equation
Note that there are 4 unknowns, so there is no single solution for a,b, and c since you can just multiply the equation by some constant and it stays the same, so you just solve for ratio of a to b to c. Also if there is no single solution, then there is a solution set (multiple planes can satisfy the conditions).
Get the equation of a circle through the points $(1,1), (2,4), (5,3) $. I can solve this by simply drawing it, but is there a way of solving it (easily) without having to draw?
