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What is the definition for inverse proportional?
A variable, Y, is inversely proportional to another variable, X if XY = k for some positive constant k. An equivalent formulation is Y = k/X. What this means is that if you double X, then Y is halved. If you treble X then Y is reduced to a third etc.
What are the possible values of k if the line y equals 2x plus k meets the curve of y equals x squared -2x -7 at 2 distinctive points or at only 1 point?
The two lines are y = 2x + k and y = x² - 2x - 7 Which means they meet at: 2x + k = x² - 2x - 7 → x² - 4x - (k+7) = 0 This can be solved using the formula for quadratics: x = (- -4 ± √((-4)² - 4×1×-(k+7)))/2 = 2 ± √(4 + k + 7) = 2 ± √(k + 11) This has one solution when the determinant (the part in the square root) is 0, ie k + 11 = 0 → k = -11 If the determinant is positive, there are two solutions, ie k + 11 > 0 → k > -11 Thus the there are two distinctive points if k > -11, and only 1 point if k = -11.
What is the correct formula for compound interest?
Suppose the amount invested (or borrowed) is K, Suppose the rate of interest is R% annually, Suppose the amount accrues interest for Y years. Then the interest I is 100*K[(1 + R/100)^Y - 1]
What does variation mean in math terms?
There are different types of variation in math - direct variation, inverse variation, and joint variation for a start. Direct variation is just simply that x and y vary directly. What this means is that they do the same thing - as x increases so does y, or as x decreases so does the value of y. In general the formula for direct variation is y=kx where k is the constant of variation. (For example we could have a direct variation equation such as y=2x. The constant of variation is 2, which just means that as x increases, y doubles that amount and thus also increases) Inverse variation is when x and y do the opposite of each other. So as x increases, y decreases or as x decreases the value of y increases. One fun example of where this happens in real life is with Ramen Noodles - the less money people make the more Ramen Noodles they buy. We would say that people's income and the amount of Ramen Noodles they buy vary inversely. In general the formula for inverse variation is y = k/x where again k is the constant of variation. Joint variation is when you have three variables that are related. The general formula for joint variation is y=kxz where z is just a third variable and k is still the constant of variation.
If y equals kx then what is the relationship between x y and k?
Various options: y is directly proportional to k, with x as the constant of proportionality; y is directly proportional to x, with k as the constant of proportionality; x is inversely proportional to k, with y as the constant of proportionality; x is directly proportional to y, with 1/k as the constant of proportionality; k is directly proportional to y, with 1/x as the constant of proportionality; and k is inversely proportional to x, with y as the constant of proportionality.
