What does it mean if "is directly proportional to" "is indirectly proportional to" "is the derivative of" "is proporional to" "is the proportion of" sorry for my questions
directly proportional: y=kx proportional: y=kx+f(...) such as y=mx+b (just a straight line) f(x) is derivative of F(x) means f(x) it is obtained by differentiating F(x). by definition this is f(x)=lim(h->0) [F(x+h)-F(x)]/h have you had any calculus?
The best way for you to think of the derivative, until you have studied more maths, is a rate. So speed = miles per hour is a rate and is a derivative. So is miles per gallon a rate - but a diffferent one - the rate of consuption of fuel. Is the proportion of is a ratio. So the aspect ratio of an older compter screen was 4 : 3. That is it was in the proportion of 4 units wide by three units high. Don't confuse this with is 'the portion of' where portion of means part of. When something is proportional to something else ( a very common situation in the physical world) we mean that there is a simple number that we can multiply any value of the first something by to get the value of the second something. So the amount of heat needed to melt a given block of ice is proportional to the weight (mass) of the ice. Twice the weight of ice reuqires twice the heat to melt it and so on. You can also have proportionality to the square of something so the area of a square is proportional to the square of the length of a side. Or proportionality to any other more complicated algebraic expression such as the reciprocal, which we call inverse proportionality, because unlike all my previous examples as the amount of the first quantity increases the amount of the second decreases in inverse proportionality. does this help?
-Directly proportional means when the value of one variable changes, the value of the other changes in the same way. -Indirectly proportional means that when the value of one variable changes, the value of the other changes in a different way. -The derivative is a mathematical "operation". Basically, it is the slope of the tangent line to a graph, at any given place. -Is proportional to just means two or more variables are related. -In order to answer the last one, I'd need to know the context. Never apologize for your questions. That's what we're here for
Indirectly proportional to...etc Well picked up DerStrom I mentioned inversely proportional to which is not the same. I should read more carefully!
an example for which one? All of them? -Directly proportional: you have two variables, x and y. x increases by a specific amount, y will also increase by a specific amount. When it's graphed, you will get a straight, positive-going line. In this picture, B is the x value, and A is the y value. -Indirictly proportional: sometimes it is used interchangeably with inversely proportional, like studiot mentioned. Inversely proportional means as x increases, y will decrease. It looks very much like the graph above, except the slope is negative -The derivative is the slope of the straight line that is tangent to a specific point on the graph. Basically, it's the slope of your original graph at any given time. The curved line is your original function (e^x). The straight line is a line tangent to a specific point, and shows the slope of the e^x graph at that point. THAT is the derivative. -Proportinal to simply means the variables are related, and depend on each other.
Ok, hopefully you can see in the picture--a tangent line is a line that just barely touches the graph (at a single point). that's all it is.
Don't get too discouraged. Math really is a different language. Most of what you named also have symbols, like letters in an alphabet.