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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
The step-work involved in proving this would be too long and detailed to show here, but the end result is this:
We're given three verticies, defined by the points (x1, y1), (x2, y2), and (x3, y3). We want to use them to define a parabola in this format:
f(x) = ax2 + bx + c
We can find our a, b and c coefficients with the following equations:
a = [y1(x2 - x3) + y2(x3 - x1) + y3(x1 - x2)] / [x12(x2 - x3) + x22(x3 - x1) + x32(x1 - x2)]
b = (y1 - y2) / (x1 - x2) - a(x1 + x2)
c = y1 - a(x12) - b(x1)
Why can't we write equals in place of equals?
You can write "equals".
It would be perfectly fine to say "2 + 2 equals 4".
It's jsut that, it's much more common to use "=", just because it's easier probably.
1/3 - 2/(2y + 1) = 3/y
Provided that y ≠-1/2 and y ≠0,
multiply through by 3y(2y+1) to give
y(2y + 1) - 6y = 9(2y+1)
that is, 2y2 + y - 6y = 18y + 9
or 2y2 - 23y - 9 = 0
The quadratic formula then gives y = [23 ± sqrt{232 - 4*2*(-9)}]/(2*2)
= [23 ± sqrt(601)]/4
so that y = -0.3788 or y = 11.8788
Is 18 x 52 stronger than 10 x 50?
Two numbers multiplied together produce a number. A number is neither strong nor weak.
Is 5 a solution to -3x plus 211?
( -3x + 211 ) is not an equation, so it doesn't have a 'solution'. It's not asking
a question, so it doesn't need an answer.
It's just an expression that stands for a number, and there's no way to tell
what number it stands for until you find out what number 'x' is .
If 'x' is 5, then the expression stands for the number 196 .
If 'x' is 17, then the expression stands for 160 .
If 'x' is 55, then the expression stands for 46 .
If 'x' is something else, then the expression stands for some other number.
How do you factor x2-20 plus 100 equals 0?
I'm guessing you meant to say x2 -20x +100. This equation is in ax2+bx+c=0 (1 is the "a" term, -20 is the "b" term, and 100 is the "c" term. You have to think to yourself, what factors of the "c" term (100) will add to the "b" term (-20) These factors are -10 and -10 because when you add these two terms you get -20 and when you multiply these two terms you get 100. Now your equations should read like this: (x-10)(x-10) = 0 . then you have to get x by itself by adding 10 to both sides. Thus, 10 is your factor.
Whats property is used to solve the equation x plus 5 12?
Without an equality sign it is not an equation
Is -2x plus y equals 3 a function?
To be a function, every x has only one y. Meaning that the y's CAN repeat for different x's, but the x's CANNOTrepeat for different y's.
To prove that -2x+y=3 is a function or not, you might first want to make the equation into y= form.
-2x+y=3
y=2x+3 ;Add 2x to both sides, on the left it cancels
Now, to prove it, you need to either graph it or plug in x's into the equation and find out if any x's ever produce more than one y-value. If you do plug in an x, and you get, let's say, 2 y's, then it is NOT a function.
If you graph it, then you can find out if it is a function or not by performing the line test. Which means that on your graph, draw a vertical line down. If at any time your line crosses two points, then it is not a function.
y=2x+3 looks like an upward sloping line, however. So it does pass the vertical line test. Therefore, it is a function.
Type that into the Wolfram Alpha website. It's a maths website that will pretty much do anything to any maths function you require (e.g graph, factorise, integrate etc...) See related links for the website address - alternatively, Google "Wolfram Alpha" and it takes you straight there. Happy maths-ing!
