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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
How do you solve 5x plus 5 equals 14 plus 2x?
5X + 5 = 14 + 2X
subtract 2X from both sides
3X + 5 = 14
subtract 5 from both sides
3X = 9
divide both sides integers by 3
(3/3)X = 9/3
X = 3
=======check in original equation
5(3) + 5 = 14 + 2(3)
15 + 5 = 14 + 6
20 = 20
=======checks
How many solutions exist for x2 plus y2 equals 2 assuming x and y are positive integers?
X2 + Y2 = 2
X = sqrt(2 - Y2)
Y can not be greater than 2 or a complex number would be yielded from under the radical. So, - infinity to 2, or something like that for Y's value.
Same procedure for X.
How do you solve 9x plus 2y equals 0 and 3x-5y equals 17 using the linear combination method?
9x + 2y = 0
3x - 5y = 17
Multiply the second equation by -3 so now the system looks like:
9x + 2y = 0
-9x + 15y = -51
So now when we add the two equations together (in their like-terms columns), we are left with just one variable:
0x + 17y = -51
Solve for y:
17y = -51
y = -3
And plug y = -3 into either of the original equations to get the value of x:
9x + 2y = 0
9x + 2(-3) = 0
9x - 6 = 0
9x = 6
x = 2/3
So the answer is x = 2/3 and y = -3.
How do you graph an equation like y equals x x plus 1 x minus 2 squared?
The equation is y=x(x+1)(x-2)2
How do you graph y equals 2 over 3x?
Division by 0 is not defined so 3x cannot be zero. That is, x cannot be zero.
Establish the domain of the graph and select a number of values of x in the range. Calculate y for each of these values.
Mark the x and y coordinates on the Cartesian plane and then join these together by a smooth curve. However, ensure that the curve does not join points on either side of x = 0 (for example x = 1- and x = +1).
What is x in 2x2 plus 9 equals -41?
2x2+9 = -41
2x2 = -41-9
2x2 = -50
x2 = -25
x = -5
Check: (2*-52)+9 = -41
Sorry, you can't have -5 as square root of -25.
x = 5i, where i is the imaginary square root of -1
The slope of the line on the graph remains constant, but the line
moves up or down, cutting the y-axis at different points.
-x + y = -7.
There is nothing more that can be done with just one equation and two unknowns.
What is the first step in solving the equation -4x - 16 equals 20?
Combine the constants on one side.
-4x = 36
What does 2x plus 5y equal 4 and x plus 5y equal 7?
Is this a system of equations?
2X + 5Y = 4
X + 5Y = 7
solve for X using bottom equation
X = 5Y - 7
insert into top equation
2(5Y - 7) + 5Y = 4
distribute
10Y - 14 + 5Y = 4
solve for Y
15Y = 18
Y = 18/15 = 6/5
use bottom equation to find X
X +5(6/5) = 7
X = 1
check with bottom equation
1 + 5(6/5) = 7
7 = 7
not true for top equation
( sorry, I forgot what happens then-resubmit question )
What is -6x plus 2y equaling -2 on a graph look like?
The graph is a straight line, because there's no x2 or y2 in the equation.
Now give us a second to massage it around a bit, and then we'll show you how
you can tell the line's details easily. We're not changing anything, just presenting
it in a different light:
-6x + 2y = -2
Add 6x to each side of the equation:
2y = 6x - 2
Divide each side by 2:
y = 3x - 1
That's exactly the same equation, but you can look at this form and see immediately
that the slope of the line is 3, and it cuts the y-axis at the point [ y= -1 ].
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals".
There is no symbol between 4 and 6.
What are the rules of continuity of a graph?
If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous.
That is, there should be no "jumps", "holes", or "asymptotes".
How do you do y equals -3x plus 7 and y equals 2x minus 8?
You have two equations with two unknowns, y and x
To solve,
y = -3x +7
y = 2x -8
since they are equal
-3x + 7 = 2x-8
7= 5x -8
15 = 5x
3 = x
substitute in either equation to get y
y = -2
What is the slope of 5x plus 3y equals 6?
First, it would be beneficial to change the equation into slope-intercept form:
(y = mx +b)
5x + 3y = 6
-5x -5x [add -5 to both sides]
3y = -5x+6 [divide everything by 3]
y = -5/3x +2
Since "m" represents the slope, we can now see that the slope is equal to -5/3
It seems that the endpoints of the segment are (-6, 3) and (-5, -x).
(3 + x)/(-6 + 5) = 1/3
(3 + x)/-1 = 1/3 cross-multiply
9 + 3x = -1 subtract 9 to both sides
3x = -1 - 9
3x = -10 divide by 3 to both sides
x = -10/3.
How to solve 4x3 plus 0.4x2 plus 0.01x-2.4x10-18 equals 0?
There are a number of ways. One possibility is the iterative method.
Rewrite the equation so as to make x the subject:
4x3 + 0.4x2 + 0.01x - 2.4*10-18 = 0
4x3 = 2.4*10-18 - 0.4x2 - 0.01x
x3 = (2.4*10-18 - 0.4x2 - 0.01x)/4 x = cuberoot[(2.4*10-18 - 0.4x2 - 0.01x)/4]
The original equation is approximately equal to
4x3 + 0.4x2 + 0.01x = 0
or x*(20x - 1)2 = 0
which has roots at x = 0 and x = -0.05
Start with a value, x1 near one of these roots and use the iteration:
xn+1 = cuberoot[(2.4*10-18 - 0.4xn2 - 0.01xn)/4] where n = 1, 2, 3, etc to improve your estimates.
The resulting roots are, not surprisingly, 0 and -0.05 to 10 decimal places.
What property is 3x plus 5 equals 32?
It is not a property of any kind. It is an equation that is true for one specific value of x.
