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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 many ways can you solve this simultaneous equation x plus 2y equals 5 2x-y equals 15?
This system has the unique solution (7, -1). Solving the first equation for x and substituting gives us y = -1; substituting that into either of the original equations gives x = 7.
You can see the steps in between using the link in the "related links" section below.
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If you graph this it will be a parabola that has each end pointing down. It crosses the x-axis at:
y=-2x^2+3x+5
y=-1(2x^2-3x-5)
y=-1(2x-5)(x+1)
y=5/2
y=-1
What is the soulition to y equals x plus 3 equals 2x plus 4?
x + 3 = 2x + 4
Subtract x from both sides: 3 = x + 4
Subtract 4 from both sides: - 1 = x
y = x + 3 = -1 + 3 = 2
The solution is (x, y) = (-1, 2)
What is the answer to3x-9 equals x plus 7?
3x - 9 = x + 7
Add 9 to each side of the equation:
3x = x + 16
Subtract 'x' from each side:
2x = 16
Divide each side by 2 :
x = 8
What are the coordinates of the x-intercept of the line x - 3y equals 6?
Put in function/point slope form.
X - 3Y = 6
- 3Y = - X + 6
Y = (1/3)X - 2
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zero out the Y
(1/3)X - 2 = 0
(1/3)X = 2
2 divided by 1/3 same as 2 * 3/1 = 6
X = 6
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of course you can just zero out the Y in original equation
X - 3(0) = 6
X = 6
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What is the equation answer for x over 2 plus 9 equals 24?
x/2 + 29 = 24
Subtract 29 from both sides: x/2 = -5
Multiply both sides by 2: x = -10
How do you solve 3x equals 6y plus 8 in standard form?
A single linear equation in two variables cannot be solved: you need two independent equations.
What is the anti derivative of e x2?
The integral of x^2:
f(x)= A . x^n
f´(x)= A . n . x^(n-1) = x^2
Hence, n must be 3 for (n-1)=2 which automatically means that A must be 1/2 in order for A . n= 1
Thus, f(x)=0,5 . x^3 (antiderivative)
0,5e . x^3
How can the graph of y equals kx be interpreted for different contexts?
It is a straight line through the origin and, if k > 0 reflects a direct relationship between x and y. This means that each unit increase in x is associated with y increasing by k.
If k < 0 it reflects a direct but negative relationship and this means that each unit increase in x is associated with y decreasing by k.
If k = 0 then the result is the x-axis. This means that changes in x are not associated with changes in y.
None of the above imply causation.
What is rage mathematically speaking?
a notation showing all of the y-values produced by the indicated function.
Domain is a notation showing all of the x-values that produce real answers.
Can x-x be a binomial expression?
if the bar between the x's means multiply...
x2 is a binomial because if you have an x squared this indicates that...
x2 + 0x + 0 which is a binomial expression
