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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 easiest way to do this would be to put the equation for y in terms of x.
We have x+y = 6
subtracting x from both sides gives y = 6 - x
This is of the form y = ax + b where b is 6 and a is minus 1.
So the graph will be a line, with gradient minus 1, that crosses the y axis at y=6
What does x stand for in an equation?
an unknown. eg x+1=3 means something plus 1=3. the unknown, or 'something' must be 2. therefore x=2
If 12x equals 4 parenthesis x plus 5 parenthisis what does x equal?
12x = 4(x+5)
3x = x+5 divide by 4
2x = 5 subtract x
x = 2.5 divide by 2
6c-18=4c
Why can rearrange this and simplify to 2c=18, which means that c = 9
(3+2x)*(3-2x) = 9 - 4x2
[remember that (a+b)*(a-b)=a2 - b2]
How do you do x raised to the 3rd power multiplied by x square?
x3*x2 = x5
Same base so just add the powers
What is the volume of a cylinder if r equals 3 and x equals 12?
You should probably say what x represents if you want someone to answer this...
Do y equals 2x-1 and y equals 2x plus 1 have the same lines?
The lines are parallel, but not the same.
A way of defining the sum from 1 to the number, similar to the factorial function but with sums, represented with the '?' symbol:
4? = 4 + 3 + 2 + 1 = 10
An easy simplification, known from Gauss, is to compute it with n(n+1)/2.
Is y equals 2x a linear function?
Yes it is. the two numbers will always have the same proportion to each other.
Ingetral(dy) = y + c
(c is a constant. A point would have to be given to find the value of c.)
Is this symmetric with y x origin or all y 20x?
y = 20x is symmetric about the origin. (If you rotate it around the origin, it will look the same before it is rotated 360 degrees).
What is the difference between x plus x and xx?
Say x is 5
so 5 + 5 = 10
where as 5 times 5 = 25
The difference is "x + x" is a addition and "xx" (x times x) is a multiplication.
How do you factor x cubed minus four x squared plus x plus 6?
x3 - 4x2 + x + 6
The sum of the odd coefficients equals the sum of the even coefficients, so (x + 1) is a factor.
So
x3 - 4x2 + x + 6 = x3 + x2 - 5x2 - 5x + 6x + 6
= x2(x + 1) - 5x(x + 1) + 6(x + 1)
= (x + 1)(x2 - 5x + 6)
= (x + 1)(x - 2)(x - 3)
How do you solve 4x plus 10 plus 3x equals 52?
x = 6.
4x + 10 + 3x = 52
We can add the x's together (combine the terms) to get:
7x + 10 = 52 (the plus 4x and the plus 3x become plus 7x here).
Now we can combine the constants (the numbers) by moving the plus 10 to the same side of the equation as the plus 52. When we move something from one side of an equation to the other we must swap the sign (a plus becomes a negative and a negative becomes a plus). So we get:
7x = 52 - 10 (in effect we have actually subtracted 10 from BOTH sides of the equation to keep the equation balanced).
Now we simplify:
7x = 42
x = 42/7
x = 6.
How do you solve 3x-28-5x equals 5x plus 13?
3x-28-5x=5x+13
Let us first solve the variables
-2x-28=5x+13
Transposing -28 to Right hand side
-2x=5x+13+28
-2x=5x+41
Transposing 5x to left hand side
-2x-5x=41
-7x=41 equation 1
x=41/-7
x=-41/7
Hence the required answer is -41/7.
You can verify it by substituting the value of x in the given equation. If Right hand side is equal to Left hand side the answer is right.
Let us verify
Substituting the value of x=-41/7 in the given equation1
-7(-41/7)=41
-7 X -41/7 =41
41=41
LHS=RHS
Hence Verified
