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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
Use the substitution method to solve the system -x plus y equals 2 and 4x-3y equals -7?
-x + y = 2
4x - 3y = -7
-x + y = 2 (add x to both sides)
y = x + 2 (substitute x + 2 for y into the second equation of the system)
4x - 3y = -7
4x - 3(x + 2) = -7 (solve for x)
4x - 3x - 6 = -7
x - 6 = -7 (add 6 to both sides)
x = -1
y = x + 2 (substitute -1 for x)
y = -1 + 2
y = 1
Thus (-1, 1) is the solution of the given system of the equations.
4x - 3y = 12
-3y = -4x + 12
y = (4/3)x - 4
^plug this transformed version of the equation into your graphing calculator or do it out by hand.
How do you solve 4x plus 2 equals 38?
4x + 2 = 38
To tackle this problem, it is essential that you remember that whatever you do to one side of an equation, you have to do to the other.
First, subtract 2 from both sides of the equation to get the x term on one side, and the rest of the equation on the other
4x+2=38
-2 -2
4x=36
Now, all we have to do is divide both sides by 4 in order to get the x all by itself. 36/4=9, so x=9.
Can you solve neg 4x minus1 minus 3x minus4 plus 5 equals neg 7x minus 1 minus 2x plus 1 plus 6?
-4x-1-3x-4+5 = -7x-1-2x+1+6
-7x = -9x+6
2x = 6
x = 3
What is the exact solution of e to the x power subtract 2 equals 8?
e^x - 2 = 8
e^x = 10
So x = ln(10) = 1/log10(e)
What is the difference between range and codomain?
Sometimes it is useful to distinguish between the set of images of the domain of a function, which is called the RANGE of the function, from the super-set of the range. For example, for the real function x^2 without any additional qualification, its domain is the set of real numbers and its range is the non-negative reals. The codomain is the entire set of reals that the non-negative reals are part of. So the codomain is the super-set of the range. Curiously, there is no corresponding term for the domain, which might be called the "co-range" but we have no single word for it. If we did, it would simply mean the entire set of which the domain is a subset. So, for example, the domain of the real (otherwise unrestricted) square root of x is the set of non-negative reals and its co-range, if we spoke of it, would be the entire set of reals. We can think of these as the difference between a family and a subset of individuals.
What is the value of p if 4p plus 6 equals 2?
4p + 6 = 2
4p = -4 (subtracting 6 from both sides)
p = -1 (dividing both sides by 4)
Is x2 plus y2 equals 4 a function?
No. By definition, a function has a single unique value for every value passed into it. The equation given here describes a circle, which can not be rearranged to meet this condition.
How do you solve 6x-4y equals 54 -9x plus 2y equals -69 using substitution?
-9x + 2y = -69
So 2y = 9x - 69
The other equation can be written as
6x - 4y = 54 or 6x - 2*2y = 54
Substituting for 2y gives
6x - 2*(9x - 69) = 54
6x - 18x + 138 = 54
12x = 84
x = 7
and then 2y = 9x - 69 = 9*7 - 69 = 63-69 = -6
so that y = -3
What limitations does the domain of this function have?
It would appear that the domain is so very limited that the function may not be seen!
How do you solve x 37.260 with all steps?
Unfortunately, the website dropped whatever symbol you typed between the 'x'
and the '37.260' and I can't tell what's supposed to be in that space. It could be
the sign for 'equals', 'plus', 'minus', 'times', or 'divided by'. I'll have to answer the
question for every possibility:
-- equals . . . . x = 37.260
That's an equation. The solution is the number that 'x' must be
in order to make it a true statement. The solution is
x = 37.260
-- any other symbol
- x + 37.260
- x - 37.260
- x times 37.260
- x/37.260
None of these is an equation. None of them asks a question, or needs a solution.
Each of them is just an expression that stands for a number. There's no way to
know what number it stands for unless you know what 'x' is. And if 'x' changes,
then the value of the expression changes immediately. There's nothing to solve
with any of these.
What are limitations of double indicator method?
I know I know!!!! Its my fat juicy coc that you gotta slurp to get the answer.
If x equals 1.5cm and z equals 2.5cm what is the length of y?
The question is underspecified. As it stands, y can have any value.
If the question is, What x 3 equals 15?
Then 5 x 3 = 15
If the question is, What is 15 x 3?
Then 15 x 3 = 45
