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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 graph a complex equation?
"Color wheel graphs" are commonly used. At each point in the complex plane, the graph is a color, where the brightness represents the magnitude, and the hue represents the complex angle.
Thus, positive values are cyan, negative values are red, and pure imaginary values are green or magenta. Other complex numbers are mixtures of these. Zero is black, and infinity is white. (Other schemes are also in use)
How do you simplify 6x plus x?
Perform the addition.
You know that 6 cows plus one cow is 7 cows, 6 kittens plus 1 kitten is 7 kittens,
and 6 computers plus 1 computer is 7 computers.
It should not surprise you to discover that [ 6x + 1x ] = 7x .
What are the 10 most stressful situations?
Death of a spouse: 100 Points
2. Divorce: 73 Points
3. Marital Separation: 65 Points
4. Jail Term: 63 Points
5. Death of Close Family Member: 63 Points
6. Personal Injury or Illness: 53 Points
7. Marriage: 50 Points
8. Job Firing: 47 Points
9. Marital Reconciliation: 45 Points
10. Retirement: 45 Points
11. Change in Health Of A Family Member: 44 Points
12. Pregnancy: 44 Points
13. Sexual Difficulties: 39 Points
14. Gain of a New Family Member: 39 Points
15. Business Readjustment: 39 Points
16. Change in Financial State: 38 Points
17. Death of a Close Friend: 37 Points
18. Change to a Different Line Of Work: 36 Points
19. Change in Number Of Arguments With Spouse: 35 Points
20. Mortgage More Than $50,000: 31 Points
21. Foreclosure: 30 Points
22. Change in Responsibilities at Work: 29 Points
23. Departure of Son or Daughter From Home: 29 Points
24. Trouble with In-laws: 29 Points
25. Outstanding Personal Achievement: 28 Points
26. Spouse's Beginning Or Stopping Work: 26 Points
27. Beginning or Ending of School: 26 Points
28. Change in Living Conditions: 25 Points
29. Change of Personal Habits: 24 Points
30. Trouble With Boss: 23 Points
31. Change in Work Hours or Conditions: 20 PointsChange in Residence: 20 Points
33. Change in Schools: 20 Points
34. Change in Recreation: 19 Points
35. Change in Church Activities: 19 Points
36. Change in Social Activities: 18 Points
37. Mortgage or Loan Less Than $50,000: 17 Points
38. Change in Sleeping Habits: 16 Points
39. Change in Numbers of Family Gatherings: 15 Points
40. Change in Eating Habits: 15 Points
41. Vacation: 13 Points
42. Christmas: 12 Points
M Cronje - Somerset West, South Africa
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!
