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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
What is the x-value when y equals 8?
Since the relationship between x and y is not defined, x can have any value whatsoever.
What is the answer for 3x plus 5y equals 2z?
"3x + 5y = 2z" doesn't ask any question.
If you're looking for numbers for 'x', 'y', and 'z' that make the statement true, there are
an infinite number of sets that do it.
A few of them are:
x=1, y=3, z=9
x=2, y=4, z=13
x=3, y=5, z=17
If you want to set up a puzzle where there's only one correct answer ... only one secret set of
values for 'x', 'y', and 'z' that solves the puzzle, then you need two more equations.
The one equation you gave us is the equation of a line in 3 dimensions. Every point on the line
has the coordinates (x, y, z), and every point satisfies the equation.
2 - 8y + 6 = 4y - 70
2 + 6 + 70 = 4y + 8y
78 = 12y
y = 78/12
y = 6.5
Why are milliter and cubic centimeters the same?
Every unit in the International Standards of Units ("SI units") has a universal standardized definition. By universal, it is used everywhere. For instance, a meter is defined as "Length of the path travelled by light in a vacuum in 1⁄299,792,458 of a second (17th CGPM)" Yes. The definitions are usually pretty weird, but they stay consistent, which is important.
Now, the reason why the milliliter and the cubic centimeter are the same is much simpler. The liter was originally created as another word for a cubic decimeter. Because there are 1000 milliliters in a liter, and 1000 cubic decimeters in a cubic centimeter[see note], a milliliter and a cubic centimeter and therefore, the same.
Note: millimeter, centimeter, decimeter. While the centimeter is 10 times smaller than the decimeter, we are also dealing with cubic terms, so a cubic centimeter is therefore, 103 or 1000 times smaller than a cubic decimeter.
Describe what it means for a function to be one to one?
It is the function for which all the elements of the range of the function corresponds to exactly one element of the domain.
How do you solve x squared plus x squared plus x?
Add the x's squared together to get 2x^2+x. You cannot add anymore so the answer is 2x^2+x
What is the history of limits in calculus?
newton and Leibniz were first introduced the concept of limit independently
4x+5 = 8x+10
But you are saying
4x+5 = 8x+4
If this were the case, 8x+10 = 8x+4, and so 10=4
Thus there is no possible solution for X.
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Honk! Go to your room.
8x + 4 = 4x + 5
Subtract 4x from each side:
4x + 4 = 5
Subtract 4 from each side:
4x = 1
Divide each side by 4:
x =1/4
Check:
Left side: 8x + 4 = 8/4 + 4 = 2 + 4 = 6
Right side: 4x + 5 = 4/4 + 5 = 1 + 5 = 6
6 = 6 yay!
What is the solution for x plus y equals 1 and -4x plus 2y equals -2?
OK, there's two ways to solve systems of linear equations. The first way is substitution and the second way is called elimination/addition, but we're only going to solve it this way (because it's hard to show the other way just with text).
Let's do the simplest first, the substitution. You have:
x+y=1 and -4x+2y=-2
Solve for one of the variables (x or y) on the first equation. For example, solve for y in x+y=1:
x+y=1
y=1-x ;Subtract x on both sides
Now substitute 1-x into every y on the other equation:
-4x+2y=-2
-4x+2(1-x)=-2 ;Plug in 1-x into all the y's
-4x+2-2x=-2 ;Distribute the 2
-6x+2=-2 ;Combine the x's
-6x=-4 ;Subtract 2 to both sides
x=(-4/-6) ;Divide both sides by -6
x=2/3 ;Simplify the fraction
Now that you have what x is equal to, plug that back into y=1-x:
y=1-(2/3) ;Plug in 2/3 for x
y=1/3
Your solution for both equations is ( 2/3 , 1/3 ).
Why is natural log given the initials ln instead of nl?
Euler came up with the log, and being Swiss, would've spoken french. In French the natural log would be le logarithme naturel, and his notation would've just caught on. I might be wrong, I've not really looked this up, just seems like a logical assumption...
A is less than b and b is less than c is a greater than c?
NO it is not because if a<b<c it could also be said without the b as a<c.
The graph of the equation below is a hyperbola What are the slopes of the hyperbolas asymptotes?
7/12 and 7/12 is the answer
What is the inverse of y equals 3X3?
Since the equation is in terms of x, you need to switch the x's and y's, and then solve it for y again.
y=3x^3 --> x=3y^3 --> y=(x/3)^(1/3)
