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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 line in the graph is it if the equation is y equals x plus 3?
y = x + 3
The graph of that equation is a straight line with a slope of 1 (45° rising to the right)
and passing through the point y=3 on the y-axis.
(x+13)(x+4)
How can you tell if a relation of a graph has a function?
A relation is any set of ordered pairs (x, y), such as {(2, 5), (4, 9), (-3, 7), (2, 0)} or {(2, 3), (5, -2)}.
A function is a special type of relation in which each x-value is assigned a unique y-value. So in the two examples given above, the first relation is NOT a function because the x-value of 2 is assigned two different y-values: 5 and 0. The second example above is a relation, since each x-value given (i.e., 2 and 5) is only assigned to one y-value (i.e., 3 and -2, respectively).
Two additional examples:
{(0, 5), (1, 3), (1, 8), (4, -2)} is NOT a function, because the x-value of 1 is assigned to two different y-values.
{(0, 3), (1, 4), (3, -2), (4, 7), (5, 0)} is a function, because there is no x-value that is assigned to more than one y-value.
When graphed in the Cartesian plane, you can determine if a relation is a function or not by the "vertical line test", which says that if there is any place where a vertical line can be drawn that will pass through the graph more than once, then that relation is NOT a function. But if every vertical line that can possibly be drawn only passes through the relation at most once, then that relation is a function.
What is the inverse function of y equals x 3?
Unfortunately, limitations of the browser used by WA means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols with "plus", "minus", "equals".
What the answer for 3x plus 7 equals 25 and what step method?
3X + 7 = 25
subtract 7 from each side
3X + 7 - 7 = 25 - 7
3X = 18
divide each sides integers by 3
(3/3)X = 18/3
X = 6
--------------check in original equation
3(6) + 7 = 25
18 + 7 = 25
25 = 25
-------------checks
Can you graph sin or cos sideways?
If I understand you correctly, yes. Normally we write y=sin(x) or y=cos(x), and because we make our x-axis run horizontally and our y-axis run vertically, this gives us a wave running left-to-right. If instead we wrote x=sin(y) or x=cos(y), the waves would run bottom-to-top. However, notice that in the first case, y is a function of x, but in the second case, x is a function of y. If we wished to make x=sin(y) or x=cos(y) into a function of x, we need to restrict the values of y in the domain so that it will pass the vertical line test. These "restricted" functions have a name, namely arcsin and arccos, and they are referred to as the inverse trigonometric functions.
How do you solve y4-84 plus 5y2?
You cannot solve it since only one side of an equation is given. If the equation was y4 + 5y2 - 84 = 0 then y4 + 12y2 - 7y2 - 84 = 0 or y2*(y2 + 12) - 7*(y2 + 12) = 0 or (y2 - 7)*(y2 + 12) = 0 then y2 = 7 or y2 = - 12 y = +or- sqrt(7) and, if you are in the complex domain, also y = +or- i*sqrt(12) where i is the imaginary square root of -1.
If you have the zeros of a polynomial, it is easy, almost trivial, to find an expression with those zeros. I am not sure I understood the question correctly, but let's assume you have the zero 2 with multiplicity 2, and other zeros at 3 and 5. Just write the expression: (x-2)(x-2)(x-3)(x-5). (Example with a negative zero: if there is a zero at "-5", the factor becomes (x- -5) = (x + 5).) You can multiply this out to get the polynomial if you like. For example, if you multiply every term in the first factor with every term in the second factor, you get x2 -2x -2x + 4 = x2 -4x + 4. Next, multiply each term of this polynomial with each term of the next factor, etc.
What are the similarities of differential and integral calculus?
One directly undoes the process of the other.
Why was newtons development of calculus important?
I love Newton. He is my idol.
If we didn't have Newton, then we wouldn't have AP Calculus courses, which would be two less A's in my report card.
Also, Newton's calculus contributed to his 3 laws, and are very important in the fields of mathematics, physics, and numerous other disciplines such as gynecology and courses like: "The Science of Batman".
If you would like to worship Newton, like numerous others do, please contact your local Newton obsessor ASAP.
Who is the father of calculus Newton or Leibniz?
Both of them came up with the concept (semi-) independently; both were aware that the other was working on it and in fact they exchanged letters on the subject, but they approached it from different directions (Newton started with differentiation, Leibniz started with integration).
Going by their private papers it appears that Newton was further along earlier than Leibniz, but Leibniz published a full description much earlier than Newton did.
How is a real value stored in a computer?
Real (arbitrarily precise) values cannot be stored in a computer. They are generally approximated with either floating-point or fixed-point approximations.
A commonly used data type is "double-precision" which stores numbers accurately to about 16 decimal places, suitable for most real-world applications. More complex data structures known as "Bignum"s can be used to represent real numbers to arbitrary precision, depending on the amount of computer memory available. The programmer should always be aware that the computer cannot represent any real number.
If the computer has N bits of memory (including disk space), then it can be in one of 2^N possible states. No matter what N is, there are more real numbers between 0 and 1 than that. So a computer cannot possibly represent a continuum of real numbers between 0 and 1, let alone a wider range.
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How do you solve problems like y equals x2?
y = x2 is not even a problem or a question. As it stands, it doesn't have
a solution, and it doesn't require any.
Your best approach is to go back and review the material that you have
learned in your algebra class, so that you improve your understanding
of the fundamental concepts. As you review the course, it would be most
helpful to you to work the exercises that offer practice at each step of the
way, such as those that are typically assigned as homework during the
normal presentation of the course.
Ok, lets start with the basics:
let x = some distance [units = m]
let the area of some shape be a = x*x [units = m^2]
let the volume of some object be v = x*a [units = m^2]
we can see from above that the volume of an object contains information on its area.
So..
P [N/m^2]
rho [units = kg/m^3]
G [units = m/s^2]
h [units = m]
P = rho * G * h
N/m^2 = kg/m^3 * m/s^2 * m
N = kg*m/s^2 therefore:
N/m^2 = N/m^3 * m
canceling out m on top and bottom:
N/m^2 = N/m^2
The extra (* A / A) is not required. It reduces to 1. It is redundant to included this, as described above, because information on the objects area is already included within the volume.
Thank you for expanding the formulae from basic proofs. Actually this improves d
Thank you for showing the proofs from which this formulae derives. Actually this set of proofs improve the question. Personally I do and did realise how the formulae is derived from these basic proofs. What i was trying to impart to any enquiring mind is how the equation arrives at its final result and in nature takes no account of the millions of pounds of distributed atmospheric pressure, pressing down on the whole area of say the Atlantic Ocean, and because, and only because, of this equation has no effect on pressure at any depth. AS IF TO SAY THAT SOME `EXISTANCE` Who or Whatever has decreed " THIS IS HOW IT IS BECAUSE I SAY IT IS" Personally I wonder!
Lets work through an example here, involving water in the ocean. We will look at depths of 1m, 10m, 100m and 1,000m
rho sea water = ~1027kg/m^3
P = rho * G * H
1m
P = 1027kg/m^3 * 9.81m/s^2 * 1m = 10.07kPa_gage
10m
P = 1027kg/m^3 * 9.81m/s^2 * 10m = 100.7kPa_gage
100m
P = 1027kg/m^3 * 9.81m/s^2 * 100m = 1,007kPa_gage
1000m
P = 1027kg/m^3 * 9.81m/s^2 * 1000m = 10,007kPa_gage
The important part here is "gage". It means that all pressure is relative to the atmosphere. 1 ATM = 14.7psi or 101kPa. So if we wanted to find the pressure relative to a vacuum, "absolute", we simply add 101kPa to the number. After about 100m, atmospheric pressure only add 10% to the overall pressure. After 1000m, atmospheric pressure only adds 1% to the overall pressure. This is not to say that the atmospheric pressure is not great. 14.7 psi on your hand would be about the same as trying to hold up 235lb! (Its canceled on front and back so you don't notice). It most cases, water for example is about 1,000 times denser than air, pressures are indicated as "gage".
Simplify e raised to the power of lnx plus lny?
There are 2 interpretations of your question:
First: e^[lnx + lny]
=e^[ln(xy)]
=xy
Second: lny + e^(lnx)
=lny + x
What are the possible values for x if x squared plus 5x equals 6?
x2 + 5x =6
x2+5x -6 = 0
(x+6)(x-1) = 0
x+ 6 = 0
x = -6
x-1 = 0
x = 1
