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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 value of x and y if y plus y equals 25 to the power of 25?
Well you can find what it equals in terms of x. If you know that y plus y equals 25 to the power of 25 then you know that 2y=25^25 which means that y=(25^25)/2 - this is a huge number. To find x+y you just add x to what y equals so you get x+(25^25)/2
What is the correct way to write the solution of 2x - 5y equals 9 and 8x - 20y equals 5?
The two equations contradict.
If you recast the first in terms of x
2x-5y=9
2x=5y+9
x=2.5y+4.5
Then substitute for x in the second equation
8x-20y=5
8(2.5y+4.5)-20y=5
20y+36-20y=5
36=5 (False)
which is not true - so the equations have differing values for x and/or y and so are not solveable.
How do you find out the period of y equals 3 sin x?
You look at it, and think about it, and say to yourself:
"The period of sin(x) is (2 pi) or 360 degrees.
Multiplying it by a number makes it bigger or
smaller, but doesn't change its period."
The most important part of finding out the answer is to look at the question
and think about it. In fact, in school, that's the whole purpose of the question.
Nobody needs the answer. And if they did, they would not ask somebody who's
just learning how to find it. They give you the question to look at and think about,
so that you can use it to teach yourself how to look and think.
What is it mean for a possible solution of an equation to be extraneous?
This usually refers to a word problem. For example, say you have a rectangle with an area of 6 and sides of length (x-3) and (x+2) and you have to find the value of x. Solving said equation, you find that x=-3 or 4. Substituting these values back into the (x-3) and (x+2), you find that if x=-3, one of the sides of the rectangle would equal −6. Since you can't have a distance of -6 (distance is always positive), that answer is considered extraneous. In essence, an extraneous solution is one that does not make sense in the context of the problem.
What is this equation 4 bracket x plus 3 bracket equals 4x plus 12 open sentence or identity?
4[x+3]=4x+12
4x+12=4x+12
it's open.
Justify that if x plus y equals x plus z then y equals z?
The requirements are that the operation of addition is associative, the existence of an additive identity and additive inverses.
Associativity: a + (b + c) = (a + b) + c = a + b + c
Identity: The set contains a unique element, called the additive identity and often denoted by 0 with the property that a + 0 = 0 + a = a for all a in the set.
Inverse: For each element in the set, x, there exists an element which is its additive inverse. For addition, this is denoted by -x, and has the property that -x + x = 0.
x + y = x + z
Add the inverse of x to both sides: -x + (x + y) = -x + (x + z)
By associativity: (-x + x) + y = (-x + x) + z
-x is additive inverse of x, so: 0 + y = 0 + z
0 is additive identity, so y = z
Why instantaneous rate of change called derivative?
Because it is calculated as the limiting value of the change divided by the time taken for the change, the limit being taken as the time interval becomes infinitesimally small. That is how the derivative with respect to time is defined.
Is every on-to function a one-one function?
No.
The function y = x2, where the domain is the real numbers and the codomain is the non-negative reals is onto, but it is not one to one. With the exception of x = 0, it is 2-to-1.
Fact, they are completely independent of one another.
A function from set X to set Y is onto (or surjective) if everything in Y can be obtained by applying the function by an element of X
A function from set X to set Y is one-one (or injective) if no two elements of X are taken to the same element of Y when applied by the function.
Notes:
1. A function that is both onto and one-one (injective and surjective) is called bijective.
2. An injective function can be made bijective by changing the set Y to be the image of X under the function. Using this process, any function can be made to be surjective.
3. If the inverse of a surjective function is also a function, then it is bijective.
What is an example of fluid friction?
example of fluid friction are air resistance or drag
because an object moving through air actually collides with miniature particles, specially dust particles .
How do you use skewed in a sentence?
Skewed is an irregular adjective because it ends in -ed. An example of a sentence would be, "The results of his test were skewed due to the teacher's mistakes." Or you could say something like, "His conception of religion was skewed."
Everything inside your body is going to be body temperature. So no matter what the temperature is outside or anywhere else. Unless you die and lose you body temp your urine will always be warm.
It is math that was invented to solve physics problems.
If you're talking about food, it is fried fish, Angola-style.
