0
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 range of y equals -2x plus 3?
The Range is all the Real numbers you can think of.
The Domain is also all Reals.
Is x squared minus x minus twelve a prime?
Just like numbers, polynomials can be prime in some way, although this is usually referred to as being irreducible. Your polynomial is not in fact irreducible since it can be decomposed into (x-4)(x+3). This also means that plugging in any integer value for x gives a factorisation for the number x^2-x-12, which is (x-4)(x+3), so the value of x^2-x-12 for any integer x can only be prime if either x-4 = 1,-1 or x+3 = 1,-1 so for x=5,3,-2,-4. Now for x=5 we get 25-5-12=8, which is not prime. For x=3 we get 9-3-12=-6, which is not prime either. For x=-2 we have 4+2-12=6, which again is not prime. And for x=-4 we have 16+4-12=8 again, which of course is still not prime. So not only is your polynomial reducible, also any value it takes when plugging in an integer x will be composite. An alternative way of establishing this fact would have been to note that this polynomial only takes even values for any integer x and that the value 2 is not in fact attained for any integer x.
An invented term that is too vague to answer when queried in this manner.
What is the next level in inverse functions?
The "next" level depends on what level you are starting from!
You are given sin x equals 5 over spare root 34 . Work out the value of tan x. URGENT?
Brute force method,
with calculator:
Sin(x) = 5/sqrt(34) = 0.85749 (rounded)
x = 59.0362 degrees
tan(x) = 12/3
================================
Better method, with elegance
and no calculator:
Sin(x) = 5/sqrt(34) = (opposite side)/(hypotenuse) of the right triangle.
What is the length of the other leg of the same triangle ?
(5)2 + (leg)2 = [ sqrt(34) ]2
(leg)2 = [ sqrt(34) ]2 - (5)2 = 34 - 25 = 9
leg = 3
tan(x) = (opposite side)/(adjacent side) = 5/3 = 12/3
How do you solve radical 14x to the 4th and y to the 6th?
The answer will depend on what you mean by "and": addition or multiplication.
x = -0.5 + 2.397915761656359i
x = -0.5 - 2.397915761656359i
where i is the imaginary square root of negative one.
What is 77r plus 74r-16 factored completely?
77r + 74r - 16 = 151r - 16 and that cannot be factored further.
Is there any other anti derivative of 1 divided by x?
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
What is x cubed plus 10x squared plus 25x?
X3 + 10X2 + 25X
factor out an X
X(X2 + 10X + 25)
factor inside parentheses
X(X + 5)(X + 5)
X(X + 5)2
=======
X = 0
X = - 5
What is x 4x plus 5 plus x equals 25?
4x + 5 + x = 25
5x + 5 = 25
Subtract 5 from both sides: 5x = 20
Divide both sides by 5: x = 4
Can a pentomino be 5 equal spuares in a line?
Sure. A pentomino is any figure you can make by laying squares side by side on a plane, with two adjacent squares touching with their entire length. This includes five in a line. In total (eliminating duplicates due to rotations and reflections), 12 different figures can be made this way.
How do you factor 4x4 plus 34x plus 42?
You cannot factor 4x4 + 34x + 42
The expression has a minimum value of approx 9.21616 when x = -1.286 (= 0.5*cuberoot(17). Since the expression is always positive, it does not cross the x-axis and so does not have any real roots. Consequently, it does not have any real factors.
