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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
Factorise x squared -2x plus 3?
Despite my serious qualms with the wording of your question, I am assuming it to be the factoring of x2-2x+3
This is not factorable. As long as there is a positive 3 in the position of the constant element, there can only be -4 or 4 for the coefficient of the single x. Perhaps you made an error in entering the question, so I will provide some likely alternatives.
If the trinomial read as x2-2x-3, then it would be factorable and would be (x-3)(x+1)
If the trinomial read as x2-4x+3, then it would be factored as (x-3)(x-1)
If the trinomial read as x2+4x+3, then it would be factored as (x+3)(x+1)
If 4x-5y equals 4 and 6x-7y equals 10 what is the value of x?
4x - 5y = 4 & 6x - 7y = 10
This is a pair of simultaneous equations. Re-write as
4x - 5y = 4
6x - 7y = 10
To find the value of 'x; we need to eliminate 'y'
To do this multiply the top eq'n by '-7' and the bottom equation by '5' . This brings the coefficients of 'y' to the same value, but one is plus(+) and the other is negative(-).
Hence
-28x + 35y = -28
30x - 35y = 50
Add the two eq'ns, this will eliminate 'y'
2x = 22
x = 11
What is the x value in x2-4 equals 0?
x^2 - 4 = 0
What you have to recognise is that the constant '4' is a 'squared number.
4 = 2^2
So we can write
x^2 - 2^2 = 0
Next remember that two squared terms with negative between then, factors.
Hence
x^2 - 2^2 = 0
=>
( x - 2)(x + 2) = 0
NB Note the plus (+) sign in the second bracket.
Hence
x - 2 = 0
x = 2
&
x + 2 = 0
x = -2
So 'x' can take two values, they are '(+)2, & -2'.
NB Note that two squared terms with a plus(+) between then , does NOT factor. e.g. the Pythagorean equation. c^2 = a^2 + b^2
What is the most difficult mathematics?
It is not possible to answer this question because people find different things easy or difficult. What you find easy I might find difficult, and conversely.
30 ml is equal to 30 ml. You have not given us any other unit to convert, so that's the answer.
What is the derivative of one third x cubed?
f(x) = 1/3x3
f'(x) = ∫ 1/3x3 dx
f'(x) = 1/3∫ x3 dx
f'(x) = 1/3 * 3 * x2
f'(x) = x2
How do you use the substitution method?
When finding an antiderivative, substitution can be very helpful. In your integral expression, look for a term that, if you took the derivative and perhaps manipulated it a bit, would give you another term in the same equation. For example, if your integral is ∫tanxdx or ∫((sinx)/(cosx))dx , you can choose cosx as your arbitrary variable (often u or w). If u=cosx, du=-sinxdx. Therefore, your expression using u becomes -∫du/u. We know that the antiderivative of 1/u is ln (absolute value x) +C. So, our answer with u is -ln (abs. val. u) +C. But BE CAREFUL, this is not your final answer. You must plug in the value you originally designated as u. Therefore, the final answer is -ln (abs. val. cosx) +C, with C as an arbitrary constant.
If y=-42,
then
y = -42.
QED
? ? ?
============
Another answer:
THERE it is ===> Y = -42
Does -3x-2y equals 4 have one solution?
No, it has an infinite number of solutions. The coordinates of each and every point on the line 3x + 2y + 4 = 0 is a solution.
What is the solution to 2y - 2x equals 10?
Any pair of numbers where the 'y' is 5 more than the 'x'. There are an infinite number of suitable pairs.
2y-2x=10
2y-2x+2x=10+2x
2y=2x+10
divide both side by 2.
y=x+5
x2 - 3x - 4 = 0 so (x+1)(x-4) = 0, so x+1 = 0 and x-4 = 0, so x = -1 or 4
365 divided 2 is:
365/2 = 182.5
If by fraction, then 182 1/2.
By words: one hundred two and one half.
What is the ordered pair of 14x - 2y equals 78 2x - 2y equals 6?
You can answer this by the method of substitution, which means that you find what one variable equals and you substitute it into the second equation to find the other variable.
14x-2y=78; solve for y
-2y=78-14x; subtract 14x on both sides
y=-39+7x; divide both sides by -2
y=7x-39
Substitute 7x-39 for y in the second equation.
2x-2(7x-39)=6; solve for x
2x-14x+78=6; distribute the -2
-12x+78=6
-12x=-72; subtract 78 on both sides
x=6; divide both sides by -12
Now go back to the first equation and for x, substitute 6. You can either substitute in 14x-2y=78 or the y=7x-39, but it's easier where you already have y isolated.
y=7(6)-39
y=42-39
y=3
You got that x=6 and that y=3; therefore, the ordered pair is (6,3).
What is the derivative of tan?
If it's tan(x3), the the thingy is 3x2/(cos2(x3)) i think
Else, if it's tan(3x), then it's 3/(cos2x)
If you need more help with this, search "chain rule" and "derivative" on wikipedia.
X plus 3y equals 2 2X-3Y equals 22?
x + 3y = 2
2x - 3y = 22
Add the two equations: 3x = 24
Divide both sides by 3 to give x= 8.
Substitue this value of x in the first equation to give 8 + 3y = 2
Subtract 8 from both sides: 3y = -6
Divide both sides by 3: y = -2
Solution: (X, y) = (8, -2)
How do you solve a percentage equation?
its really easy say you wanted to find the percentage correct if you got 20/30 for an exam you simply divide 20 by 30 and then times the answer by 100 eg 20/30 = 0.6666 0.6666 x 100 = 66.66 so your percentage is 66.66% !!!
