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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 solution-set for x-2y equals 0?

x-2y=0

x=2y

The solution set is the set of all (x,y) such that x=2y

What dos x equal?

'X' is the unknown term in a problem. It can be anything depending on the equation or terms involved.

Is there a simple way to solve 7 divided by x minus 5 equals x without having to use the abc-formula it seems there would as it is easy to solve 7 divided by x equals x and with solve is meant find x?

I assume you mean the quadratic formula. Alternative methods include factoring. In this case, it is not easier, since the factors are not obvious. Another alternative method is completing the square, but it isn't really simpler than the quadratic formula, either - at least, not in this case.

If you want to solve it by using the graphing calculator:

7/(x - 5) = x

x2 - 5x = 7

So graph y = x2 - 5x and y = 7, then find the point of interception where its x-coordinate is the solution of the given equation.

Can you give the absolute value of x plus 1 equals 5?

The answer will depend on whether the question refers to

|x| + 1 = 5

or |x + 1| = 5

What is 3 plus 7 x 5-1?

Remember BODMAS/PODMAS (or variants).

3 + 7 * 5 - 1 = 3 + 35 - 1 = 38 - 1 = 37

Show the square root of two is irrational?

Suppose to the contrary that square root of two is rational. This means we can write square root 2 = a/b where a/b is a fraction that CANNOT be reduced..that part is important. Now, 4a^2=b^2 from square both sides and multiplying So we know the left side is even since it is a multiple of 4. So the right hand side must be also even since they are equal, but that implies they were not relatively prime to start with which is a contradiciton. we conclude square root of 2 is irrational. I will help to make this a little clearer, just in case some people to not fully understand the proof. We assumed a/b was in reduced form which is equivalent to saying there are NO COMMON Factors. For exampel 1/2 or 1/3 is in reduced form but 2/4 is not because they have a common factor of 2. No if b^2 is even, then b must be even (easy to prove) . This causes a problem because if b is even then a cannot be even or they would not be relatively prime (that means they have no common factors) Here is an example of a rational number so you can see how it works 8 for example 8=a/b 8b=a so 8b is even since it is 2(4b) now that means a is even. b can be odd since even x odd is even, we can write 8=8/1 and this is inreduced form Try it with 2/3...3b=2 etc.. it works! The conclusion is that square root of two is irrational There are many many other ways to prove this, some people understand some proofs more than others. I will put some more here later.

Work this problem Given R equals x parenthesis A plus B close parenthesis solve for B Put answer in form of isolated variable formula?

Like all middle school algebra problems, first convert what is given into an equation. In this case, we have:

R = x(a+b)

The question is "what is b =" ?

first we divide both sides of the equation by x to get:

R/x = (a+b)

Then subtract a from both sides:

R/x - a = b.

Thus, b = R/x - a.

Y equals 2x-4andx-y equals 1?

1) Y=2x-4

2) x-Y=1

Since you already have Y alone in the first equation, plug the first equation into the second equation. This will give you:

2) x-(2x-4)=1

Now solve for X. To do this, first change the signs of (2x-4) since it is being subtracted. This gives you:

2) x-2x+4=1

Subtract 4 from both sides, giving you:

2) x-2x=-3

Combine like terms, giving you:

2) -x=-3

Of course, from this we can see that x=3.

Now plug x=3 into equation 1) Y=2x-4 which gives you:

1) Y=2(3)-4

Solve for Y. Y=2

X=3 Y=2

This was on my homework............. Are there an infinite amount of multiples of 11 that have an odd digit sum?

Yes! Any multiple of 11 that is in the form of 11x10^n +209 will have an odd digit sum and will be divisible by 11. 209 is divisible by 11, and 11X10^n is too. Remember that n has to be over 1,000 for it too work.

ex. 11x10^5+209=1100209.

1100209/11=100019

What is the fraction for the 45 percent?

The fraction for 45% is 45/100 or 450/1000 or 4500/10000, and finally 45000/100000. Also, reduced to lowest terms, it is 9/25.

How do i Solve 7x equals 20 plus 20x?

7x=20+20x

collect terms containg x on one side and then factorize

-13x=20

0r, x=-20/13

How do you solve 11 x -7 equals 5-x?

11x - 7 = 5 - x

Subtract 'x' from each side:

10x - 7 = 5

Add 7 to each side:

10x = 12

Divide each side by 10 :

x = 1.2

What is the square root of x squared plus 12x -2 equals x plus 4?

It's a second-degree equation in 'x' that screams "trouble". But we laugh in the

face of adversity and, with no thought for our personal safety, we plunge right in

and pursue solution[s].

sqrt( x2 + 12x - 2) = x + 4

Square each side . . . . . . . . . . x2 + 12x - 2 = x2 + 8x + 16

Subtract x2 from each side . . . 12x - 2 = 8x + 16

Add 2 to each side . . . . . . . . . 12x = 8x + 18

Subtract 8x from each side . . . 4x = 18

Divide each side by 4 . . . . . . . . x = 9/2