Calculus

4x2 + 28x + 49 = 4x2 + 14x + 14x + 49 = 2x(2x + 7) + 7(2x + 7) = (2x + 7)(2x + 7) or (2x + 7)2

If the length of the second pendulum of the earth is about 1 meter, the length of the second pendulum should be between 0.3 and 0.5 meters.

There is no specific rule.

y = -sqrt(x)

y = x - 12

y = -x/3

y = x2 - 84

are all possible.

5x + 3y + 6 is an algebraic expression. It is not an equation (or inequality) and so cannot be solved. In any case, one linear equation with two variables cannot be solved.

Assuming it is int((x/(1-x2)dx)) then the answer is -.5ln|1-x2|+C. You have to use "u" substitution and isolate the 1-x2 and make it "u". A negative one-half is put out in front when you derive the value of "u" and the equation is -.5int(du/u). The integral of one over "u" is ln|u|+C. Substitute the "u" value back in and the answer becomes -.5ln|1-x2|+C.

I apologize for the impolication that I'm "improving" on Rusty's answer, not my intent.

Instead I'd like to point out that when you write "x over 1 minus x squared," I don't know if you mean:

x/1 - x^2 (it's a safe bet this isn't it, but your notation isn't clear)

x/(1-x)^2

x/(1-x^2) This is the one Rusty explained.

Writing your question as I've done above, or even using parentheses in plain English, e.g., "1 - (1 minus x) squared" will clarify your question.

Use u substitution:

u = 1-x -> x = 1+u

du = -dx -> dx = -du

x/(1-x)^2 dx = (1+u) / (u^2) = [1/u^2 + 1/u] * (-du)

= -du/u^2 + du/u

Int[-du/u^2 du] = -(-1/u) = 1/u

Int[du/u] = ln(u)

Now change back to x:

1/u + ln(u) = 1/(1-x) + ln(1-x) + C <- this is your answer.

Is this right? Let's take the derivative and find out.

d/dx (1/(1-x)) = d/dx ((1-x)^(-1)) = -1*(1-x)^(-2)) * -1 = 1/(1-x)^2

d/dx (ln(1-x)) = -1/(1-x) = -(1-x) / (1-x)^2

Adding these gives:

(1 - (1-x)) / (1-x)^2 = x / (1-x)^2

So the answer's correct.

- If 3X - 1 = 11, what is the value of X^2 + X?

1) Makes work easier and faster

2) It can hold huge amount of information

3) Reliable

4) Information management

5) Accuracy

6) Improve information

This can easily be integrated by substitution.

Integrate[(6x3+8)418x2 dx]

let u=(6x3+8)

du/dx= 18x2

du=18x2 dx

Substituting u in gives...

Integrate [u4 du] = (1/5)(u5) + C

Substituting x back in gives..

(1/5)(6x3+8)5 + C

no.

Because this equation has complex roots, you need to use complex numbers. The easiest way is to use the quadratic formula

This will give you (-3 +/- (-23)1/2 ) / 8.

Thus, the answer is -3/8 + i(23)1/2 and -3/8 - i(23)1/2

Giving you factors of (x + (3/8 + i(23)1/2 ))(x + (3/8 - i(23)1/2))

A zero of a function is where it crosses the X-Axis. Multiple zeroes mean that the function crosses the X-Axis more than once. They are also known as roots.

there is an infinte amount of ordered pairs in this equation

a few examples could be...

(1,-3)

(2,-13)

(3,-23)

(234652,-2346513)

(-25,257)

(x^2 - 3x + 5)(x^2 + 3x + 5)

The period of the pendulum is (somewhat) inversely proportional to the square root of the length.  Therefore, the frequency, the inverse of the period, is (somewhat) proportional to the square root of the length.

Seven and seven thousandths in standard form is 7.007 × 100

It depends on what calculator you are using. Often, shift log is inverse log, or natural log, but it could have other meanings. Please restate the question and specify the model number of the calculator.

It is: (-5)4 = 625

there is 116 ones in the 1000 digits of pi. heres a site with the answer

http://www.eveandersson.com/pi/precalculated-frequencies

100x - 89x = 110

∴11x = 110

∴x = 10

In more detailed explanation;

The first line means "100 times x minus 89 times x equals 110"

We can apply the distributive rule here. Both "100x" and "89x" are divisible by x. This means we can factor it out of both terms giving us the expression:

x (100 - 89) = 110

We can then subtract 89 from 100, giving us:

x(11) = 110

or:

11x = 110

Finally, both sides are divisible by 11, so we can divide it from both sides, giving us:

x = 10

The two inequalities define a region of the coordinate plane: there is no unique solution.

(that weird integral or antiderivative sign) x^(-6/5) dx =

-5*x^(-1/5)

ill say a positive number

you just used it in a sentence... How do you use mathematical in a sentence? is a sentence