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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 the solution to this system of equation y-3x-2 6x2y-4?

There is none because its not an equation but some kind of algebraic expression.

How do you factor 2x squared minus 77x plus 119?

2x^2-77x+119

It is not factorable if you are looking for integral factors (whole numbers). You might be able to use the quadratic formula if you wish to solve for the zeros (x-intercepts) of it.

What is dydx of sincostanx?

If y = sin(cos(tan(x)))

Using the chain rule: (f(g(x)))' = f'(g(x)).g'(x)

Then dy/dx = cos(cos(tan(x))).-sin(tan(x)).sec2(x)

= -cos(cos(tan(x))).sin(tan(x)).sec2(x)

Unfortunately I don't think this can be simplified much more.

( sec = 1/cos )

How do you get the volume of an irregular and regular shape?

Any regular shape,like a cube or sphere, can be described mathematically and its volume can be calculated easily. An irregular shape, such as a rock can be mesured by displacment of water, or by scanning it in three dimensions.If the object's density is known, it need only be weighed.

volume is a amount of mater space takes up TY! PEOPLE!

How do you factor 2x squared minus13x plus 20 equals 0?

Usually the easiest way to solve this kind of problem is to find two numbers whose sum is equal to the coefficient of the middle term, and whose product is equal to the product of the coefficients of the first and last terms. So in this case, we would want a product of 40, and a sum of -13. The only numbers that meet that condition are -8 and -5, so we'll use those, breaking the middle term down into two separate terms:

2x2 - 13x + 20 = 0

∴ 2x2 - 8x - 5x + 20 = 0

Now you can take a common factor out of both the first two terms and the last two terms, and group the like terms together, resulting in the answer you seek:

∴ 2x(x - 4) - 5(x - 4) = 0

∴ (2x - 5)(x - 4) = 0

∴ x ∈ {2.5, 4}

How do you figure out the intervals of increasing and decreasing of the function y equals x divided by square root of x squared then plus one?

The intervals are determined by when the derivative is positive or negative, because the derivative is the slope and a negative slope means the function is decreasing. The function y=(x/sqrt(x2))+1, however, can be rewritten as y=x/absolutevalue(x) + 1, and as such will be represented as a pair of parallel lines, y=0 for x<0 and y=2 for x>0. As the lines are horizontal, the function is never increasing or decreasing.

How do you graph the equation y equals x - 3?

y = x - 3

The graph is a straight line, passing through the point [ y = -3 ] on the y-axis,
and having a slope of [ 1 ].

What is the answer to slope to -5y plus 2x equals -10?

-5y +2x = -10

-5y = -2x -10

y = 2/5x +2

So the slope = 2/5 and the y intercept = 2