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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 are the points of intersection of the line x -y equals 2 with the curve x squared - 4y squared equals 5?

If: x-y = 2 then x = 2+y

If: x^2 -4y^2 = 5 then (2+y)^2 -4y^2 -5 = 0

Removing brackets: 4+4y+y^2 -4y^2 -5 = 0

Collecting like terms: 4y-3y^2 -1 = 0

Dividing all terms by -1: 3y^2 -4y+1 = 0

Factorizing the above: (3y-1)(y-1) = 0 meaning y = 1/3 or y = 1

Points of intersection by substitution are at: (7/3, 1/3) and (3, 1)

What is the difference between copying a range and moving a range in excel?

Usually, in computer science, "moving" is equivalent to "copying" something, then deleting the original. In other words, after copying something, you have two copies of the thing you copy; if you move something, only one, at the new place. However, specifically in Excel (and probably other spreadsheet programs as well), when you move a cell or a range, any formulae that refer to the cell (or to one of the cells in the range) will be updated; thus, in this sense, moving is no longer equivalent to "copy, then delete the original". For example: Cell B1 has the formula "=A1*10". If you move the contents of cell A1 to A5 (you can do this in several ways; one is by selecting the cell, and dragging the border), then the formula in B1 will change to "=A5*10".

What is the equation of 5 over 8 x equals 30?

is it 5/8x or 5x/8

let me solve both ways

for 5/8x = 30

then x = 1/48

for 5x/8 = 30

x = 48

Does the graph x-y2 equals 1 represent x as a function of y?

X - Y^2 = 1

- Y^2 = - X + 1

Y^2 = X - 1

Y = (+/-) sqrt(X - 1)

now, X is represented as a function of Y. Function values are generally Y values.

Does x have 2 or 4 lines of symmetry?

The letter x has 4 lines ofsymmetry. (horizontal, vertical, and the two diagonals)

How do you size a ac condenser for a home?

There is only one way to properly size an ac unit or a furnace. That is by performing a load calculation. This is a process that takes into account the construction features of the home. It is also based on weather data for the specific location of the home. For more information you can click on the load calculation page at http://www.hvac-for-beginners.com

What is the structure and biological function of one structural and one storage polysaccharide?

Polysaccharides are mainly used for energy storage because they are big, and are able to shift into sugars if needed.

Graph the equation y equals 8?

The graph of the equation y=8 is a horizontal line through the y-intercept of 8. This is because since y=8, any point on the graph will have a y-coordinate of 8. This is why it is a horizontal line through (0,8).

How do you factor 2x to the second power minus 5x minus 3 equals zero?

2x2 - 5x - 3 = 0

The coefficients here are (2,-5,-3) so you want two numbers whose multiple is 2*(-3) = -6 and whose sum is -5. The numbers are 1 and -6.

So 2x2 - 6x + x - 3 = 0

2x(x-3) + 1(x-3) = 0

(2x+1)*(x-3) = 0

Answer to 8x plus 2 equals 50 plus 3x?

Balance the equation.

8x + 2 = 50 + 3x
8x - 3x + 2 = 50
5x + 2 = 50
5x = 50 - 2
5x = 48
x = 9.6

... are you sure that you asked the question correctly? Normally, basic Algebra works out to whole numbers....

What is X plus 5 equals x minus 5?

x+5=x-5 can be written as
x=x-5-5 so x-x=-10 or 0=-10

we end up with 0=-10 which is not true. This tells us the there is no solution.
One way to see this is think of the line y=x+5, this is a line with slop 1 and y intercept 5.
Now the other line y=x-5 has slope 1 also and y intercept -5.
When we set the two equations equal to one another, we are asking, what is the intersection of the graphs of the two lines. Since they have the same slope and different y intercepts, the lines are parallel and hence have no intersection.

How matrix X1 X2 equals matrix X1 X2?

i think its pretty much the same thing because matrix X1 X2 IS ACTUALLY X1 X2

What is Trager psychophysical integration?

Trager psychophysical integration therapy, also known as the Tragerwork system of physical integration, is a combination of hands-on tissue mobilization, relaxation, and movement reeducation called Mentastics.

How do you simplify 2x plus 4 over 2?

(2X + 4)/2

factor out 2 from numerator

2(X + 2)/2

eliminate 2; top and bottom

X + 2

is the simplest form

12 plus x if x 9?

Possibly 21, but it is difficult to be sure because the browser does not support symbols and so we cannot see exactly what you asked.

How do you find the solution to system of equations?

Parenthesis, exponents, multiplication, division, addition, subtraction. PEMDAS

What are the x solutions for the equation 10x2 64 equals 36 plus 6x2?

If the 64 has a minus sign, then the solution is x = +/-5

Simplifying gives 4x squared = 100 ie x squared = 25...

What does the temperature tell you about the particles of a substance?

Temperature is the measure of the internal kinetic energy of a body.

How are the graph of an equation and the set of all solutions of an equation related?

The coordinates of every point on the graph, and no other points, are solutions of the equation.

What are the factors of 3X squared minus 14X plus 8?

(x - 4)(3x - 2)

3X2 - 14X + 8 = 0

X = - b (+/-) sqrt(b2 - 4ac)/2a

a = 3

b = - 14

c = 8

X = - (- 14) (+/-) sqrt[(- 14)2 - 4(3)(8)]/2(3)

X = 14 (+/-) sqrt(196 - 96)/6

X = 14 (+/-) sqrt(100)/6

X = [14 (+/-) 10]/6

X = 4

----------

X = 2/3

-----------------check one at least

3(4)2 - 14(4) + 8 = 0

48 - 56 + 8 = 0

0 = 0