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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 perpendicular to y equals -8x plus 6?
The equation of a line that is perpendicular to 3y = -x + 9 and that has a y intercept of 6 is y = 3x + 6.
The slope of the first line is -1/3, from the slope-intercept form y = mx + b, or y = -x/3 + 3. The perpendicular slope is 3, by negating and inverting -1/3. Add the intercept to the slope-intercept form and you get y = 3x + 6.
What is the product of a X 10b when b equals 0?
Any number multiplied by zero is zero. (10b also means 10 times zero.)
Can a fraction be put into a ratio without changing it's form?
A fraction is a ratio... even when you don't change its form.
1/2 is "one half/ one over two/ one to two ratio"
How do you solve x-2y equals 5 and x equals y plus 2 with method of substitution?
OK, one way to solve systems of linear equations is using substitution. You have:
x-2y=5 and x=y+2
The first step is to solve for one of the variables (x or y) on the easiest-to-solve equation. However, they have already solved for x in the second equation:
x=y+2
Now substitute y+2 into every x on the other equation:
x-2y=5
(y+2)-2y=5 ;Plug in y+2 into all the x's
y+2-2y=5 ;Distribute the "understood" 1
2-y=5 ;Combine the y's
-y=3 ;Subtract 2 to both sides
y=(-3) ;Divide both sides by -1
Now that you have what y is equal to, plug that back into x=y+2:
x=(-3)+2 ;Plug in -3 for y
x=-1
Your solution for both equations is (-1,-3).
What is differential calculus?
That is the part of calculus that is basically concerned about calculating derivatives. A derivative can be understood as the slope of a curve. For example, the line y = 2x has a slope of 2 at any point of the line, while the parabola y = x squared has a slope of 2x at any point of the curve.
6x - 3 = 2x + 1
Add 3 to each side:
6x = 2x + 4
Subtract 2x from each side:
4x = 4
Divide each side by 4:
x = 1
What is the slope and y interecpt of y equals -2x plus 3?
Slope = -2 and y-intercept = 3 In general, if you write the equation of a straight line in the form y = mx + c then the slope of the line is m and the y-intercept is c.
How do you differentiate x sinx with respect to y?
If you actually mean "... with respect to x", and that y is equal to this function of x, then the answer is:
y = x sin(x)
∴ dy/dx = sin(x) + x cos(x)
How do you factor x minus 1 cubed minus x plus 1 cubed?
(x - 1)(x - 1)(x - 1) - (x + 1)(x + 1)(x + 1)
What is 6x2-2x plus 36 equals 5x2 plus 10x?
6x2-2x+36 = 5x2+10x
6x2-5x2-2x-10x+36 = 0
x2-12x+36 = 0
(x-6)(x-6) = 0
x = 6 or x = 6 It has two equal roots.
What is the relationship between 2 cooking square pans The sizes are 10 x 10 x 2 and 8 x 8 x 2?
200:128 or 16:25
i.e. to switch from the small to the large you would need 1.5625 times as much batter.
say, 1 and a half cup flour instead of 1
