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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
How about derivative of principal applicant?
Placing a question mark at the end of a phrase does not make it a sensible question. Try to use a whole sentence to describe what it is that you want answered.
What is the value of x and y when x2 divided by y2 equals 45?
There could be a few values. 45 divided by 1 could work, and X=root 45 and Y=1
There are two variables, so two equations would be needed to determine the values. Otherwise, there are many solutions.
B2 -4ac in the quadratic equation ax2 plus bx plus c equals 0?
Full equation is (-b +/- sqrt(b2 - 4ac))/2a.
Try it with x2 - 2x - 3, where a = 1, b = -2 and c = -3...
How do you solve x for 2 minus 2 over 3x equals 4 over 5x?
2-2/3x = 4/5x
The common denominator of 3x and 5x is 15x so multiply all terms by 15x in order to eliminate the fractions:
30x-10 = 12
30x = 22
Divide both sides by 30 in order to find the value of x:
x = 22/30 = 11/15 in its lowest terms
Substituting the value of x into the original equation: 12/11 = 12/11
Therefore the solution is correct
Range
Why do come function graphs have just points and some have a line connected?
Most functions are continuous (connected line), and not just two points... 2 points are simply just coordinates on a graph, and would be very hard (perhaps impossible) to make into a function (unless you have a restricted domain)
I may be wrong, but I don't think I am
A function has to be a graph that can be expressed through an equation, and only has a max of one y coordinate for each x coordinate, although it may have zero
What is the vertex form for y equals x to the secound power plus 4x?
set to 0
X^2 + 4X = 0
you must complete the square. halve the coefficient of the linear term (4X) and square it and add it to the other side.
(X + 2)^2 = 4
now subtract the 4 from both sides
(X + 2)^2 - 4 = 0
The graph of y = x2 (vertex (0,0) is shifted 2 units to the left, and 4 units down.
the vertex is....
(-2,-4)
my TI-84 confirms this answer
or
Since x = -4/2 = -2 is the equation of the axis of symmetry, and the vertex lies on it, then the x-coordinate of the vertex is -2 and the y-coordinate is f(-2).
f(-2) = (-2)2 + 4(-2) = 4 - 8 = -4
thus, the vertex is (-2, -4)
What is the measure of these angles of a triangle x plus 4x plus x plus 6 equals?
The three angles are 'x', 4x, and (x+6) .
We know that the sum of the interior angles of every triangle is always 180°,
so
x + 4x + (x+6) = 180°
Remove parentheses on the left side:
x + 4x + x + 6 = 180°
Subtract 6 from each side:
x + 4x + x = 174°
Combine the 'x' terms on the left side:
6x = 174°
Divide each side by 6:
x = 29°
The three angles are:
'x' . . . . . 29°
4x . . . . . 116°
x+6 . . . . 35°
Check:
29° + 116° + 35° = 180°
What is the exact solution of 10 to the x power equals 97?
Take logs of both sides - you can use any base, to give the answer:
10^x = 97
→ log(10^x) = log(97)
→ x log(10) = log(97)
→ x = log(97) ÷ log(10)
If you use common logs (logs to base 10) - highly recommended in this case), then:
lg(10) = 1
→ x = lg(97)
Is 1- cos 2 x 1 plus cos 2 x equals sin squared x cos squared x an identity?
No, (sinx)^2 + (cosx)^2=1 is though
How would you graph an inequalities x-s less than or equal to y?
Mark a point on the x-axis as 's', then draw a solid line through this point, with a slope of 1. Then shade in the area above this line. The region above the line is shaded because if x-s < y then y > (x-s). The line is drawn as a solid line to represent that it can be equal, as well. At the point x=s, y = 0, which is where you marked s on the x-axis.
