0
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 the slope of the following equation y equals 15 x plus 4?
The slope of the line that represents the graph of that equation is 15.
The first successful English colony in America was established in 1492 1620 1607 or 1630?
The first successful English colony in America was established in 1607
How do you solve 5 raised to 8-2x equals 25?
Use natural logs.
5^(8-2X) = 25
ln5^(8-2X) = ln25
8-2X ln5 = ln25
8-2X = ln25/ln5
8-2X = 2
subtract 8 from each side
-2X = -6
divide each side by -2
X = 3
check
5^(8-3(2)) = 25
5^2 = 25
25 = 25
checks
What does x equal in X over -5 plus 4 equals 24?
X/-5 + 4 = 24
multiply through by -5
X - 20 = -120
add 20 to each side
X = -100
check
-100/-5 + 4 = 24
20 + 4 = 24
checks
Writing equations in questions is problematic - some symbols regularly get eliminated.The integral of e to the power x is: e to the power x + C
If your expression contains no variables, for example e times e, or e to the power e, then the entire expression is a constant; in this case, the integral is this constant times x + C.
How many real solutions are there in the equation x2 plus 2x- 4 equals 0?
X2 + 2X - 4 = 0
Use the discriminant to find out.
b2 - 4ac
a = 1
b = 2
c = - 4
22 - 4(1)(- 4)
4 + 16 = 20 > 1
=============so,
Two real solutions.
What are the x and y values for y equals 0.1e2x-4?
When an equation has two variables, there are an infinite number of (x,y) pairs
that solve it. The equation can be graphed as a straight, curved, or wiggly line,
and every point on the line is a solution of the equation.
There's no single (x,y) point until you have two separate equations. Then
the solution is the point ... or few points ... where their graphs intersect.
Can you integrate -cos x plus c?
Why not? Just a second integration. Drop the constant.
int[- cos(x)] dx
the negative implies - 1 and can be brought out side the integrand
- int[cos(x)] dx
= - sin(x) + C
==========
Fourier analysis began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions.
The attempt to understand functions (or other objects) by breaking them into basic pieces that are easier to understand is one of the central themes in Fourier analysis.
Fourier analysis is named after Joseph Fourier who showed that representing a function by a trigonometric series greatly simplified the study of heat propagation.
If you want to find out more, look up fourier synthesis and the fourier transform.
Graph the line perpendicular to 7x plus 10y equals 4.5?
7x + 10y = 4.5 : 10y = -7x + 4.5 : y = -x.7/10 + 0.45, the gradient of this line is -7/10
Two straight lines are perpendicular if the product of their gradients is -1.
Let the equation for the perpendicular line be y = mx + c
Then m x -7/10 = -1 : m = 10/7
The equation for the perpendicular line is y = x.10/7 + c
If the values of x and y for the point of intersection are provided then these can be substituted in the perpendicular line equation and the value of c obtained.
If appropriate, the equation can then be restructured to a format similar to the original equation.
4 x plus 3 equals 19 what is x?
4x + 3 = 19
Subtract 3 from each side:
4x = 16
Divide each side by 4:
x = 4
True
