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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
Inconsistent linear equations in two variables.
What is the rate of change in position or rate of motion?
Velocity, which is different than speed in that it has a directional component to it.
How do you solve the quadratic equation 42 equals y2-y by factoring?
Rewrite equation as:
y2-y-42=0
So you need two numbers that:
multiply to -42 and
add to -1
Those two numbers are: -7 and 6
so to factor you get:
(y-7)(y+6)=0
y=7 y=-6
If X produces 8000 articles in 4 hours, it produces (8000/4) = 2000 articles per hour.
If Y produces 8000 articles in 8 hours, it produces (8000/8) = 1000 articles per hour.
Therefore, the total number of article produced in six hours is: 2000+1000+2000+1000+2000+1000=9000. Machine X (which is on in the seventh hour then works for half an hour to produce 1000 more articles, so the total time is 6.5 hours.
How do you solve 3 dimensional equations?
You can solve the system of equations with three variables using the substitute method, or using matrix operations.
What is the radius for a circle with the equation x squared y squared 25?
Equations of circles are usually in x2+y2=(radius)2 form, so if you have
x2 + y2 = 25
x2 + y2 = 52
then radius = 5.
How do you do the elimination method of 2X plus 3Y equals 1?
Usually elimination is used on two equations and is called linear combination. You could solve for "y." That is customary.
2x+3y=1
3y=-2y+1
y=(-2/3)x+1/3
What is the value of x in the following equation ln x equals 4?
The answer is;
54.6
But I used my TI-84 to get that answer and I can not remember how to do these.
What are the points of intersection of X equals y squared plus 2y?
More values are required to solve this question since there are only two unknowns given. To solve this equation, there has to be only a single unknown value. In this example, assuming x is 0,
0 = y2 + 2y
0 = y (y+2)
y = 0 or y+2 = 0
y = 0 pr y = -2
Therefore, in this case, the points of intersection are (0,0) and (0,-2)
If x=y
Y = y2 + 2y
0 = y2 + y
0 = y(y+1)
y = 0 or y+1 = 0
y = 0 or y=-1
When y=0
x=0
When y=-1
x=-1
Therefore, in this case, the points of intersection are (0,0) and (-1,-1)
Note: to solve quadratic equations, cubic equations or any equation with any unknowns not to the power of 1, you must get a value of 0 on one side of the equation before you can get the final values.
What ordered pairs is not a solution to 2x 2y equals 4?
Great. A multiple choice question without the choices.
(y-y)/(x-x) is very simple. y-y is obviously 0. The same goes for x-x. This results in a final fraction of 0/0. This could be considered 1 because if you think about it like 2/2=1, then you would get 0/0 =1 since the numerator and the denominator are the same. It could also be considered 0 because the numerator is 0 which obviously means there is nothing.
However, the answer to this is "undefined" because anything divided by 0 is undefined.It's a linear equation in 'x'.
To solve it:
x + 19 = 42
Subtract 19 from each side of the equation:
x = 23
