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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
Largest volume of a cylinder inscribed in a cone of semivertical angle x?
(4/27)*pi*R3*tan(x)
R being the radius of the base of the cone.
X squared plus 2x plus 40 equals x squared-x plus 190 what is the value of x?
x^2+2x+40 = x^2-x+190
Subtract x^2 from both sides
2x+40 = -x+190
Add x to both sides
3x + 40 = 190
Subtract 40 from each side
3x = 150
Divide both sides by 3
x = 50
Solving 2x plus y equals 10 and y equals x-5 subtitution?
2x+x-5 = 10
2x+x = 10+5
3x = 15
x = 5 and y = 0
What is the soultion to the equality of x2 25?
That's not an equality, since it doesn't have an equal sign.
What is the rule if x is 80 and y is 1?
There are infinitely many rules. SOme of these are:
y = x/80
y = 80/x
y = x + 79
y = 81 - x
y = sqrt(x+1) - 8
Equations: 7x-8y = 9 and 11x+3y = -17
Multiply all terms in the 1st equation by 11 and all terms in the 2nd by 7
So: 77x-88y = 99 and 77x+21y = -119
Subtract the 1st equation from the 2nd equation: 109y = -218 => y = -2
Through substitution the solutions are: x = -1 and y = -2
Quarters struck (not "printed", btw) in Philadelphia prior to 1980 did not carry mint marks. The "rope" you describe is almost certainly some form of damage that occurred after the coin was released to circulation. Unfortunately that means it's only worth its face value.
How so you slove y equals 6x and 2x plus 3y equals -20 by using the system of substitution?
To solve a system of equations using substitution you solve one of the equations for one of the variables then substitute that into the other equation to solve for the other variable.
For example.
y = 6x
2x + 3y = -20
The first equation has already been solved for y. So, you simply substitute that into the second equation.
2x + 3(6x) = -20
2x + 18x = -20
20x = -20
x = -20/20 = -1
Now you have solved for x. You can substitute your answer for x back into the first equation to solve for y.
y = 6x = 6(-1) = -6
Putting it all together...
x = -1
y = -6
What is the slope of 8x plus 2y equals 5?
You have to get your equation into slope intercept form. Slope intercept form is y=mx+b
Now use algebra on your equation to get "y" on the left side and "x" and the numbers on the right side..
2y = 5 - 8x
y = -(8/2)x + (5/2)
y = -4x + 2.5
Now it is slope intercept form. In the previous y=mx+b equation your m=slope
Therefore in your equation m=-4 so your slope is -4/1
This means it go down four units and left one unit. This is rise over run.
What is the remainder when 2x cubed -3x squared plus x plus 5 is divided by 2x -1?
f(x) = 2x3-3x2+x+5
f(x) becomes f(0.5) because 2*0.5-1 = 0
f(0.5) = 2*(0.5)3-3*(0.5)2+0.5+5 = 5
So the remainder is 5
What is x in this equation 7x plus 8 equals 5x plus 32?
7x + 8 = 5x + 32
7x = 5x + 24
2x = 24
x = 12
hope this helps
Why is process of finding a first derivative called differentiation?
When finding the first derivative, you calculate the slope of the curve at a point by determining the ratio of delta y over delta x. You make delta x and delta y smaller and smaller; in fact, you take the limit of delta y over delta x as delta x goes to zero.
At this zero limit point, delta y is called dy, and delta x is called dx. They are also called differentials, hence the term differential calculus. They represent the rate at which x and y change at various x's and y's.
Since we are working with differentials, the process of determining the slope, also known as the first derivative, is call differentiation.
