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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 the answer to -12x equals 72?
We'll go ahead and find the answer, even though we're not completely convinced
that you know what the question is.
-12x = 72
Divide each side of the equation by -12:
x = -6
How do you find the value of x in 17Xequals 17 plus x?
17x = 17 + x
Subtract x from both sides.
16x = 17
Divide each side by 16.
x = 17/16 or 1 and 1/16 or 1.0625
Check it.
17 x 1.0625 = 18.0625
17 + 1.0625 = 18.0625
It checks.
How do you plot 3x minus 4y equals 4?
Put it into slope intercept form and then proceed to use your favorite method of graphing.
slope-intercept:
y = -3x + 1
How do you factor 2x2 plus 10-9x equals 0?
2x2 + 10 - 9x = 0 or 2x2 - 9x + 10 = 0
So (x - 2)*(2x - 5) = 0
What is the answer for 6x plus 3 in factoring?
6X + 3
3(2X + 1)
==========( all the factoring I see to do here )
7x + 5 + 3x is [ 10x + 5 ].
That's the same thing as [ 2 times (5x + 1) ] .
The idea is to replace "x" by its value, to replace "y" by its value, and then to do the calculations.
How do you derestrict a SYM Jet50-Euro X?
hi there i have a sym jet 50 and i want to know the best way to deristrict it or to make it go faster does anyone have any surgestions?
How to solve for the Quadractic formula 5x2-3x-7 equals 0?
5x2 - 3x - 7 = 0 where a = 5, b = -3, and c = -7
x = [-b ± √b2 - 4(a)(c)]/2a
x = [-(-3) ± √(-3)2 - 4(5)(-7)]/2(5)
x = [3 ± √(9 + 140)]/10
x = (3 ± √149)/10
x = (3 ± 12.21)/10
x = (3 + 12.21)/10 = 15.21/10 = 1.521 or
x = (3 - 12.21)/10 = -9.21/10 = -0.921
The EXACT answer would be x = 3/10 ± √149 /10
Note: 149 is not divisable by a perfect square
Why is X to the minus 2nd power equal to 1 over x to the 2nd power?
when a variable is to a negative power, the answer is always the variable with the additive inverse of the power, (ex. -2 changes to 2) and is divided by one.
such as X to the -5 power equals 1 over X to the 5th power. I will use the symbol "^" for power. Let's se a numeric example, with 10 instead of "x". Consider this sequence:
10^3 = 1000
10^2 = 100
10^1 = 10
10^0 = ???
10^(-1) = ???
10^(-2) = ???
How should this sequence be completed? In the left-hand column, the exponent decreases one at a time; in the right-hand column, the number decreases by a factor 10 each time. It seems logical to continue this pattern - so the missing question marks can be replaced by 1, 0.1, and 0.01.
More specifically, several laws for powers continue being valid if these definitions are used (a^0 = 1; a^(-b) = 1/a^b). For example, the addition of exponents: x^a * x^b = x^(a+b) continues being valid, even if a or b, or both, are negative.
It is only defined that way; there is no way to "prove" it. The common definition, however, turns out to be very useful.
What is the slope x 4y equals 12?
I presume that since you labeled this as a Calculus problem that you mean x * 4y = 12?
x * 4y = 12 --->
4y = 12 / x --->
y = 3 / x --->
y = 3 * x^(-1)
You will notice that this function is not a line, but a curve. The slope will be different at different points on the line. Thus, we can't find the slope of the entire function, but we CAN find a function which gives us the slope of a tangent line at any point on the function. We do this by taking the derivative.
For f(x) = a * x^(n)
f'(x) = a * n * x^(n-1)
Using a = 3 and n = -1, we have:
y = f(x) = 3 * x^(-1)
dy/dx = f'(x) = 3 * -1 * x^(-1 - 1) = -3 * x^(-2)
So your answer will be:
dy/dx = -3 * x^(-2)
