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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 are the ratings and certificates for F-Zero X - 1998 VG?
F-Zero X - 1998 VG is rated/received certificates of:
Argentina:E
USA:E
Need help solving this arethmetic series?
There are no example metric series in the question on which to supply a possible answer.
1.67 days.
1,000,000 pennies / 60 = 16666.66667
Significant digits hace to be between 1 and 10 so you move your decimal 4 times to the left.
1.67 or 1.67 x 10^4
Or something like that .
Better AnswerThere are 86,400 seconds in a day. 1,000,000/86,400=11.574 days, that is 11 days, 13 hours, 46 minutes, 34 seconds. You can work out the significant digits however you'd like to.
What is the solution for x plus y equals 1 and -4x plus 2y equals -2?
OK, there's two ways to solve systems of linear equations. The first way is substitution and the second way is called elimination/addition, but we're only going to solve it this way (because it's hard to show the other way just with text).
Let's do the simplest first, the substitution. You have:
x+y=1 and -4x+2y=-2
Solve for one of the variables (x or y) on the first equation. For example, solve for y in x+y=1:
x+y=1
y=1-x ;Subtract x on both sides
Now substitute 1-x into every y on the other equation:
-4x+2y=-2
-4x+2(1-x)=-2 ;Plug in 1-x into all the y's
-4x+2-2x=-2 ;Distribute the 2
-6x+2=-2 ;Combine the x's
-6x=-4 ;Subtract 2 to both sides
x=(-4/-6) ;Divide both sides by -6
x=2/3 ;Simplify the fraction
Now that you have what x is equal to, plug that back into y=1-x:
y=1-(2/3) ;Plug in 2/3 for x
y=1/3
Your solution for both equations is ( 2/3 , 1/3 ).
I think what they may mean is "use washers to find the volume of the solid obtained when revolving the region bounded by y=x-2, y=0, x=10 about the y-axis".
Washers:
PI*INT(10^2-(y+2)^2)dy, y=0..8
=1408PI/3
Shells:
2PI*INT(x(x-2))dx, x=2..10
=1408PI/3
what you typed made no sense. please clarify your question. what is y x - 2 y 0 and x 10 supposed to mean?! you are missing a lot of equal signs and commas
3x+2=5x-y 3x-5x=-2-y -2x=-2-y x=1+y/2 y=2x-2 I can only stop until here because an algebraic equation with two different variables on the left-hand side and the right-hand side respectively has infinte solutions. I hope this will be of help to you. ;)
Ab = 25 CD
Integrate cos 3x over sin squared 3x?
okay I'll use a / to represent the fraction and F(x) as the integration sign
F(x)cos(3x)/sin2(3x)dx
- This problem requires substitution
- U=problem ; DU=anti-derivative
U=Sin(3x) ; DU=-(3)Cos(3x)
- note that U is not squared in the substitution
- also note that DU is multiplied by -3
- you will have to balance the above by canceling
- Rewrite the Equation with the substitutions/cancellations in place
- I have put in bold the changes necessary for substitution
F(x)-(1/3)DU/U2dx
- put the -1/3 of the DU behind the integration sign
- separate the fraction in the equation to make it easier
-1/3F(x)1/U2*DUdx
- to eliminate the fraction make the exponent on U negative
-1/3F(x)U-2DUdx
- integrate the function using the formula Nx=[1/(x+1)]N(x+1)
(-1/3) [1/(-2+1)] U(-2+1)
- simplify the equation
(-1/3)[-1]U(-1)
(1/3)U-1
- then plug in U (U=sin(3x))
(1/3)sin-1(3x)
Your Answer Is:
F(x)cos(3x)/sin2(3x)=(1/3)sin-1(3x)
Also written as:
1/[3sin-1(3x)] or -1/(3sin3x)
Assume you want to know what is the formula of the gradient of the function in multivariable calculus.
Let F be a scalar field function in n-dimension. Then, the gradient of a function is:
∇F = <fx1 , fx2, ... , fxn>
In the 3-dimensional Cartesian space:
∇F = <fx, fy, fz>
What is the use of successive differentiation?
There are several uses.
For example:
* When analyzing curves, the second derivative will tell you whether the curve is convex upwards, or convex downwards.
* The Taylor series, or MacLaurin series, lets you calculate the value of a function at any point... or at least, at any point within a given interval. This method uses ALL derivatives of a function, i.e., in principle you must be able to calculate the first derivative, the second derivative, the third derivative, etc.
How do you graph the equation y equals -1?
y=-1
No matter what value x has, y is always -1, so the graph is a horizontal line passing through (x,y)=(0,-1).
What is y equal x and y equal x plus 2?
That is irrelevant, there is not possible way y=xy, and there is no possible way xy=x.
Does the suspension material affect the period time of a pendulum?
No. Period does not depend on the suspending material. Since the expression derived is:
T = 2Pi(l/g)-1
Of course we rely on some conditions.
1) the string is torsion less
2) the amplitude of oscillation is to be small
3) some massive material is to attached so as to keep the string under tension.
How do you evaluate f x equals 3x plus 2 at f 2?
if f(x) = 3x + 2 and you're looking for f(2), just plug in 2 for x: f(2) = 3(2) + 2 = 6 + 2 = 8.
