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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 inverse of y equals 3X3?
Since the equation is in terms of x, you need to switch the x's and y's, and then solve it for y again.
y=3x^3 --> x=3y^3 --> y=(x/3)^(1/3)
4x+5 = 8x+10
But you are saying
4x+5 = 8x+4
If this were the case, 8x+10 = 8x+4, and so 10=4
Thus there is no possible solution for X.
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Honk! Go to your room.
8x + 4 = 4x + 5
Subtract 4x from each side:
4x + 4 = 5
Subtract 4 from each side:
4x = 1
Divide each side by 4:
x =1/4
Check:
Left side: 8x + 4 = 8/4 + 4 = 2 + 4 = 6
Right side: 4x + 5 = 4/4 + 5 = 1 + 5 = 6
6 = 6 yay!
How do you factor 16 plus 6x minus x2?
16 + 6x - x2 = 16 + 8x - 2x - x2 = 8*(2 + x) - x*(2 + x) = (8 - x)*(2 + x)
Why is natural log given the initials ln instead of nl?
Euler came up with the log, and being Swiss, would've spoken french. In French the natural log would be le logarithme naturel, and his notation would've just caught on. I might be wrong, I've not really looked this up, just seems like a logical assumption...
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)
