0
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
r + 2t = -3 . . . . (A)
3r - 4t = -9 . . . . (B)
2*(A) + (B): 2r + 4t + 3r - 4t = -6 - 9
5r = - 15 so r = -3
substituting in (A), t = 0
So the answer is (r, t) = (-3, 0)
r + 2t = -3 . . . . (A)
3r - 4t = -9 . . . . (B)
2*(A) + (B): 2r + 4t + 3r - 4t = -6 - 9
5r = - 15 so r = -3
substituting in (A), t = 0
So the answer is (r, t) = (-3, 0)
r + 2t = -3 . . . . (A)
3r - 4t = -9 . . . . (B)
2*(A) + (B): 2r + 4t + 3r - 4t = -6 - 9
5r = - 15 so r = -3
substituting in (A), t = 0
So the answer is (r, t) = (-3, 0)
r + 2t = -3 . . . . (A)
3r - 4t = -9 . . . . (B)
2*(A) + (B): 2r + 4t + 3r - 4t = -6 - 9
5r = - 15 so r = -3
substituting in (A), t = 0
So the answer is (r, t) = (-3, 0)
How do you solve x plus 3y equals 6?
You can't. From that much information, you can't figure out the values for both 'x' and 'y'.
All you can tell is that whatever they turn out to be:
x = 6 - 3y
and
y = x/3 - 2.
In order to calculate what 'x' and 'y' both are, you need another equation besides
x + 3y = 6.
There's nothing wrong with that one, but you need one more.
You need the same number of equations as the number of unknowns.
How do you solve 3x over 8 equals 3x over5 minus 9?
I think the question is:
(3/8)x = (3/5)x - 9
Simplify by dividing everything by 3
x/8 = x/5 - 3
Get rid of the fractions by multiplying everything by 40.
40.x/8 = 40.x/5 -3.40
5x = 8x -120
Rearrange
120 = 8x - 5x
120 = 3x
x = 120/3 = 40
What is 12 as a fraction in simplest form?
1.2 is a fraction. It is a fraction in decimal form rather than in the form of a ratio. However, that does not stop it being a fraction. And, being a decimal, there is no simpler form. Its rational equivalent is 12/10 which can be simplified to 6/5.
Let x, y, and a be sets and X,Y,x',y' be elements.
Denote X *x as X in (is an element of) x, I as intersection, and U as union.
If we can show that for all X *x, X *y (and similarly, if for all Y *y, Y *x), then we are done.
Case 1) xIa is empty
Then x, a and y, a have no elements in common. So, if xUa and yUa are equal, then for all y' *yUa but y' not*a, y' *y. Since xUa and yUa are equal, either y' *a or y' *x. But we supposed y' is not*a, so y'*x. Similarly, for all x' *x, x'*y. QED
Case 2) xIa is non-empty
Define a' as a - {x| x *xIa}. Then xIa' is empty, and you can use the same prove as above, replacing a with a'. QED
How do you solve x times x equals 5.4 solve for x?
X * X = 5.4
multiply X's
X^2 = 5.4
take square root of each side
X = 2.32379
4mn + 8 is an expression: it is not an equation (or inequality) and therefore there is nothing that can be solved.
What value for x makes the following equation TRUE 6x 5 equals 31 a 1 b 2 c 5 d 6?
If that's 6x - 5, x = 6
How do you graph the equation y -x 3?
Start at the origin (0, 0) plot a mark there, then move down 3 and to the right 1 (1, -3) plot a mark there, move down 3 and to the right 1 again (2, -6) and plot a mark there then with a ruler make a line threw the three marks and its graphed!
What is the difference between Integration and differentiation?
integration is reverse of differentiation and vice versa
How many diagonals in a 9 sided polygon?
It depends. It doesn't have to always be the same shape. So it can be 0, it can be 1, as long as it has straight lines and is a closed figure, it's a polygon.
* * * * *
What? A polygon with n sides has n*(n-3)/2 diagonals. Simple as that. So a 9 sided polygon has 9*6/2 = 27 diagonals.
How would you solve the integral of 1 plus tan2x plus tan squared 2x?
Integral of 1 is x Integral of tan(2x) = Integral of [sin(2x)/cos(2x)] =-ln (cos(2x)) /2 Integral of tan^2 (2x) = Integral of sec^2(2x)-1 = tan(2x)/2 - x Combining all, Integral of 1 plus tan(2x) plus tan squared 2x is x-ln(cos(2x))/2 +tan(2x)/2 - x + C = -ln (cos(2x))/2 + tan(2x)/2 + C
