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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 anti-derivative of 5 to the x power?
ex and ln(x) are inverse functions.
With this you can get 5x = eln(5^x)
Therefore you can anti-differentiate this to get eln(5^x)/(ln(5x))
Which equals 5x/ln(5x)
What is the trinomial for x square plus 2x?
Complete the square.
X^2 + 2X
halve the linear term ( 2 ), square it and add to polynomial
X^2 + 2X + 1
Xsquared minus 7x plus 10 equals 28?
x2 - 7x + 10 = 28; whence,
x2 - 7x - 18 = 0, and
(x - 9)(x + 2) = 0.
The above is true exactly when, either,
x - 9 = 0, or
x + 2 = 0.
Therefore, the solution is:
x = 9 or -2.
Checking,
92 - (7)(9) + 10 = 81 - 63 + 10 = 28; and
(-2)2 - (7)(-2) + 10 = 4 + 14 + 10 = 28;
verifying the solution found above.
mensos yo no me la seee
Solve X -2x plus 10 plus 4x equals to 70?
x - 2x + 10 + 4x = 70
Combine like terms: 3x + 10 = 70
Subtract 10 from both sides: 3x = 60
Divided both sides by 3: x = 20
Does a short or a long pendulum have a longer period?
The time of swing of a pendulum is T = 2π √ (l/g) where l is the length of the pendulum.
As T ∝√l (Time is directly proportional to the square root of l) then, the longer the pendulum, the greater is the period. Therefore longer pendulums have longer periods than shorter pendulums.
14y - 51 = 187 + 4y
Subtract 4y from each side:
10y - 51 = 187
Add 51 to each side:
10y = 238
Divide each side by 10:
y = 23.8
How solve 7w plus 4-3w equals 15?
7W + 4 - 3W = 15
gather the w's together
4W + 4 = 15
subtract 4 from each side
4W = 11
divide each sides integers by 4
W = 11/4
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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)
What will be the formula when mean and variance of 3 population are given?
The formula for WHAT? Since you have not bothered to specify that crucial bit of information, I cannot provide a more useful answer.
The formula for WHAT? Since you have not bothered to specify that crucial bit of information, I cannot provide a more useful answer.
The formula for WHAT? Since you have not bothered to specify that crucial bit of information, I cannot provide a more useful answer.
The formula for WHAT? Since you have not bothered to specify that crucial bit of information, I cannot provide a more useful answer.
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
