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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
Can 20 over 132 be simplified?
20/132
factor out a 4
4*5/4*33
as the factor 4 appears in both numerator and denominator once each it can be eliminated
= 5/33
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If: 850 = 0.30x
Then: x = 850/0.30 = 2833.333 ... recurring
What is the third iterate of the expression 2X plus 2 when X initially equals 1?
22.
The iterates are 1, 4, 10, 22, 46, 94, ...
How do you answer 2x plus 6y equals 32 and 5x-2y equals 12 using subtitution?
First, change 2x+6y=32 to x+3y=16. Then solve for x, which is x=-3y+16. Then substitute -3y+16 as x into 5x-2y=12 and solve for y.
5(-3y+16)-2y=12
-15y+80-2y=12
-17y+80=12
-17y=-68
y=4
Then substitute 4 as y in either equation to solve for x.
5x-2(4)=12
5x-8=12
5x=20
x=4
The answer is x=4 and y=4, or (4,4)
What is the derivative of x plus root x?
Derivative of x = 1, and since sqrt(x) = x^(1/2), derivative of x^(1/2) = (1/2)*(x^(-1/2))
Add these two terms together and derivative = 1 + 1/(2*sqrt(x))
x+x/2 = 700
Multiply all terms by 2 to eradicate the the 2 denominator:
2x+x = 1400
3x = 1400
Divide both sides of the equation by 3 to find the value of x:
x = 466 and 2/3
What is an inverse of a function?
The opposite of another function - if you apply a function and then its inverse, you should get the original number back. For example, the inverse of squaring a positive number is taking the square root.
What number is missing out of the first thrity digits of pi?
There is no 0 in pi until the 32nd digit.
What is -3x plus -18 equals 2x plus 7?
-3x + (-18) = 2x + 7
+18 +18
-3x = 2x +25
-2x -2x
-5x = 25
----- -----
-5 -5
x=-5
*------- equals a division line
2x plus 1divided by3x-2 equals 0.9?
2x + 1
_____ = 0.9
3x - 2
0.9 * ( 3x - 2) = 2x + 1
2.7x - 1.8 = 2x + 1
2.7x - 2x = 1 + 1.8
0.7x = 2.8
x = 2.8/0.7 . ....... . X = 4
Is 4 over x plus 3 over y equals 2 linear or nonliner?
Multiply through by xy to bring terms in x and y to the top, and you find an xy term popping up as well. So it's non--linear.
On the other hand if you plot (1/y) vs (1/x) it is linear in terms of those particular variables
What is the real value of x in the equation log345 - log35 log7x?
This isn't an equation because there is no "=" sign present". If we choose to put one before the last term then log345 - log35 is just log (345/35), and that is equal to log7x, so then 345/35 = 7x so that x is 345/(35x7) or 69/49
As y is inversely proportional to x, the equation relating x to y is given by:
y = k/x
where k is the constant of proportionality.
Using this we can find expressions for the value of y when x = 2 and x = 6 in terms of k:
x = 2 → y = k/2
x = 6 → y = k/6
The difference between these is k/2 - k/6 = 3k/6 - k/6 = 2k/6 = k/3
But this, we are told is 5; thus:
k/3 = 5
→ k = 15
Thus y = 15/x
Now that we have found the equation relating x to y, we can plug in the value for x = 4 and find the value of y:
The value for y when x = 4 is y = 15/4 = 3.75
