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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 -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
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))
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
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)
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 third iterate of the expression 2X plus 2 when X initially equals 1?
22.
The iterates are 1, 4, 10, 22, 46, 94, ...
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
You know that 15 x 16 equals 240 how can you use this to work out 16 x 16?
Simple. 15 x 16 is really saying add 16 to itself 15 times. So when you change the problem to 16 x 16, you just add another 16.
15 x 16 = 240
16 x 16 = 256
2x > -6 and x - 4 < 3
x + 3 > 2x + 1 and -4x < -8
-6 < x + 3 < 6
-3x > -6 or x - 5 < 2
x - 2 > 2x + 1 or 10 > -2x + 2
can someone please help me!
When the equation of the line is written is standard form, ie y = mx + c, then the slope is m.
Here, y = -3x + 5 so m = slope = -3
