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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 does 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 equals?
Either 10000000000, 10^(10) or ten billion. Depending on how you wish the answer to be
73.35+4.37+y
Add 4.37 to 73.35 to get 77.72.
(d)/(dy) 73.35+4.37+y=77.72+y
Since 77.72 does not contain y, the derivative of 77.72 is 0.
(d)/(dy) 73.35+4.37+y=0+(d)/(dy) y
To find the derivative of y, multiply the base (y) by the exponent (1), then subtract 1 from the exponent (1-1=0). Since the exponent is now 0, y is eliminated from the term.
(d)/(dy) 73.35+4.37+y=0+1
Combine all similar expressions.
(d)/(dy) 73.35+4.37+y=1
The derivative of 73.35+4.37+y is 1.
1
The golden ratio is not a ratio of two whole numbers but an irrational number. It is 0.5*(1+sqrt(5)). Because it is irrational you cannot find two whole numbers such that their ratio equals the golden ratio. All you can do is get closer and closer to it.
62/38 = 1.6315789
618/382 = 1.6178010 and so on.
How can you Solve this problem by substitution 6X- Y equals -9 4 plus 7X equals -Y?
We have two equations.
6x-y=-9 and -y=7x+4.
We substitue 7x+4 into the first equation and we have
6x+7x+4=-9 or 13x=-13 so x=-13/13 of -1
Now plug that into either equation and we have
-y=-7+4 or -y=-3 so y=3.
The solution is (-1,3)
No - because it can be represented as a ratio :
5.2 = 520/100 = 52/10 = 26/5 etc.
Any number that can be represented as a ratio of 2 integers is classified as a rational number (other than that you can't use 0 for the denominator)
What is the derivative of ln1 divided by x?
Given y=ln(1/x)
y'=(1/(1/x))(-x-2)=(1/(1/x))(1/x2)=x/x2=1/x
Use the chain rule. The derivative of ln(x) is 1/x. Instead of just "x" inside the natural log function, it's "1/x". Since the inside of the function is not x, the derivative must be multiplied by the derivative of the inside of the function.
So it's
1/(1/x) [the derivative of the outside function, natural log]
times
-x-2=1/x2 [the derivative of the inside of the function, 1/x]
This all simplifies to 1/x
So the derivative of ln(1/x) is 1/x
What is the polynomial in descending order for 12x2 plus 20x - 25?
12x2 + 20x - 25 IS a polynomial that factors into (2x + 5)(6x - 5)
How do you solve x plus y equals 9?
In a problem where you are given two letters to add, subtract, multiply, divide, ect, you can put in any number you want for the letters. The only rule is that the two numbers must equal the number given.
For Example:
X=4 Y=5
X=3 Y=6
X=2 Y=7
X=1 Y=8
X=9 Y=0
X=10 Y=-1
x2 - (-b/a)x + (c/a) = 0 or
x2 - (sum of the roots)x + (product of the roots) = 0
Let the roots be r1 and r2. So we have:
r1 + r2 = 5
(r1)2 + (r2)2 = 15
r1 = 5 - r2 (express r1 in term of r2)
(5 - r2)2 + (r2)2 = 15
25 - 10r2 + (r2)2 + (r2)2 = 15
2(r2)2 - 10r + 25 = 15 (subtract 15 to both sides)
2(r2)2 - 10r + 10 = 0 (divide by 2 to both sides)
(r2)2 - 5r + 5 = 0 (use the quadratic formula)
r2 = [-b + &- sq root of (b - 4ac)]/2a
r2 = {-(-5) + &- sq root of [(-5)2 - 4(1)(5)]}/2(1) = [5 + &- sq root of (25 - 20)]/2 = (5 + &- sq root of 5)/2
r1 = 5 - r2
r1 = 5 - (5 + &- sq root of 5)/2
Thus, when r2 = (5 + sq.root of 5)/2, r1 = (5 - sq.root of 5)/2 or vice versa.
Since the given equation is x2 + bx + c = 0, a = 1, then c equals to the product of roots.
So that,
c = (r1)(r2) = [(5 - sq.root of 5)/2][(5 + sq.root of 5)/2] = [52 - (sq.root of 5)2]/4 = 5
Is x pluse y equals 7 direct or inverse variation?
Inverse: as x increases so y diminishes and vice-versa.
