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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
Start with the first equation: 8=2x-6 so 14=2x so x=7
Now insert the answer for x into the second equation:
So y=2(7)-6 so y=14-6 so y=8
So at a certain point x=7 and y=8 so a coordinate would be (7,8)
x=3
That wasn't hard at all.
5x-10=-7+4x
-4x -4x
_____________
x-10=-7
+10 +10
_____________
x=3
If f(x) -7x plus 5x2 plus 10 what does f(-2) equal?
Given f(x) = - 7x + 5x^2 + 10
So f(-2) = - 7(-2) + 5 (-2)^2 + 10 = 14 + 20 + 10 = 44
If Y = y, then it is 9y4 or 9Y4. If Y is not the same as y, then you can't simplify it any.
How do you solve four to the x power minus two to the x plus one power all equaling 15?
So you have (4^(x-2))^(x+1)=15. Using a law of exponents (b^a)^c=b^(a*c) and 4=2^2, you get
4^((x-2)*(x+1))=15=2^(2(x-2)(x+1)).
Take log base two and use the rule about logs of products you get
2(x-2)(x+1)=Log_2(15)
Simplifying and substituting u for Log_2(15),
2x^2-2x-4=u, which means
2x^2-2x-(4+u)=0, using quadratic formula.
X=(1/4)(2(+or-)sqrt(4-4*2*(-4-u))) or
(1/2) plus or minus (1/4)(sqrt(36+8u))
Where sqrt(b) is the square root of b
What is the derivative of e-3x?
f'(x)=-3
the derivative of e is zero because its a constant. Derivative of -3x is -3. Bring the exponent of x down in front of the -3 and subtract the original exponent by 1. Ex. -3(1...which is the first exponent of the x)x^0(n-1 or 1-1=0)
all this is -3(1)x^0
x^0 is 1 so the derivative of -3x is -3
-4x - 1 = -7
add 1 to both sides to get...
-4x = -6
divide both sides by -4 to get
x = 1.5
What is 5x plus 35 equals -30?
Start by subtracting 35 from both sides to get 5x = -65
Now, divide both sides by 5 to get x = -13
If: 2x+y = 1 then y =1-2x and y^2 = (1-2x)^2 which is 1-4x+4x^2
If: x^2 -xy -y^2 = -11 then x^2 -x(1-2x) -(1-4x+4x^2) = -11
Expanding brackets: x^2 -x +2x^2 -1 +4x -4x^2 = -11
Collecting like terms and adding 11 to both sides: -x^2 +3x +10 = 0
Dividing all terms by -1: x^2 -3x -10 = 0
Completing the square: (x-3/2)^2 -9/4 -10 = 0 => (x-3/2)^2 = 49/4
Square root both sides: x-3/2 = -/+ 7/2
Add 3/2 to both sides: x = 3/2 -/+ 7/2
Therefore: x = 5 or x = -2
Solutions by substitution are: (5, -9) and (-2, 5)
