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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
Does The Function X2 plus 4x-5 equals 0 Have A Minimum Or Maximum?
f(x) = x2 + 4x - 5 ( a minimum since the coefficient of x2 is positive, the parabola opens upward)
f'(x) = 2x + 4
f''(x) = 2
At a maximum or minimum, f'(x) = 0
2x + 4 = 0
2x = -4
x = -2
f(-2) = 4 - 8 - 5 = -9
The stationary point occurs at (-2, -9)
f''(-2) = 2
The second derivative is positive at this point, so the gradient is becoming more positive. This means that before this point the gradient was negative and after this point the gradient is positive, so the point is a minimum.
What are all the solution x2 equals 36?
x = 6
or
x = -6
This is because a negative multiplied by a negative gives a positive.
How do you solve 5x minus 2 divided by x squared minus 2x minus 3?
The question contains an expression but not an equation. You cannot solve an expression.
What is long wave approximation?
Well, are you saying goodbye or hello? Waving goodbye usually lasts longer than waving hello to someone.
-1
What is the solutions to the equation x2 plus x - 1 0?
x2 + x - 1 = 0
Using the quadratic formula this gives us:
x = (-1 + or - (-12 - (4 * 1 * -1))1/2) / 2 * 1
x = (-1 + or - (1 - - 4)1/2) / 2
x = (-1 + or - 51/2) / 2
x = 0.618 and -1.618 (Both given to 3 decimal places only)
Note: x1/2 means the square root of x.
What is the answer to the problem x divided by 0.4 equals 2x plus 1.2?
x/0.4 = 2x + 1.2
x/0.4 = (2x + 1.2)/1 (cross multiply)
x = 0.4(2x + 1.2)
x = 0.8x + 0.48 (subtract 0.8x to both sides)
0.2x = 0.48 (divide by 0.2x to both sides)
x = 2.4
Using the ordering rules of BODMAS:
Brackets
Of
Division
Multiplication
Addition
Subtraction
= 4 x 2 + 1
= 8 + 1
= 9
How do you work out what x means in theis equation 5x plus 7 equals 84-6x?
you say:
5x+7=84-6x
5x+6x+7=84-6x+6x
11x+7=84
11x+7-7=84-7
11x=77
x=77/11
x=7
5x plus 2 equals -18 what is x?
-4
5x + 2 = -18
0x + -2 = -2
----------------
5x + 0 = -20
5x / 5 = -20/5
x = -4
How do you solve 4x squared minus 21 equals negative 11x?
The Quadratic Formula gives the value of x in equations of the form ax2 + bx + c.
In this instance a = 4, b = 11 and c = -21.
((-b +/-(sqrt(b2 - 4ac))/2a
= (-11 +/- sqrt (121 + 336))/ 8
= (-11 +/- 21.4)/8
x = 1.3 or 4.05
Y equals -5x plus 5 and 3x plus 2y equals 3 solve this equation using substitution?
y = -5x+5 (Equation 1)
3x+2y = 3 (Equation 2)
you see the the first equation is equal to y. just put that into the second equation.
3x + 2(-5x+5) = 3 (now do algebra and find x)
3x - 10x + 10 = 3
-7x = -7
-x = -1
x = 1
Now put x into one of the equations to find y
y = -5(1) + 5 (Equation 1)
y = -5 + 5
y = 0
Now put both the x and y into both equations to see if it is truee.
0 = -5(1) + 5 (Equation 1)
0 = -5 + 5
0 = 0 CORRECT
3(1) + 2(0) = 3 (Equation 2)
3 + 0 = 3
3 = 3 CORRECT
Therefore your answers are
x = 1
y = 0
Centre = (4, -3)
Radius2 = (4 + 2)2 + (-3 + 7)2 = 36 + 16 = 52
Equation = (x - 4)2 + (y + 3)2 = 52
or x2 - 8x + y2 + 6x = 27
