0
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
It is a parabola which doesn't touch the X-axis.
i.e., It has no real roots.
8x-7y equals 42 and 24x plus y equals 170 what is x and y?
8x-7y=42
24x+y=170
An easy way to begin is to solve for one variable in one of your two equations. I will use the second equation to solve for y:
24x+y=170
y=170-24x
This solution for y will then be plugged into the first equation so the equation will be of one variable, and therefore solvable:
8x-7y=42
8x-7(170-24x)=42
8x-1190+168x=42
176x=1232
x=1232/176=7
x=7
The solution we made for y can now be used with the solved value of x to find y's numerical value.
y=170-24x
y=170-24(7)
y=170-168
y=2
So, finally, we get that x=7 and y=2
is an equation of a straight line.
It cannot be solved since the solution of an equation with two unknowns (x and y) requires 2 independent equations.
the integral of ln(sin(x)) is:
-x*ln|1 - e2ix| + x*ln|sin(x)| + (i/2)*(x2 + Li2(e2ix)) + C
where Li2 is the second order ploylogarithmic function.
If y is a positive integer and the median of 3y y 5y 2y and 4y is 27 what is the value of y?
The median is the value that lies halfway along the series when arranged in ascending or descending order.
When arranged in ascending order : y, 2y, 3y, 4y, 5y : the median is 3y.
If 3y = 27 then y = 9.
How many solutions will the equation 25 equals 2x squared-6x have?
2x2 - 6x - 25 = 0. Solutions are 5.34 and -2.34
Explain why x2 plus 4x plus 4 equals 0 has 2 x intercepts?
x2+4x+4 = 0
(x+2)(x+2) = 0
x = -2 and also x = -2
When the solutions to a quadratic equation are identical this means that both values are at the turning point or vertex of the parabola just on the x axis.
d>=0,then roots of quadratic equation are real
if D<0,then roots are imaginary
Why did Carl Friedrich Gauss invent the imaginary number?
I am not sure he invented it; but the imaginary numbers were first invented to solve equations with third-degree and fourth-degree polynomials. They were at first considered an artifact to solve those problems, with no real meaning - hence the historical name "imaginary".
Nowadays it is known that complex numbers (that consist of a real and an imaginary part) have lots of applications; to name only a few: electricity; quantum mechanics; art (ever seen a fractal, like the Mandelbrot set?).
What is the aggregate expenditure function in terms of income?
the function that represents total spending in an economy at a given level of real disposable income.
What are the solutions for x squared-35x plus 300 equals 0?
x2-35x+300 = 0
(x-15)(x-20) = 0
x = 15 or x = 20
How do you solve 8X-3 equals 16?
First, you have to add 3 to each side to get 8X = 19.
Next, you have to divide both sides by 8 to get X = 19/8
What is the solution of x squared-14x plus 49 equals 4?
Notice that the left side of the equation is a perfect square (x - 7)2 = x2 -14x + 49. so (x - 7)2 = 4. Take square root of both sides: x - 7 = ± 2, x = 9, or x = 5.
Solve x²-16x plus 68 equals 5 by completing the square?
x2 - 16x + 68 = 5
(x - 8)2 + 4 = 5
(x - 8)2 = 1
x - 8 = 1 or -1
x = 9 or 7
What number is subtracted from both side of x plus 5 equals 15 when solving for x?
5 is subtracted from both sides of the equation. x + 5 = 15: x+5 (-5) = 15 (-5);
when you subtract 5 on the left side of the equal sign the +5 (-5) cancel each other out to equal 0; when you do something to one side of the equal sign you must do the same thing to the other side; so subtract 5 from 15, and you are left with x + 0 = 10
which is x = 10.
When solving for x, you want to end up with x all alone on one side of the equal sign. You have to subtract (or add) the total sum on the x side to both sides of the equal sign.
5 Additional Examples when solving for x:
x + 7 = 13: you have to subtract 7 from both sides of the equal sign
x + 7 (-7) = 13 (-7) so x = 6
---------------------------------------------------------------------------------------------------------
x + 2 + 4 = 20: you have to subtract 2 and 4 from both sides of the equal sign
x + 2 + 4 (- 2) (- 4) = 20 (-2) (-4), so x = 14
a shortcut would be to subtract 6 from both sides of the equal sign since 2+4=6
x + 2 + 4 (-6) = 20 (-6) so x = 14
---------------------------------------------------------------------------------------------------------
x - 3 = 18: you have to add 3 to both sides of the equal sign
x - 3 (+3) = 18 (+3) so x = 21
---------------------------------------------------------------------------------------------------------
x - 5 - 4 = 17: you have to add 5 and 4 to both sides of the equal sign
x - 5 - 4 (+5) (+4) = 17 (+5) (+4), so x = 26
a shortcut would be to add 9 to both sides of the equal sign since -4 - 5 = -9
x - 5 - 4 (+9) = 17 (+9) so x = 26
----------------------------------------------------------------------------------------
x + 7 - 3 = 19: you have to subtract 7 and add 3 to both sides of the equal sign
x + 7 - 3 (-7) (+3) = 19 (-7) (+3) so x = 15
a shortcut would be to subtract 4 from both sides of the equal sign since 7 - 3 = 4
x + 7 - 3 (-4) = 19 (-4) so x = 15
----------------------------------------------------------------------------------------
I hope this helps you understand. You do not have to use the parentheses when adding or subtracting on either side of the equal sign. I just used them to make it easier to read.
What is the order pair for x plus y equals 15 and 4x plus 3y equals 38?
(1) x+y=15
(2) 4x+3y=38
From (1) one gets x=15 -y, put into(2)
4(15-y)+3y=38
60-4y+3y=38
60-y=38
y=22 then x=15-y=-7
(-7,22) is the solution
