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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
How do you solve a equation using unknown variables?
You don't use unknown variables to solve an equation. The purpose of solving
an equation is to find the value of the variable so that it's no longer unknown.
What is the answer to 5x squared plus 14x - 24 equals 0?
5x2+14x-24=0
Delta = 142-4x5x(-24)=676=262
X = (-14 + sqrt(676))/(2*5) = 12/10 = 6/5
or
X = (-14 - sqrt(676))/(2*5) = -40/10 = -4
What is an application for a quadratic equation in real life?
A quadratic equation could be used to find the optimal ingredients for a mixture.
Example: if you are trying to create a super cleanser, you could make a parabola of your ingredients, finding the roots of the equation to find the optimal amount for each ingredient.
How do you factor 2x to the second power plus 13x plus 15?
2x^2 + 13x + 15 factored means that the two numbers must multiply to the constant (15) and add to equal the coefficient on the X (13). So it becomes:
(2x + 3) (x + 5). If expanded, 2x*5 = 10x and 3 * x = 3x which add to 13x. And 5 * 3 = 15
X plus y-z equals 2 -x-5y plus 2z equals 21 5x plus 4y-4z equals 12?
I used the matrix method to find the answer: x=4, y=-7, z=-5.
How do you factor x squared minus 2x minus 10 minus 5 equals 0?
x2-2x-10-5 = 0
x2-2x-15 = 0
(x+3)(x-5) = 0
x = -3 or x = 5
Converting square feet to square yards?
The conversion of one yard to feet is three feet per yard. Thus, in a single-dimensioned space, you can simply divide whatever distance is given by 3 to get yards. However, adding a second dimension means you have feet x feet and thus, must convert both dimensions to yards, meaning you have to divide by 3 twice or once by 9.
What is the logarithm of log -1?
Assuming you are asking about the natural logarithms (base e):
log (-1) = i x pi
therefore
log (log -1) = log (i x pi) = log i + log pi = (pi/2)i + log pi which is approximately 1.14472989 + 1.57079633 i
What is the slope of 7x plus 3y equals 9?
Solve for y
3y=-7x+9
y=-7/3x+3
the slope is the coefficient of x
in this case, it is -7/3
Negative x to the second power positive five x plus twenty-four?
x to the second power +11x+24 (x+_)(x+_)
Is there a question here?
What does the variable y equals mx plus b?
That is the equation of a line.
y = m*x + b
x is a changing variable to plot on the x-axis.
m is the slope of the line, or how slanted the line is.
b is the y-intercept, or where the line crosses on the y-axis.
What is the graph for x plus y equals 1 Need a step by step explanation?
The line x + y = 1 will be defined by the points that satisfy that equation. The x-axis travels horizontally, the y-axis travels vertically.
Step 1. Draw the axes on graph paper. Each line should be an integer.
Step 2. Plot points that satisfy the equation, like (0,1)(1,0)(2,-1)(1,-2)(3,-2)(-2,3)
Step 3. Draw a line through them with a pencil using a straight edge of some sort.
When one of the numbers is zero, that's where it crosses the other axis. You'll find that the line crosses the x-axis at 1 on the y-axis and crosses the y-axis at 1 on the x-axis.
What is the factor expression of x2-9x plus 4 equals 0?
That equation can not be factored. It can however be solved for x:
x2 - 9x + 4 = 0
x2 - 9x + 81/4 = 81/4 - 4
(x - 9/2)2 = 81/4 - 16/4
(x - 9/2)2 = 65/4
x - 9/2 = ± √65 / 2
x = (9 ± √65) / 2
2x to the 3 power times 5x to the 3 power?
(2 x3) times (5 x3)= 10 x6
Of course, it could also mean (2x)3 (5x)3 =(8x3 )(125x3 )=1000x6
It all depends on weather you mean the quantity 2x to the third or 2 multiplied by x to the third.
