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
How do you solve the equation 132 equals 11z?
It is the same as: 11z = 132
Divide both sides by 11: z = 12
What word problems can be written with x plus 13 equals 25?
Identify the number which, when increased by 13, equals 25.
Thirteen more than a number is 25.
How do you integrate of e -2x for x0?
The integral of e-2x is -1/2*e-2x + c but I am not sure what "for x0" in the question means.
Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.
Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.
Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.
Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.
Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.
Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.
Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.
Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.
What does b mean in y equals m times x plus b?
Y = mX + b This is the general form of the equation of a straight line graphed on X-Y coordinates. 'm' is the slope of the line 'b' is the Y-intercept, that is, the number on the Y-axis where the line crosses it
What is 8x cubed plus 4x squared plus 6x plus 3?
8x3 + 4x2 + 6x + 3 = 4x2(2x + 1) + 3(2x + 1) = (2x + 1)(4x2 + 3)
Solve and check the system Y-2x equals 0 x-2y equals 6?
y - 2x = 0 so y = 2x; x - 2(2x) = 6 ie -3x = 6 so x = -2, making y = -4
Check:
1. does -4 - 2 (-2) = 0? yes ,-4 + 4 = 0
2. does -2 - 2 (-4) = 6? yes, -2 + 8 = 6
a = 8, b = 14.
How do you find graph cordinates in this problem 5x-9y equals 43 3x plus 8Y equals 68?
5x - 9y = 43 (A)3x + 8y = 68 (B)
(A)*3: 15x - 27y = 129
(B)*5: 15x + 40y = 340
Subtracting the first from the second gives
67y = 211 => y = 211/67 = 3.15 approx
Substituting the [rational] value of y in (B)
5x - 9*211/67 = 43 => 5x = 43 + 1899/67 = 4780/67
therefore x = 956/67 = 14.27 approx.
What is answer for x divided by 3 equal 27?
X/3 = 27
multiply through by 3
X = 81
======check in original equation
81/3 = 27
27 = 27
=======checks
How do you sole X when logx-3 plus logx-2 equals log2x plus 24?
We can't see the parentheses, and there are at least two ways to read this.
Here are solutions for the most likely two:
--------------------------------------------------------
log(x) - 3 + log(x) - 2 = log(2x) + 24
Add 5 to each side:
log(x) + log(x) = log(2x) + 29
Subtract log(2x) from each side:
log(x) + log(x) - log(2x) = 29
Combine the logs on the left side, and massage:
log( x2/2x ) = log( x/2 ) = 29
Take the antilog of each side:
x/2 = 1029
Multiply each side by 2:
x = 2 x 1029
------------------------------------------------
log(x - 3) + log(x - 2) = log(2x + 24)
Combine logs on the left side:
log[ (x-3) (x-2) ] = log(2x + 24)
Take antilog of each side:
(x-3) (x-2) = 2x + 24
Expand the left side:
x2 - 5x +6 = 2x + 24
Subtract (2x+24) from each side:
x2 - 7x - 18 = 0
Factor:
(x - 9) (x + 2) = 0
Whence:
x = 9
x = -2
We have to discard the solution [ x = -2 ] because one term in the equation
is log(x-2).
If 'x' were -2 then we'd have log(-4) but negative numbers don't have logs.
