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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

What does x equal when 3x plus -1 equals 8?

x = 3

Solution:

3x + -1 = 8

3x = 8 + 1

3x = 9

x = 9/3

x = 3

Check:

3(3) + -1 = 8

9 + -1 = 8

8 = 8

What is the graph of 3x plus 2y equals 13?

3x + 2y = 13

Subtract 3x from each side:

2y = -3x + 13

Divide each side by 2:

y = (-3/2)x + (13/2)

The graph is a straight line, with a slope of (-3/2),

through the point (0, 13/2) .

What is the f dashed x or deriative of 1 over 2xcubed plus 5?

f'(x) = 1/(2x3 + 5)

rewrite

f'(x) = (2X3 + 5) -1

use the chain rule

d/dx (2x3 + 5) - 1

-1 * (2x3 + 5)-2 * 6x2

- 6x2(2x3 + 5) -2

==================I would leave like this rather than rewriting this

What happens to the equation y 2x if it changes to y 2x 5?

graphically, the line will shift upward 5 units, assuming there is + inbetween the 2x and the 5, you dont seem to have any symbols inbetween

How do you make this inequality true 4x 8 -12?

Unfortunately, there is no inequality to be seen. Limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals" etc.

What do you call the solution of a equation derived from an original equation that is not a solution of the original equation?

That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.

Why is 1 over 3 equal to 2 over 6?

1/3 is equal to 2/6 as they are equivalent fractions.

Equivalent fractions are made by multiplying (or dividing) both the numerator and denominator by the same value:

1/3 = (1×2)/(3×2) = 2/6

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This is a result of the way fractions are multiplied together (multiply the numerators together and multiply the denominators together), and a fraction with the same numerator and denominator is the same as the number 1 (since a fraction is equivalent to the the numerator divided by the denominator when converted to a decimal) and multiplying a number by 1 is the same as leaving the number alone:

2/2 = 2 ÷ 2 = 1

1/3 = 1/3 × 1 = 1/3 × 2/2 = (1×2)/(3×2) = 2/6

How many diagonals does a shape with 8 sides have?

The formula for determining the number of diagonals in a shape is n(n-3)/2 where n=vertices, (corners or intersections of geometric shapes). For an eight sided shape we replace n with 8. 8(8-3)/2 8(5)/2 (8x5)/2 40/2=20 An octagon contains 20 diagonals. For a further example we can determine the diagonals in a shape with 5 sides: 5(5-3)/2 5(2)/2 (5x2)/2 10/2=5 A Pentagon contains 5 diagonals.

12x plus 131 equals 189 plus 3x?

12x + 131 = 189 + 3x 12x - 3x + 131 - 189 = 0

9x - 58 = 0

9x = 58

x = 6,44444

Why does the derivative of sin x equal cos x reason not prove?

Because the slope of the curve of sin(x) is cos(x). Or, equivalently, the limit of sin(x) over x tends to cos(x) as x tends to zero.

How would you solve 5x-y equals 5 and 2x-y equals 1 using subsitution?

When solved by substitution: x = 4/3 and y = 5/3

From equation 2, y = 2x - 1

Substituting this expression for y in equation 1 gives 5x -(2x - 1) = 5

this simplifies to 3x + 1 = 5 making x = 4/3 and y = 5/3

How do you solve the simultaneous equations of x over 3 minus y over 4 equals 0 and x over 2 plus 3y over 10 equals 27 over 5 by the elimination method?

x/3-y/4 = 0 => multiply all terms by 12 => 4x-3y = 0

x/2+3y/10 = 27/5 => multiply all terms by 10 => 5x+3y = 54

4x-3y = 0

5x+3y = 54

Add both equations together which will eliminate 3y:

9x = 54

Divide both sides by 9:

x = 6

Substituting the value of x into 5x+3y = 54 and 4x-3y = 0 gives y a value of 8.

Therefore: x = 6 and y = 8

What is 3x to the 2nd power minus 24 x minus 60?

3x² - 24x - 60 = 0; whence,

x² - 8x - 20 = (x - 10)(x + 2) = 0; and

x = 10 or -2.

Checking, we find that

3(10)² - 24(10) - 60 = 300 - 240 - 60 = 0, and

3(-2)² - 24(-2) - 60 = 12 + 48 - 60 = 0,

thus re-assuring us that we have solved correctly.

What is fluid gradient?

Usually a fluid gradient refers to the pressure gradient in any kind of fluid. It is a quantity that shows which direction and how fast the pressure changes around a location.