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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 property is 1 x n equals n?

The property you are referring to is the multiplicative identity property. This property states that any number multiplied by 1 will result in the original number. In this case, 1 multiplied by n will always equal n, no matter the value of n. This property is fundamental in multiplication and plays a crucial role in various mathematical operations.

Solving the system of equations by graphing?

Solving a system of equations by graphing involves plotting the equations on the same coordinate plane and finding the point(s) where the graphs intersect, which represents the solution(s) to the system. Each equation corresponds to a line on the graph, and the intersection point(s) are where the x and y values satisfy both equations simultaneously. This method is visually intuitive but may not always provide precise solutions, especially when dealing with non-linear equations or when the intersection point is not easily identifiable due to the scale or nature of the graphs.

What does 10 x 10 x 10 x 10 x 10 x 10 equals?

10 x 10 x 10 x 10 x 10 x 10 =

100 x 100 x 100 =

10,000 x 100 = 1,000,000 ( one million).

The above multiplication is usually written as '10^(6).

What are derivatives of legatus?

Oh, dude, derivatives of legatus would include legati (plural), legato (singular), and legation (the act of being a legate). It's like the legatus family tree, but with fancy Latin names. So, next time you're at a toga party, you can impress everyone with your knowledge of legatus derivatives.

What is the value of x if 3x equals 3?

Well, darling, if 3x equals 3, then x must be 1. It's as simple as that. Math doesn't have to be complicated, honey.

How many town lots in 1 acre?

In a standard acre of land, there are 43,560 square feet. If each town lot is typically around 5,000 square feet, you could potentially fit around 8-9 town lots in 1 acre, depending on the layout and any additional space needed for roads or infrastructure. It's important to consider local zoning regulations and lot size requirements when determining the exact number of town lots that can be accommodated in a specific acre of land.

How do you factor x2 - 9x -8?

I think this question needs rewording. Maybe like 2x-9x-8 (144 as in a normal maths question)? Or x2x-9x-8 (x144, like a magnifiyer strength). Another rewording option is 2(-9x-8). This equals -18x-16=288 (remember a minus times a minus is a plus) === ===

What is the derivative of 2Y?

The derivative of 2Y is simply 2. In calculus, when you take the derivative of a constant times a variable (in this case, 2 times Y), the constant remains unchanged. Therefore, the derivative of 2Y with respect to Y is 2.

What is the x-coordinate of the solution to the system of linear equations 3x plus y equals 13 and x plus 6y equals -7?

3x+y=13

x+6y=-7

Multiply the second equation by -3 to cancel out the x's:

3x+y=13

-3x-18y=21

Find the sum of the y's and the numbers:

-17y=34

Divide by -17 on both sides:

y=-2

Plug the y back into one of the equations to find x:

3x -2=13

Add 2 to both sides:

3x=15

Divde each side by 3:

x=5

Plug both numbers back into the equations:

3∙5 -2=13

15-2=13

13=13

5+6∙-2=-7

5+-12=-7

-7=-7

Therefore x =5

Is 1.8 bigger than 1.25?

Yes, 1.8 is bigger than 1.25. When comparing two numbers, you can look at the digits to the left of the decimal point first. In this case, 1.8 has a higher whole number value than 1.25. Additionally, you can compare the tenths place; 1.8 has 8 tenths while 1.25 only has 2 tenths, further confirming that 1.8 is indeed larger than 1.25.

How do you write x divided among 5?

To write x divided among 5, you would use the division symbol (/) to represent the operation of division. The expression would be written as x/5, indicating that x is being split into 5 equal parts. This notation is commonly used in mathematics to show the division of a quantity into a specific number of parts.

What is 2x times 4?

This question can only be answered with additional information, such as the value of x.

Given x = 3, 2x * 4 = 2(3) * 4 = 6 * 4 = 24
Given x = 5, 2x * 4 = 2(5) * 4 = 10 * 4 = 40
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Contrary to the answer above; 2x * 4 = 8x

What is 2x squared minus x squared?

The expression 2x squared minus x squared simplifies to x squared. This is because when subtracting like terms, you subtract the coefficients while keeping the variable and its exponent the same. In this case, 2x squared minus x squared leaves you with just x squared.

What is the LCM of 3x and 2y?

Since there are no common factors, just multiply everything: 3x times 2y = 6xy

7x 52 equals 364 how come there are 365 days in a year?

Well, honey, buckle up because I'm about to drop some knowledge on you. You see, a year is actually about 365.25 days long, so we add an extra day every four years in a little thing we like to call a leap year. So, technically speaking, 7 times 52 does equal 364, but Mother Nature decided to throw in an extra day just to keep us on our toes.

Is y equals 102x exponential?

No, the equation y = 102x is not exponential. An exponential function is of the form y = a * b^x, where a and b are constants. In this case, the equation y = 102x is a linear function, as it represents a straight line with a slope of 102 and no exponential growth or decay.

2x divided by 3 equals 6?

Oh, dude, you're trying to pull a fast one on me, huh? 2 times what divided by 3 equals 6? That would be 12, my friend. So, technically, 2 times 12 divided by 3 does equal 6. Math can be sneaky like that, right?

Is the point of discontinuity considered as critical point?

y=x+3/[(x-4)(x+3)] Definition: a critical number of a function f is a number c in the domain of f such that f'( c) = 0 or f'(c) doesn't exist. Since we have a rational function, the domain is all real numbers except the numbers that make the denominator zero. Therefore, x cannot be -3 and 4. There is a hole on the graph of the function at x = -3, and x = 4 is a vertical asymptote. Simplify first, then take the derivative of y. y = (x + 3)/[(x - 4)(x + 3)] = 1/(x - 4) y' = [1/(x - 4)]' use the quotient rule y' = [(x - 4)(0) - 1(1)]/(x - 4)^2 = -1/(x - 4)^2. Since the numerator is a constant, then y' is never zero, so there is not a critical point.

What is 144 x 5?

Oh, dude, like, math time! So, 144 times 5 equals 720. It's like, you take 144, multiply it by 5, and boom, you get 720. Math, man, it's wild.

How do you solve 12x equals 24?

Well, isn't that just a happy little equation we have here! To solve for x, we can divide both sides by 12, which gives us x equals 2. And just like that, we've found the value of x that makes our equation balanced and complete. Keep up the good work, friend!

Level G mathematics Measuring up book answers?

Oh, dude, you're looking for the answers in the Level G Measuring Up math book? Well, technically, I can't just give you all the answers because that would be like cheating, right? But hey, I can tell you that the answers are probably somewhere in the book, like hidden in plain sight or something. Good luck on your math journey, my friend!

What is the gradient of y 3x 5?

The gradient of the function y = 3x + 5 is simply the coefficient of x, which is 3. In this context, the gradient represents the slope of the line that the function represents. This means that for every unit increase in x, y will increase by 3 units.

What is y times 2?

When you see "y times 2," it means you are multiplying the variable y by the number 2. So the expression "y times 2" can be written as 2y. This is a simple algebraic expression where the coefficient of y is 2.

What is 3 divided into y How do you write it?

The mathematical expression "3 divided by y" can be written as 3/y or 3 ÷ y. This represents the operation of dividing the number 3 by the variable y. In algebraic terms, this expression signifies the quotient obtained when 3 is divided by the value of y.