Calculus

Oh, dude, the third derivative of ln(x) is -2/(x^3). But like, who really needs to know that, right? I mean, unless you're planning on impressing your calculus teacher or something. Just remember, math is like a puzzle, except no one actually wants to put it together.

100 milligams

Standard form requires a single non-zero digit before the decimal point and a multiplier of a power of 10 which gets the decimal point back to where it was in the original number. To calculated the power of the ten count how many digits the decimal point needs to move; if it needs to move to the left make it negative:

59 = 5.9 × 10¹

The inverse function is obtained by interchanging corresponding values of x and y and then transposing the resulting equation to make y the subject.

f(x) = y = 8x + 5 therefore f-1(x) = x = 8y + 5 : 8y = x - 5 : y = (x - 5)/8

The inverse function of y = 8x + 5 is y = (x - 5)/8

To find the product of 8x and 2x, you multiply the coefficients (8 and 2) to get 16, and then multiply the variables (x and x) to get x^2. Therefore, 8x * 2x equals 16x^2.

The expression 2x + 4 represents a linear equation where x is a variable. To simplify this expression, you would combine the like terms, which in this case are the 2x and the 4. Therefore, the simplified form of 2x + 4 is 2x + 4.

The algebraic expression for "7 increased by x" is 7 + x. In this expression, the variable x represents the amount by which 7 is being increased. Adding x to 7 results in the total value after the increase.

To find the population density of a country, you divide the amount of people in the country by the amount of squared kilometres. For example, Bangladesh has the highest population density; it is 1000 people per squared km!

When a number is raised to the power of 2, it means that the number is multiplied by itself. In mathematical terms, X to the power of 2 is written as X^2, or X * X. This is equivalent to X squared, and represents the area of a square with sides of length X.

Say it out load. "If it take me 6 minutes for 1,000, how many of the 6 minutes (1,000) go into 100,000?"

The answer is 100 (100,000 / 1,000) = 100

So it would take 600 minutes or (600/60) = 10 hours to count to 100,000

Well, isn't that just a happy little math question! When you see "log base 81 of 9," you're looking for the power you need to raise 81 to get 9. Since 81 to the power of 1/2 equals 9, the answer is 1/2. Just a little mathematical magic to brighten your day!

42

Oh, what a happy little question! When you multiply 500 by 100, you get 50,000. Isn't that just a lovely number to work with? Just imagine all the wonderful things you could do with 50,000 - maybe paint a beautiful landscape or spread some joy to others.

Well, honey, if Y divided by 5 equals 3, then Y must equal 15. It's simple math, darling. Just plug 3 back into the equation and see for yourself. Math doesn't have to be a headache, dear, just embrace the numbers and move on with your fabulous self.

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 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.

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).

16.6667

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.

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.

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.

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) === ===

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.

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

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.