Calculus

Oh, absolutely! When we talk about x to the power of 2, we're simply saying x multiplied by itself, which is the same as x squared. It's like painting a beautiful little tree with just a few brushstrokes - different ways of saying the same thing, but all leading to a lovely result.

To calculate 5c x 100, you would first convert the percentage to a decimal by dividing by 100, which gives you 0.05. Then, you would multiply 0.05 by 100, resulting in 5. Therefore, 5c x 100 equals 5.

what is it i did not come on this app to tell you to tell me

In the expression 3x + y, when x = 3 and y = 5, we substitute these values into the expression: 3(3) + 5. This simplifies to 9 + 5, which equals 14. Therefore, when x = 3 and y = 5, the value of 3x + y is 14.

If the lines are straight lines , then there is only one solution, which is the point of intersection of the two lines. It will have ( x,y) coordinates.

However, if the lines are curved in any way , there may be more than two or more points of intersection.

Well, isn't that a happy little math problem! To find the answer, you can multiply 88 by 100 and then subtract 88 from that result. So, 88 x 100 = 8800, and 8800 - 88 = 8712. There you go, a beautiful answer just waiting to be discovered!

To calculate the number of 18 mm plywood sheets in a cubic meter, we first need to determine the volume of one sheet. The volume of one sheet can be calculated by multiplying its dimensions (typically 4 feet by 8 feet) by the thickness (18 mm). Once we have the volume of one sheet, we can then divide the volume of a cubic meter (1000 x 1000 x 1000 cubic mm) by the volume of one sheet to find the number of sheets that will fit in a cubic meter.

The square root of a negative number is considered an imaginary number, denoted as "i". In this case, the square root of -3 would be √(-3) = √3 * i. Therefore, the square root of -3 is not a real number, as real numbers are those that can be represented on the number line without involving "i".

To calculate 0.4 multiplied by 10, you simply move the decimal point of 0.4 one place to the right, resulting in 4. Therefore, 0.4 x 10 equals 4.

0.75

The expression 7X + 8 represents a mathematical operation where the variable X is multiplied by 7 and then 8 is added to the result. The expression cannot be simplified further without knowing the specific value of X. If X is a known value, you can substitute it into the expression to find the numerical result.

The equation y = -2.5 represents a horizontal line on the Cartesian plane passing through the point (-2.5, 0). This line is parallel to the x-axis and has a slope of 0. The solution to this equation is all real numbers on the y-axis that have a value of -2.5.

Well, let's take a moment to appreciate the beauty of this function. The domain for 3sin(2x) is all real numbers, as there are no restrictions on the values of x that can be plugged in. As for the range, it will be from -3 to 3, since the sine function oscillates between -1 and 1, and multiplying by 3 stretches these values. Remember, there are no mistakes in math, just happy little accidents!

Well, darling, 3 liters is equal to 3,000 milliliters. It's like comparing a shot glass to a swimming pool - same difference, just a whole lot more liquid. So next time you're measuring out your fancy drinks, just remember, 3 liters is where the party's at.

Well, darling, 3 multiplied by 10 raised to the 9th power equals 3 billion. So, if you're feeling like a math wizard today, that's the magic number you've been looking for. Now go forth and conquer the world with your newfound knowledge!

3xy

h - 25 =< 14

Add '25' to both sides

h =< 14 + 25

h =< 39

NB Treat Inequalities like an 'Equals' except when multiplying negative numbers or fractions, whereupon , turn the sign around.

Verificstion

When h = 38

Substitute

38- 25 = 13 which is less than 14. as required.

When h = 40

40 - 25 = 15 > 14 So NOT True.

By the 'Chain Rule'

dy/dx = dy/du X du/dx

Y = Cos (pi*x).

Let pi*x = u

Y = Cos(u)

u = pi*x

dy/du = -Sin(u)

du/dx = pi

Hence

dy/dx = dy/du X du/dx => ( Chain Rule)

dy/dx = -Sin(u) X pi

Substitute u for pi*x

Hence

dy/dx = -Sin(pi*x) X pi

Tidying up

dy/dx = -piSin(pix) Done!!!!

Sine(pi/2) = 1

This is 'Radian' measure of an angle.

pi/2 radians = 90 degrees.

When you see something like 'Sine(pi/2)' make sure your calculator is in RADIAN mode. ' NOT degree mode.

One million is one thousand multiplied to one thousand.

1000^(2) = 1000 x 1000 = 1,000,000

In UK currency 1 guinea = £1. 1s. op. in old style Sterling.

In modern sterling(GBpounds) 1 guinea = £1.05p.

x^(2) - 36 =

x^(2) - 6^(2)

Remember two squared terms , as above, with a NEGATIVE between them can factor to

(x - 6)(x + 6)

NB

#1 ; The different signs in the brackets.

#2, Two squared terms with a POSITIVE (+) between them, does NOT factor.

#3 ; Inspect the constant, to see if it is a squared number ; 36 = 6^(2) in this case.

Well, isn't that a happy little question! The natural log of 100 is approximately 4.605. Just like painting a beautiful landscape, math can also create its own kind of beauty. Keep exploring the wonders of numbers and you'll uncover even more delightful surprises along the way.