Calculus

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.

The product of 7926 multiplied by 4 is 31,704. This can be calculated by multiplying the units digits first (6 x 4 = 24) and carrying over the tens place to the tens digit (2 x 4 = 8, plus the carried over 2 = 10). Then, multiply the tens digits (2 x 4 = 8) and add the carried over 1 from the previous step. Finally, multiply the hundreds digit (9 x 4 = 36) and add any carried over values.

Oh, what a happy little question! If we imagine a beautiful garden with flowers and trees, we can see that two times four equals eight, and one more two makes it nine! So, two times four plus one more two equals nine, creating a lovely balance in our mathematical landscape. Just remember, there are no mistakes in math, only happy little miscalculations.

You want me to run three times a day, but how will that help me to make new friends?

365 x 40 is equal to 14,600. This can be calculated by multiplying 365 by 40, which is the same as adding 365 forty times. In other words, it represents the total when you have 365 groups of 40 items each.

first you divide both sides by 2 then add brackets in front of the number:

1. divide 8x+12= 4 and 6 divide again = 4 and 2 and 3

2. add brackets= 4{2x=3}

Hope This Helped

Ah, let's take a moment to appreciate the beauty of this equation. When we have y - 18, we are simply subtracting 18 from the value of y. It's like taking a peaceful stroll through the forest of mathematics, where each step brings us closer to understanding the harmony of numbers.

Well, darling, if x equals 0 in the equation, then y can be whatever the heck you want it to be! When x is 0, y is undefined, honey. So, go ahead and pick a number, any number, and call it y. Just don't expect it to make much sense in the grand scheme of things.

1.08 is a fraction. It is a fraction in decimal form rather than in the form of a ratio. However, that does not stop it being a fraction. And, since it is a decimal fraction, there is not another simpler decimal form. Its equivalent, in rational form, is 108/100 which can be simplified to 27/25.

The expression x^2 - x represents a quadratic equation in standard form. It is a polynomial of degree 2, with x raised to the power of 2 and a coefficient of -1 for the linear term. This expression can be factored as x(x-1), which shows that it has two factors, x and (x-1). It is a parabolic function that opens upwards and crosses the x-axis at x=0 and x=1.

To simplify the number 830, we need to find the greatest common factor (GCF) between 830 and any other number. In this case, the number 830 is already in its simplest form because it cannot be divided evenly by any other number except 1 and itself. Therefore, 830 in simplest form remains as 830.

YES!!! Especially when converting decimal to inifinyt to a fraction.