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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

How do you work out the volume of a square?

Since a square is a 2 dimensional object, it does not have a volume. You can however calculate the area of a square = length x width. Squares are also very useful in trigonometry.

However, you can calculate the volume of a cube (6 squares arranged edge to edge to form a box)

The volume of a cube = length x width x height

Does pi over 4 equal 45 degrees?

pi/4 radians = 45 degrees.

2pi radians = 360 degrees

pi radians = 180 degrees

pi/2 radians = 90 degrees

pi/4 radians = 45 degrees

pi/3 radians = 60 degrees.

et seq.,

What consecutive integers equal 207?

You don't say whether they've to be added or multiplied!

103 + 104 = 207; 207 = 3 x 3 x 23 so there is no solution in integers.

What is the value of x when 3x-5 equals 20?

Applying the systematic method, we get:-

3x-5+5=20-5(cancelling -5 from both sides)

3x=15

3x/3=15/3

Therefore, x=15

Derivative 3 plus 2 x - 4 x2?

y = 3 + 2x - 4x^(2)

dy/dx = 2 - 8x ( The derivative).

How do you do 5x plus 6y plus 4-3x-3 equals?

All that you can do is to simplify the left hand side of the "equation" to the expression 2x + 6y + 1.

Since the right hand side of the original "equation" is not given, it is, in fact an expression and cannot be solved. In any case, one linear equation in two variables cannot be solved.

What is the true number for pie instead of 3.14?

There is NO true number!!!!

'pi' is an irrational number, which means that the decimal digits go to infinity, and there is no regular order in the decimal digits.

'pi does NOT equal 3.14, nor 3.1416, nor 3.141592

These are only approximations.

pi = 3.141592.... ( to infinity).

Super Dupa computers have calculated 'pi' to at least 50 billion places and still going.

However, for school work.or technical /scientific work , pi is equated to 3.14 or 3.1416.

How do you solve 2x squared equals 200?

2x2 = 200

Divide both sides by 2: x2 = 100

Take square roots of both sides: x = -10 or x = +10

What is the answer when you multiply 2 with 9?

18. Let me show you why:

If I have 1 set of 9, I have 9

. . . . . . . . .

2 sets of 9 makes 18

. . . . . . . . . . . . . . . . . .

How much soil is there in a soil measuring by 1meter by 1 meter by 1 meter?

It depends on the density of the soil. If the soil is compacted or stepped on or moist of dry the amount of soil in 1m x 1m x 1m is going to vary.

The density of loose soil is about 1200 kg per m3

How do you solve 7w equals 42?

I understand this equation to be 7w = 42. The principle we use for solving equations like this one is that we can do the same thing to both sides of the equation and the equation will still be _true_.

We want the 'w' by itself. This implies ridding the left side of the 7. We can turn it into a one (1) by dividing it by 7. But if we do that to the left side of the equation then we must also do that to the right side.

7w/7 = 42/7

1w = 6 or w = 6, the result.

What the Anserw to 4x plus 1 equals 2x plus 5?

4x + 1 = 2x + 5

4x + 1 - 2x = 2x + 5 - 2x

2x + 1 = 5

2x + 1 - 1 = 5 - 1

2x = 4

2x/2 = 4/2

x = 2

Why does AsF5 have no dipole moment?

AsF5 has no dipole moment because the bond dipoles formed between the central atom (As) and the surrounding fluorine atoms cancel each other out due to the symmetrical trigonal bipyramidal shape of the molecule. This results in a non-polar molecule overall.

What is x in 16x equals 4?

16x = 4

Divide both sides by 16:

x = 4/16

x = 1/4

What does the planck's equation e equals h x nu state?

This equation shows that the energy of a photon is inversely proportional to its wavelength.

E = Energy.

h = The Planck constant. Think of it as a tiny, discrete packet of energy for most purposes.

Nu (looks like v) = Spatial frequency of a wave.

Nu is equal to 1/Wavelength (inversely proportional). The way to think of this is that wavelength is how many meters long the wave is. Meanwhile, Nu is how many waves you can fit into a meter.

Eg: If the wave is half a meter long, you can fit 2 waves into a metre. (Nu = 1/0.5 = 2)

If Nu is large, it means we can fit a lot of waves into our unit length (remember, big Nu = small wavelength and vice versa). What does this mean for our equation? It means when Nu is high, we have high energy (remember h is a positive constant). When Nu is low, we have low energy.

In English, this means photons with smaller wavelength have higher energy than photons with larger wavelengths. This universally true, and extremely important.

For further reading, try searching for "Electromagnetic spectrum".

Is 100 a odd number?

100 is an even number, so no it is not an odd number. any number ending in 0, 2, 4, 6, or 8 is always even!! any number ending in 1, 3, 5, 7, or 9 is always odd!!

What is the difference between hypokalemic and hyperkalemic periodic paralysis?

Hypokalemic periodic paralysis is characterized by low levels of potassium in the blood during attacks, leading to muscle weakness or paralysis. In contrast, hyperkalemic periodic paralysis is characterized by high levels of potassium during episodes, resulting in muscle stiffness or weakness. Both conditions are genetic and involve dysfunction in ion channels that regulate potassium levels in muscle cells.

What is an IVP in differential equations?

It stands for "Initial Value Problem." So once you find the general solution of the Diff Eq, you plug in these given initial conditions (e.g. for a 2nd order; y(0) = 1, y'(0) = 0) to find the specific solution.

What is the foci of an eclipse?

The foci of an eclipse refer to the two points within the elliptical orbit of the Moon where the Earth is located at the time of the eclipse. These points define where the alignment between the Sun, Earth, and Moon occurs, leading to either a solar or lunar eclipse.