Calculus

1000000

d/dx sinx = cosx

In simple language, derivative is rate of change of something and integral represents the area of a curve whose equation is known.

Yes.

The ideal pendulum consists of a massive bob suspended from a frictionless pivot by a massless string. For small angles the period is given by the formula: t = 2*pi*sqrt(l/g)

However, the formula depends on the assumption that, for the angle of displacement x (measured in radians), sin(x) approximately equals x. For large x the approximation does not hold true and so the formula needs amending.

For x = 0.4 radian, the period is about 1% greater than that given by the unadjusted formula.

As a first step, I would convert everything to sines and cosines.

sin x cot x = sec x - cos x

thus becomes:

(sin x) (cos x / sin x) = (1 / cos x) - cos x

Simplifying:

cos x = 1 / cos x - cos x

It doesn't look as though they are equal. In fact, if you do the calculations for some specific angle, e.g. 30 degrees, you see that they are not.

That depends on the function you are working with.

100

Draw a right triangle. To get a tangent of 2, the side opposite the angle might be 2, the adjacent side might be 1 (other combinations, in the ratio 2:1, are also possible). In this case, the hypothenuse is square root of 5 (Law of Pythagoras). Therefore, the cosine is 1 / square root of 5.

(x + 6)(x + 1) = 0 so x = either -1 or -6

Given:

x2 + y2 - 6x + 4y = -4

We'll start by rearranging for clarity:

x2 - 6x + y2 + 4y + 4= 0

We can already get a perfect square with our y-value, so let's do that

x2 - 6x + (y + 2)2 = 0

Now to get x down to one term, you need to complete the square:

x2 - 6x + 9 + (y + 2)2 = 9

(x - 3)2 + (y + 2)2 = 32

And that gives you the answer. The circle has a center point of (3, -2), and a radius of 3.

5y - 2 = 28 - y

5y + y = 28 + 2

6y = 30

y = 30/6

y = 5

Question: 2x + e = 5x

- 2x

3x = e

x = e/3

'Y' is a function 'f' of 'x':

Y = f(x) .

'Z' is a function 'g' of 'y':

Z = g [ f(x) ] .

(x+1)(x-1) ;)

3x + 8 = 2x +28

3x - 2x = 28 - 8

x=20

The answer depends on whether the shape is 2-dimensional or 3-d. For a 2-dimensional polygon with n sides, the minimum number is n-3 diagonals.

- cos(1 - X) + C

Yes

The answer to 1 over 2x plus 13 equals 9 is x equals -8.

If you mean: 3x-(2x+4x-6) then 3x-2x-4x+6 simplifies to 6-3x

47 centimeters is 470 millimeters.

100 centimeters

distance