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Featured 6 months ago

Set your compass to a radius of 6, put the center point at

Multiply both sides of the equation by r:

Substitute

The standard form of this type of equation (a circle) is:

To put the equation in this form, we need to complete the square for both the x and y terms. The y term is easy, we merely subtract

To complete the square for the x terms, we add

We can use the pattern,

Substitute 6 for h into the equation of the circle:

We know that the first three terms are a perfect square with h = 6:

This is a circle with a radius of 6 and a center point

Featured 6 months ago

we know euler's theorem states that

so,

=

=

now

so we get

=

again similarly we get

=

so,

=

=

=

=

Featured 5 months ago

Let CB be the cliff . From point A the angle of elevation of the peak C of the cliff is

DF and DE are perpendiculars drawn from D on CB and AB.

Now

Let

For

Now

For

Featured 3 months ago

Start from a "basic cycle" for the

Starting with the "basic cycle" for

Then consider what values of

(Yes; I know: because

Giving us the "basic cycle" for

Adding

In the image below, I have added the "non-basic cycles" as well as the "basic cycle" used for analysis:

Featured 1 month ago

The maximum and minimum of any

Multiply these by

The maximum is therefore

To find at which point this occurs, work backwards.

Divide both sides by

Do a backwards

Now we have our

Featured yesterday

The given function representing the height

(a) h is a cosine function of t, So it will have maximum value when

and the maximum height of the swing becomes

(b) it takes

c) The minimum height of the swing will be achieved when

Minimum height

(d). Again

Here

e) For

when

So in

f) The height of the swing at 10 s can be had by inserting

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