##### Questions

##### Question type

Use these controls to find questions to answer

Featured 5 months ago

In order to prove this i am assuming that s is the semiperimeter of the triangle #

ok so first let

on solving for

Now ,

and we know that

As Arithmetic mean of

so ,

Hence

Featured 5 months ago

Rotating the coordinate system around the origin by an angle

and substituting we have in the conic now in the coordinates

the coefficient of

Featured 3 months ago

see explanation.

Given

Given

In

In

Hence,

proof of

cross multiplying :

Featured 2 months ago

Longest diagonal:

Since the area is given as

the height of the parallelogram must be

Taking the extension of the base to a point perpendicularly below the opposite vertex of the parallelogram and denoting the length of this extension as

by the Pythagorean Theorem

Denoting the longest diagonal as

and re-applying the Pythagorean Theorem using the base plus its extension (

We can use a calculator to derive the approximation

Featured 2 months ago

Any point on the line

or

if the given line **perpendicular** bisector then

Apology:

Even omitting some details, this explanation is quite long.

Consider the vertical line

This vertical line will intersect

A point twice as far above

That is the line segment from

Furthermore, as we can see from similar triangles any line parallel to

so any line parallel to it must also have a slope of

and

if such a line passes through

or simplified as

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

It is possible, since this question was asked under the heading "Perpendicular Bisectors" that it was intended that

In this case the perpendicular line to

would have a slope of

an equation of

The system of equations:

can be solved for the point of intersection:

Featured 2 weeks ago

minimum value of

See Fig 1.

Reflect

As long as

See Fig 2.

When

When

Hence, min. value of

Ask a question
Filters

Ã—

Use these controls to find questions to answer

Unanswered

Need double-checking

Practice problems

Conceptual questions