How are polar and rectangular planes related?

Polar coordinates (r,ϑ) and Cartesian coordinates (x,y) are related as follows:

Cartesian -> Polar
x = r cos(ϑ)
y = r sin(ϑ)

Polar -> Cartesian
r^2 = x^2 + y^2
ϑ = arctan( y/x)

The polar coo's can be extended to cylindrical by introduction a dimension z - which is perpendicular to the polar plane, it follows that:

z = z 
in between the systems (r,ϑ,z) and (x,y,z)

The polar coordinates are particularly useful when a problem has circular or cylindrical symmetry, i.e. it is usually "easier" to perform calculations on a circle (for example) using the polar coordinates.

median is the value separating the higher half of a data sample, a population or probablity distribution from the lower half.

step-by-step explanation:

say you have 3,8,7,3,1,9,8 order them from lowest to highest

if orderd it would be 1,3,3,7,8,8,9 now you take away from the lowest and the highest until you end up in the middle.

so you would remove the 1 and 9 leaving you with 5 digits remaining

when you've reached the middle that would be your answer so in this case the answer is 7

if there were two numbers left say 7 and 5 you'd and them together so 12 then divide by 2 witch would equal 6 so the answer would be 6

good luck on that project hoped i you at all

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it