CPhill

sec(θ)=2

r/x  = 2

sqrt [ x^2 + y^2] / x  = 2

sqrt [ x^2 + y^2 ]  = 2x     square both sides

x^2 + y^2  = 4x^2

y^2  = 3x^2         take the square root of both sides

y =  ±√(3)x

If the width is x, the length is twice this  = 2x

And

Perimeter = 2 (W + L)      so

Perimeter =  2 ( x + 2x)

Perimeter  = 2 (3x)

Perimeter  = 6x

42  =  2 ( x + 2x )

42  = 2 ( 3x)  

42  =  6x

I assume this is the area of a circle.....if so, we have

452.16 =  pi *  r^2

452.16  =  3.14 * r^2        divide both sides by 3.14

452.16 / 3.14   =  r^2       

144  = r^2                     take the positive square root of both sides

12 ft  =  r

x^2  =  4   subtract 4 from both sides

x^2 - 4  =  0       factor

(x + 2) (x - 2)  =   0

Set  both factors to 0

x + 2  = 0                                                   x - 2  =  0

subtract 2 from both sides                      add 2 to both sides

x =  -2                                                        x  =  2

And those are the two solutions

Just type "5"   and the hit the "±" key

Two of the parallel sides of the plane will each equal NP  = 6

The  other two parallel sides will each equal PU  =  sqrt ( 6^2 + 15^2)  =  sqrt (36 + 225) =

sqrt ( 261)

So.....the perimeter  of NPUR  =  2 [ 6 + sqrt (261) ] ≈ 44.3 ft

Note that  1  = 3^0    ....so we have

3^(2 - 2x)  =  3^0      since the bases are the same, we can solve for the exponents

2 - 2x  = 0        add 2x to both sides

2  = 2x             divide both sides by 2

1  = x

An

O - Y - S - T - E - R........!!!!!

Thanks for that, Rosy.......!!!!

Note  what happens when we expand   (x + 0.5) ( x - 6.5)

Distribute the terms in the first set of parentheses over the terms in the second set

x ( x - 6.5)  +  0.5 ( x - 6.5)   =

x^2  - 6.5x  + 0.5x - 3.25        combine like terms

x^2  - 6x  -  3.25

Now just apply the (-4/13)  over these to get the final function