Let x=ab=ac, and y=bc, and z=ad.
Since the perimeter of the triangle abc is 36, you have:
Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36
The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.
Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).
The perimeter of the triangle abd is 30:
Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60
So, we have two equations on x, y and z:
(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60
Substitute 2x + y by 36 from (eq.1) in (eq.2):
(eq.2') 36 + 2z = 60
And solve for z:
36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12
The measure of ad is 12.
If you prefer a less algebraic reasoning:
- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).
- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:
ad = 30 - (36/2) = 30 - 18 = 12
Let x be the cost of gum 20 years ago.
3x - 3 = 75
3x = 78
X = 78/3
X = 26.
So the write answer is A) 3x - 3 = 75.
<span> y^2 = (3x + 1)^3 / 9x + 2
2*y*(dy/dx)=(9</span>(3x + 1)^2*(9x + 2) -((9*(3x + 1)^3))/ ((9x + 2)^2)
(dy/dx)=(9(3x + 1)^2*(9x + 2) -((9*(3x + 1)^3))/ (2*y*(9x + 2)^2)
(dy/dx)=(9(3x + 1)^2*(6x + 1))/ (2*y*(9x + 2)^2)
answer
A
