You need to use Pythagoras’ Theorem.
A² + B² = c² and c is the hypotenuse of the right angled triangle.
The height of the tower (5 feet) is A and the distance from the end of the cable and the base of the tower (12 feet) is B. The length of ONE cable is c. So:
A² + B² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c. This is the length of one cable.
3 x 13 = 39 therefore the total length of the cables is 39 feet.
25
The rate of change is 2om per hour
The length of the rectangle is = 72 cm
The width of the rectangle is = 56 cm
Area of the rectangle is = 
=
cm²
As given, the other rectangle has the same area as this one, but its width is 21 cm.
Let the length here be = x


Hence, length is 192 cm.
We can see that as width decreases, the length increases if area is constant and when length decreases then width increases if area is constant.
So, in the new rectangle,constant of variation=k is given by,
or 
Hence, the constant of variation is 
To find the equation, identify the slope and the y-intercept.
The slope is the coefficient to the variable. When you see the word 'per', you know that 2 is the slope, as she is paying 2 dollars per movie. This, in mathematical terms, is represented as 2x.
The y-intercept is the amount she starts off with. She gets 5 for free, so the y-intercept is +5.
The equation is

To solve for c = 50, plug 50 in and subtract 5 from both sides:

m = 22.5