Architectural Design The "rise to run" ratio of the roof of a house determines the steepness of the roof.
The rise to run ratio of the roof in the figure is 3 to 4.
Determine the maximum height in the attic of the house
if the house is 32 feet wide.

12 feet

Step-by-step explanation:

For an inclined roof, the rise is the vertical distance from the roof rafter to the vertical top plate while the run is the distance from the edge of the wall to half of the center of the ridge.

The slope is the ratio of the rise to run. Given a rise to run ratio of 3 to 4. The house is 32 feet wide.

The run of the roof =  half of the width of the roof = 1/2 × 32 feet = 16 feet

Let the rise of the roof (height of the attic) be x, hence:

rise to run ratio = height of attic/ run of roof

3/4 = x/16

x = 3/4 × 16

x = 12 feet

The height of the attic is 12 feet

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation:

the linear relationship that represents a variation in direct proportion is the linear function that varies according to the numbers of its domain, for example the cost of producing x number of items can be represented in direct proportion by f (x) = mx + b, where m is the constant of proportionality, x the number of articles produced and b the fixed cost