Find two positive numbers satisfying the given requirements. the sum of the first and twice the second is 240 and the product is a maximum.

The two numbers are 120 and 60

Let's call the two numbers x and y. The first sentence translates into

from which we can derive

So, their product can be written as

This expression is a quadratic polynomial with negative leading coefficient, so it represents a parabola concave down. So, the vertex of the parabola is its maximum, which we can find as usual: given the parabola , its extreme point is located at .

So, in your case, since and , the maximum is located at

Now that we know y, we can deduce the value of x:

So, the two numbers are 120 and 60

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:

$452.90 because you needed to round to the nearest cent