Step-by-step explanation:
F ( x ) = x² + 2x - 24
{ factorising by middle term splitting method }
[ 24 = 2 × 2 × 2 × 3 ]
F ( x ) = x² + 6x - 4x - 24
F ( x ) = x ( x + 6 ) -4 ( x + 6 )
F ( x ) = ( x + 6 ) ( x - 4 )
1. Find the equation of the line AB. For reference, the answer is y=(-2/3)x+2.
2. Derive a formula for the area of the shaded rectange. It is A=xy (where x is the length and y is the height).
3. Replace "y" in A=xy with the formula for y: y= (-2/3)x+2:
A=x[(-2/3)x+2] This is a formula for Area A in terms of x only.
4. Since we want to maximize the shaded area, we take the derivative with respect to x of A=x[(-2/3)x+2] , or, equivalently, A=(-2/3)x^2 + 2x.
This results in (dA/dx) = (-4/3)x + 2.
5. Set this result = to 0 and solve for the critical value:
(dA/dx) = (-4/3)x + 2=0, or (4/3)x=2 This results in x=(3/4)(2)=3/2
6. Verify that this critical value x=3/2 does indeed maximize the area function.
7. Determine the area of the shaded rectangle for x=3/2, using the previously-derived formula A=(-2/3)x^2 + 2x.
The result is the max. area of the shaded rectangle.
Answer:
- No, there is no proportional relationship
Step-by-step explanation:
<u>The proportional relationship is:</u>
- y = kx, which is a special form of linear equation, with zero y-intercept
<u>In the given case we have:</u>
This is a linear function but not proportional relationship because it has y-intercept, different than zero
Answer:
whatttt!!!!!!!!!!
Step-by-step explanation:
