Answer:
a
Step-by-step explanation:
Answer:
Step-by-step explanation:
-6 ≥ x
-2 ≤ x
I don't think you can combine this into one statement.
Your line looks something like
<---------------O O------------------------->
-6 -2
Shade in the 2 Os. The shaded in Os are included in the way the line looks.
Answer:
B.y = 3x - 1
Step-by-step explanation:
Pick two points on the line
(0,1) and (2,5)
The slope using the slope formula
m = (y2-y1)/(x2-x1)
= ( 5-1)/(2-0)
= 4/2
= 2
We want a slope that is greater than 2
The slope intercept form of the equation is
y = mx+b where m is the slope
y = 3x - 1 has a slope of 3 which is greater than 2
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.
