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:
Step-by-step explanation:
The expression you want to simplify is 0-(x-y).
0-(x-y)
=-(x-y)
=-x+y
You just have to treat the negative sign in front of (x-y) as a -1 and distribute it to both x and -y.
Answer:
5/12
Step-by-step explanation:
First you add 1/4+2/3.
You need to change the denominator so that they are equal to each other
If you multiply the 1/4 by 3/3 you will get 3/12 which is equal to 1/4
Then you need to do the same to 2/3. This time you need to multiply it by 4/4 to get the same denominator which will be 2/3*4/4=8/12
Then you add 3/12+8/12=11/12. You don't need to add the denominator.
After this you will need to subtract 11/12 and 1/2. This time you need to only change the denominator for 1/2.
You multiply the denominator and numerator by 6/6 to 1/2 and you will get 6/12 then you are going to subtract 11/12-6/12 and you will get 5/12
