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:
idrk but use brainly it rly helps
Step-by-step explanation:
The following are the list of the racial injustice that king uses as effective support for his claim that african american are not free.
#1. He uses word to contrast the racial situation in the country in the past and present to what is expected in the future,
#2 The king shows that there is hope for change in the future
#3. The king uses metaphor.
<span>We let x be the length and y be the width of the rectangle. Then,
Perimeter = 2x + 2y
100 = 2x + 2y
50 = x + y
y = 50 - x
Area = xy
A = x(50 - x)
A = 50x - x^2
We then take the derivative; set it equal to zero:
A ' = 50 - 2x
0 = 50 - 2x
2x = 50
x = 25
y = 50 - x
y = 50 - 25
y = 25
Therefore, the dimensions are 25 and 25.</span>
Answer:
7x+21 = 7x + 21
Step-by-step explanation:
7(x+3)=6-(-7x - 15)
L.H.S
=7(x+3)
=7x+21 (multiply 7 by (x+3))
R.H.S:
=6-(-7x - 15)
= 6+7x+15 (multiply the -ive sign in the bracket)
= 7x + 21 ( adding 15 and 6)
now compare the two sides
7x+21 = 7x + 21 hence we prove that L.H.S= R.H.S
