Length = 2*width - 5
perimeter = 2(length + width)
89 = 2(2width - 5 + width)
89 = 6 width - 10
6 width = 99
width = 99/6 = 16.5 feet
length = 2*16.5 - 5 = 28 feet
Sum of geometric sequence
for the sum where the initial value is a₁ and the common ratio is r and the term is n
common ratio is -3
-5 times -3 is 15, -15 times -3=-45 etc
first term is -5
and we want the 8th term
the sum is 8200
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:
144 i multiplied 12x12=144
Step-by-step explanation: