Let the length = x
2 lengths are 2x.
Then you have 400 - 2x for both widths, so the width is 200 - x.
The are if the rectangle is
y = x(200 - x)
y = 200x - x^2
y = -x^2 + 200x
Take the first derivative ans set equal to zero to find a maximum value.
y' = -2x + 200
-2x + 200 = 0
-2x = -200
x = 100
Since the side of the rectangle is 100, all sides measure 100 ft, and you have a square.
The maximum area is 100 ft * 100 ft = 10,000 ft.
Answer:
Part A: 2.8 miles
Part B: 16.8 miles
Step-by-step explanation:
First, solve for how many miles Ted jogged in 1 day:
Variable x = number of miles
11.2/4 = x/1
Cross multiply
11.2 × 1 = 4 × x
11.2 = 4x
Divide both sides by 4
2.8 = x
He jogged 2.8 miles every day.
To find how many miles Ted would jog in 6 days, simply multiply his miles per day by the number of days he will jog:
2.8 miles × 6 days = 16.8 miles in 6 days
Answer: x=24
Step-by-step explanation:
x+5x/12=x/6+2x/3+14
Multiply both sides of the equation by 12, the least common multiple of 12,6,3.
12x+5x=2x+4×2x+168
Combine 12x and 5x to get 17x.
17x=2x+4×2x+168
Multiply 4 and 2 to get 8.
17x=2x+8x+168
Combine 2x and 8x to get 10x.
17x=10x+168
Subtract 10x from both sides.
17x−10x=168
Combine 17x and −10x to get 7x.
7x=168
Divide both sides by 7.
x= 168/7
Divide 168 by 7 to get 24.
x=24
From the text you can derive the following equations:
(1) A = bh/2 = 8
(2) and h = b+6
Fill in h in (1):
b(b+6)/2 = 8 => b^2 + 6b = 16 with the quadratic formula or simply trying some values for b you can find b=2, so h=8.
The answer would be 1200. hope that helped