Answer:
Maximum area = 800 square feet.
Step-by-step explanation:
In the figure attached,
Rectangle is showing width = x ft and the side towards garage is not to be fenced.
Length of the fence has been given as 80 ft.
Therefore, length of the fence = Sum of all three sides of the rectangle to be fenced
80 = x + x + y
80 = 2x + y
y = (80 - 2x)
Now area of the rectangle A = xy
Or function that represents the area of the rectangle is,
A(x) = x(80 - 2x)
A(x) = 80x - 2x²
To find the maximum area we will take the derivative of the function with respect to x and equate it to zero.
= 80 - 4x
A'(x) = 80 - 4x = 0
4x = 80
x = 
x = 20
Therefore, for x = 20 ft area of the rectangular patio will be maximum.
A(20) = 80×(20) - 2×(20)²
= 1600 - 800
= 800 square feet
Maximum area of the patio is 800 square feet.
Answer:
Aircraft carrier speed = 4.97 km/h
Step-by-step explanation:
Given that the time taken by the aircraft = 5 hours
Let the distance covered = X
Speed = V
Time taken by the ship = 7 hours
Let the distance covered = Y
Speed = 8V
Since it is 8 km/h faster than the aircraft carrier.
Using the speed formula
Speed = distance/time
Distance = speed × time
For the aircraft;
X = 5V
For the ship:
Y = 7 × 8V = 56V
Since they are 303km distance apart,
X + Y = 303
5V + 56V = 303
61V = 303
V = 303/61
V = 4.97 km/h
Aircraft carrier speed = 4.97 km/h
Answer:
2
Step-by-step explanation:
Given:
The interval, x = -2 to x = 0.
Required:
Average rate of change from x = -2 to x = 0.
SOLUTION:
From the graph,
If x = -2, f(-2) = 0.
If x = 0, f(0) = 4
Average rate of change = 
Where,
Plug in the values into the formula:
Average rate of change from x = -2 to x = 0 is 2.
Answer:
We know area of a square = side× side
Let the length of each side of the square be s
s×s= 121 sq ft
s²= 121 sq.ft
s=√121
s= 11 ft
11 ft long and wide
