First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.
P = L + 2W
A = L * W
Now that we have our equations, we need to plug in what we know, which is the 40m of rope.
40 = L + 2W
A = L * W
Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.
L = 40 - 2W
Now, we can substitute the value for L into L in the area equation and get a quadratic equation.
A = W(40 - 2W)
A = -2W^2 - 40W
The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.
V = -b/2a
V = 40/2(2) = 40/4 = 10
Derivative:
-4w - 40 = 0
-4w = 40
w = |-10| = 10
To find the other dimension, use the perimeter equation.
40 = L + 2(10)
40 = L + 20
L = 20m
Therefore, the dimensions of the area are 10m by 20m.
Hope this helps!
The average rate of change would be 9
Find the weight of one book and multiply by ten.
13.5 / 6 = 2.25
2.25 * 10 = 22.5
it moves 2 down and 1 to the left
x - 2
y - 2
I hope this helps
Answer:
Step-by-step explanation:
First, we know that the sin function is odd which means:
sin(-x) = -sin(x).
Secondly evaluating an inverse trigonometric function with a normal trigonometric function as the argument can be rewritten as an algebraic expression.
Let 
We know the certain identity.
We use it to evaluate sin(11 pi / 4).
Another helping identity is the following:
But let's not forget that t = -sin(11 pi/4) = - sqrt(2) / 2
Now we end up with the following equation.
