Let's try to tease out a function for the area of our hypothetical rectangle:
We know that the area of a rectangle is Base x Height, and the base will be the length of the x-axis portion of the rectangle. Looking at a graph of y=27 - x^2 will help with intuition on this.
The length of the base will be 2x, since it will be the distance from the (0,0) axis in the positive direction and in the negative direction.
So our rectangle will have an area of 2x, multiplied by the height.
What is the height? The height will be our y value.
Therefore,
A = 2x * y, where x is x-value of the positive vertex.
We already know what y is as a function of x:
y= 27 - x^2
That means our equation for the area of the rectangle is:
A = 2x (27 - x^2) Distribute the terms....
A = 54x - 2x^3
This is essentially a calculus optimization problem. We want to find the Maximum for A, so let's find where the derivative of A is equal to zero.
First, we find the derivative:
A = 54x - 2x^3
A' = 54 - 6x^2
Set A' equal to zero to find the maximum value for A
0 = 54 - 6x^2
6x^2 = 54
x^2 = 9
x = 3
We got our x-value! Now let's find the y value at that point:
y= 27 - x^2
y = 27 - 9
y = 18
The height our rectangle will be 18, and our base will be 2*x = 2*3 = 6
Area = base x height = 18 * 6 = 108
The answer is B) 108.
Answer:
10,24,25
Step-by-step explanation:
First we want to calculate at what height and at what time rocket stops ascending.
h' = 256 - 32t = 0
32t = 256
t = 8
h = 256*8 - 16*8^2
h = 1024
Now we want to find time at which it gets 200 feet that means our equation is:
200 = 256t - 16*t^2
-16*t^2 + 256t - 200 = 0
t1 = 0.82s
t2 = 15.17s
time t1 is when rocket is ascending and t2 when it is descending therefore answer is t2
S=sweaters, ST=shirts, SL=slacks.
Add 4S and 6ST and that should add up to 10 in total, then times 10S/ST by 3SL to get 30 as a grand total.
Step-by-step explanation:
2x + x + 57 = 90
3x = 33
x = 11
m1 = 2 × 11 = 22°
m2 = 11 + 57 = 68°
check: 22 + 68 = 90
