For the answer to the question above,
1. If we let x as the side of the square cut-out, the formula for the capacity (volume) of the food dish is:
V = (12 - 2x)(8 - 2x)(x)
V = 96x - 40x^2 + 4x^3
To find the zeros, we equate the equation to 0, so, the values of x that would result to zero would be:
x = 0, 6, 4
2. To get the value of x to obtain the maximum capacity, we differentiate the equation, equate it to zero, and solve for x.
dV/dx = 96 - 80x + 12x^2 = 0
x = 5.10, 1.57
The value of x that would give the maximum capacity is x = 1.57
3. If the volume of the box is 12, then the value of x can be solved using:
12 = 96x - 40x^2 + 4x^3
x = 0.13, 6.22, 3.65
The permissible value of x is 0.13 and 3.65
4. Increasing the cutout of the box increases the volume until its dimension reaches 1.57. After that, the value of the volume decreases it reaches 4.
5. V = (q -2x) (p - 2x) (x)
The first step is to add 5.2 to both sides.
Using the first equation:
4x = y + 3 ---> y = 4x - 3
We then substitute this into the second equation:
7x - 9(4x-3) = -2 ---> 7x - 9x + 27 = -2 ---> -2x = -29 ---> x = 14.5
3x(3x-2y)
you have to find a common factor between the two numbers. in this case it's three, so you just divide each number by three.
Answer: 4 Mph.
Step-by-step explanation: ...
