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)
Answer:
6x +24
Step-by-step explanation:
you factor out the 6 so 6x and 6*4 is 24
Answer:
<h2>4/5</h2>
Step-by-step explanation:
Look at the picture.
We need a hypotenuse length.
Use Pythagorean theorem:
We have
Substitute:
For the sine we have:
Substitute:
X+5 = -2x + 12
-5 -5
x = -2x + 7
+2x +2x
3x = 7
x = 2 1/3
y = x + 5
y = 2 1/3 + 5
y = 7 1/3
Answer:
2x-6
Step-by-step explanation:
