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)
Well 24=4*6, and 35=7*5 not 6, so 4/7 doesn't = 24/35, so no
Find the common denominator of 3 and 6. which is 6. now just subtact 2 and 1 which is 1. ur answer is 1/6
Use the tangent-chord theorem:
The included chord-tangent angle is half the size of the intercepted arc.
The intercepted arc is "c".
The included chord-tangent-angle is the supplement of 110=70 degrees.
Therefore from the tangent-chord theorem, 70 degrees = half the size of arc "c"
=>
arc "c" = 2*intercepted angle = 2*70 degrees = 140 degrees.
Hold on let me go do my research I’ll brb .