Well, if it is increasing at a fixed rate of 2 mm/s, then the volume would still be increasing at a rate of 2 mm/s when the diameter is 80 mm, if I understand your question correctly.
You need to know the equation of motion for the particle.
-9x^3-72x^2+36=3x^3+x^2-3x+8 Add 9x^3 to both sides.
-72x^2 + 36 = 3x^3 + 9x^3 + x^2 - 3x + 8 Add 72x^2 to both sides
36 = 12x^3 + 73x^2 - 3x + 8 Subtract 36 from both sides.
0 = 12x^3 + 73x^2 - 3x - 28
It does factor, but it is not very nice.
(x + 6.06)(x - 6.09)(x + 0.632)
If there is any kind of error please report it in a note below.
Given that the insurance pays 80% of the cost of surgery and the surgery cost $9600, the amount of money Vivian will pay will be given as follows:
20/100×9600
=$1960
since she will cater for the deductibles that amount to $500 before the insurance takes over, then the total amount she will have to pay will be:
1960+500
=$2420
