Variation Expression-Adv. Math

The top and bottom of a can cost 5 cents per cm^2 and the side costs 3 cents per cm^2. The surface area is Surface Area = 2pi rh +2pi r^2, and the volume of the can is 400 cm^3. What is the minimum cost to manufacture the can, to the nearest penny?

$10.69

Write a general formula to describe the variation: M varies jointly with the cube root of the difference B and b

M= k 3^sqrt(B-b)

Write a general formula to describe the variation: M varies jointly with the cube root of the difference B and b.

M=k 3^sqrt(B-b)

Write a general formula to describe the variation: M varies jointly with the inverse of the square of the sum of two bases, B and b.

M=k/(B-b)^2

Write a general formula to describe the variation: M varies jointly with the inverse of the square of B and directly with the cube of b.

M=kb^3/B^2

Write a general formula to describe the variation: S varies jointly with the inverse of the square of P and inverse of the cube of L; S=4, P=2, L=5

S= 2000/P^2L^3

Write a general formula to describe the variation: S varies jointly with the inverse of the square of P and inverse of the cube of L; S=7, P=64, L=100

S= 280/ 3^sqrt(9) sqrt(L)

P(x)=100(x-2), where x is the number of times the lie is told and P(x) is the percentage of the population what will believe the lie. Graph the function P on a relevant domain; try vary from x=0 to x=50. Interpret the meaning of the vertical asymptotes.

The vertical asymptotes is not relevant since a negative population holds no relevance.

Force F in newtons is the product of mass m in kilograms and and acceleration a in meters per second: F=ma. Let the force be 200 newton. Solve the equation for m and graph the time function on a relevant domain. What is the physical interpretation for the vertical asymptotes VA and horizontal asymptote HA?

VA: As the acceleration approaches 0, the mass to maintain a force of 200 newtons get infinitely large. HA: As the acceleration becomes infinitely large, the mass to maintain a force of 200 newtons approaches 0

A(t)= 200t/t^2+9, where t represent the time in minutes since the injection. Graph the function A(t) over the relevant portions of domain; try varying from t=0 to t= 24. What is the interpretation of any asymptotes in terms of this real-world model.

VA: none HA: As time increase, the concentration approaches 0

Write a general formula to describe the variation: W varies jointly with the inverse of the cube root h and directly with A; W=5 h=216 A=200

W= 3A/20 3^sqrt(h)

A closed box with square base has a volume of 6,000 in^3. Write a function to model the surface area s(x) of the box in terms of the side of the base, x.

s(x)= 2x^3+24,000/x

Write a general formula to describe the variation: x varies directly with the cube of y; x=-3 when y=125

x= -3/5 3^sqrt(y)

Write a general formula to describe the variation: x varies directly with the cube of y; x=8 when y=-8

x=-1/64y^3

Write a general formula to describe the variation: x varies inversely with the square of y; x=-1 when y=5

x=-25/y^2

Write a general formula to describe the variation: x varies directly with the square root of y; x=6 when y=64

x=48/sqrt(y)