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lord [1]
3 years ago
10

A two-liter cola costs $1.19 and 6 cans each containing 16 oz cost $1.59. Which is the better buy and by how much?

Mathematics
2 answers:
Lelu [443]3 years ago
6 0

Answer:

THe 16 Oz is cheaper by $0.036 per unit

Step-by-step explanation:

Given

A 2-litre cola;

Size = 2 litre

Total Cost = $1.19

6 cans;

Size = 16 Oz each

Size = 16 * 6 = 96 Oz.

Total Cost = $1.59

Required?

Which is a better buy.

By "being a better buy", we assume that it means cheaper.

To calculate the cheaper buy, first we need to convert the containers to the same unit.

We'll convert 96 Oz to litres

1 Oz = 0.0295735 litre

To get the size of 96 Oz, we can simply multiply both sides of the equation by 96. This gives

96 * 1 Oz = 96 * 0.0295735 litre

96 Oz = 2.839056

Then, we'll calculate the unit price;

Unit price is calculated by Total price / Size

For the 2-litre cola;

Size = 2 litre

Total Cost = $1.19

Unit Price = $1.19/2 litre

Unit Price = $0.596 per litre

6 cans;

Size = 16 Oz each

Size = 16 * 6 = 96 Oz = 2.839056 litre

Total Cost = $1.59

Unit Price = $1.59/2.839056 litre

Unit Price = $0.560 per litre

The unit cost of the 16oz is smaller than the 2 litre bottle, hence we conclude that the 16 Oz is cheaper.

And it is cheaper by ($0.596 - $0.560)

= $0.036

larisa [96]3 years ago
4 0
The 6 cans, containing 16 oz each is the better buy.
16x6= 96 oz
96 oz converted to liters, is 2.83906 liters.
So it's better to buy the cans by .83906
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A cylindrical tank has a base of diameter 12 ft and height 5 ft. The tank is full of water (of density 62.4 lb/ft3).(a) Write do
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Answer:

a.  71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

b.  23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

c. 99840π lb/ft-s²∫₀⁶rdr

Step-by-step explanation:

.(a) Write down an integral for the work needed to pump all of the water to a point 4 feet above the tank.

The work done, W = ∫mgdy where m = mass of cylindrical tank = ρA([5 + 4] - y) where ρ = density of water = 62.4 lb/ft³, A = area of base of tank = πd²/4 where d = diameter of tank = 12 ft.( we add height of the tank + the height of point above the tank and subtract it from the vertical point above the base of the tank, y to get 5 + 4 - y) and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdy

W = ∫ρA([5 + 4] - y)gdy

W = ∫ρA(9 - y)gdy

W = ρgA∫(9 - y)dy

W = ρgπd²/4∫(9 - y)dy

we integrate W from  y from 0 to 5 which is the height of the tank

W = ρgπd²/4∫₀⁵(9 - y)dy

substituting the values of the other variables into the equation, we have

W = 62.4 lb/ft³π(12 ft)² (32 ft/s²)/4∫₀⁵(9 - y)dy

W = 71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

.(b) Write down an integral for the fluid force on the side of the tank

Since force, F = ∫PdA where P = pressure = ρgh where h = (5 - y) since we are moving from h = 0 to h = 5. So, P = ρg(5 - y)

The differential area on the side of the tank is given by

dA = 2πrdy

So.  F = ∫PdA

F = ∫ρg(5 - y)2πrdy

Since we are integrating from y = 0 to y = 5, we have our integral as

F = ∫ρg2πr(5 - y)dy

F = ∫ρgπd(5 - y)dy    since d = 2r

substituting the values of the other variables into the equation, we have

F = ∫₀⁵62.4 lb/ft³π(12 ft) × 32 ft/s²(5 - y)dy

F = 23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

.(c) How would your answer to part (a) change if the tank was on its side

The work done, W = ∫mgdr where m = mass of cylindrical tank = ρAh where ρ = density of water = 62.4 lb/ft³, A = curved surface area of cylindrical tank = 2πrh  where r = radius of tank, d = diameter of tank = 12 ft. and h =  height of the tank = 5 ft and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdr

W = ∫ρAhgdr

W = ∫ρ(2πrh)hgdr

W = ∫2ρπrh²gdr

W = 2ρπh²g∫rdr

we integrate from r = 0 to r = d/2 where d = diameter of cylindrical tank = 12 ft/2 = 6 ft

So,

W = 2ρπh²g∫₀⁶rdr

substituting the values of the other variables into the equation, we have

W = 2 × 62.4 lb/ft³π(5 ft)² × 32 ft/s²∫₀⁶rdr

W = 99840π lb/ft-s²∫₀⁶rdr

7 0
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