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Papessa [141]
3 years ago
13

For a science experiment Marcia dissolved 1.0 kilogram of salt in 3.0 liters of water. For a different experiment,bobby dissolve

d 2.0 pounds of salt in 7.0 pints of water. Which person made a more concentrated salt solution? Explain. Use 1L=2.11 pints. Round your answer to the nearest hundredth
Mathematics
1 answer:
Vesnalui [34]3 years ago
7 0
Marcia dissolved 1 kg of salt in 3 litres of water
Bobby dissolved 2 pounds of salt in 7 pints of water
We know that
1 litre = 2.11 pints
We also know that
1 pound = 0.4535 kg
Now if we take the case of Bobby, and convert the pound to kg then
1 pound = 0.4535 kg
2 pounds = (0.4535 * 2) kg
 <span>                 = 0.907 kg</span> <span>               
                 = 0.91 kg</span>
Bobby dissolved the salt in 7 pints of water
We know
2.11 pints = 1 litre
Then
7 pints = (7/2.11) litre
 <span>            = 3.32 litres</span>
So we now see that Bobby has dissolved 0.91 kg of salt in 3.32 litres of water
Marcia dissolved 1 kg of salt in 3 litres of water.
So Marcia has made a more concentrated solution since she has dissolved more salt in less amount of water whereas Bobby has dissolved less amount of salt in more water.



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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as
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Answer:

x = ∛(2V/7)

y = ∛(2V/7)

z = 3.5 [∛(2V/7)]

{x,y,z} = { ∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)] }

Step-by-step explanation:

The aquarium is a cuboid open at the top.

Let the dimensions of the base of the aquarium be x and y.

The height of the aquarium is then z.

The volume of the aquarium is then

V = xyz

Area of the base of the aquarium = xy

Area of the other faces = 2xz + 2yz

The problem is to now minimize the value of the cost function.

The cost of the area of the base per area is seven times the cost of any other face per area.

With the right assumption that the cost of the other faces per area is 1 currency units, then, the cost of the base of the aquarium per area would then be 7 currency units.

Cost of the base of the aquarium = 7xy

cost of the other faces = 2xz + 2yz

Total cost function = 7xy + 2xz + 2yz

C(x,y,z) = 7xy + 2xz + 2yz

We're to minimize this function subject to the constraint that

xyz = V

The constraint can be rewritten as

xyz - V = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = 7xy + 2xz + 2yz - λ(xyz - V)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points and at the turning point, each of the partial derivatives is equal to 0.

(∂L/∂x) = 7y + 2z - λyz = 0

λ = (7y + 2z)/yz = (7/z) + (2/y) (eqn 1)

(∂L/∂y) = 7x + 2z - λxz = 0

λ = (7x + 2z)/xz = (7/z) + (2/x) (eqn 2)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x) (eqn 3)

(∂L/∂λ) = xyz - V = 0

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

(eqn 1) = (eqn 2)

(7/z) + (2/y) = (7/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(eqn 1) = (eqn 3)

(7/z) + (2/x) = (2/y) + (2/x)

(7/z) = (2/y)

z = (7y/2)

Hence, at the point where the box has minimal area,

y = x,

z = (7y/2) = (7x/2)

We can then substitute those into the constraint equation for y and z

xyz = V

x(x)(7x/2) = V

(7x³/2) = V

x³ = (2V/7)

x = ∛(2V/7)

y = x = ∛(2V/7)

z = (7x/2) = 3.5 [∛(2V/7)]

The values of x, y and z in terms of the volume that minimizes the cost function are

{x,y,z} = {∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)]}

Hope this Helps!!!

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A urn contains 3 red and 5 black balls. Tom first withdraws a ball from the urn and Mary withdraws a ball from the urn without r
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zubka84 [21]

Answer: Hello!

Let's start with the word TRISKAIDEKAPHOBIA wich has 17 letters (some of them repeat, but it does not matter in this problem)

We want to know how many permutations we can do with 17 letters: then think this way, Lets compose a word. The first letter of this word has 17 options, the second letter of the word has 16 options (you already took one of the set) the third letter of the word has 15 options, and so on.

The total number of permutations is the product of the number of options that you have for each letter, this is:

17*16*15*14*....*3*2*1 = 17! = 3.6e+14

(b) FLOCCINAUCINIHILIPILIFICATION now we have 30 letters in total, using the same reasoning as before, here we have 30! permutations; this is

30! = 2.65e+32

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3 years ago
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