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1 year ago

Prove that x is a subset of y then x union z is a subset of y union z for all sets x y and z

Mathematics

1 answer:

Ganezh [65]1 year ago

4 0

We are to show that if X ⊆ Y then (X ∪ Z) ⊆ (Y ∪ Z) for sets X, Y, Z.

Assume that a is a representative element of X, that is, a ∈ X. By the definition of union, a ∈ X ∪ Z. Now because X ⊆ Y and we assumed a ∈ X, then a ∈ Y by the definition of subset. And because a ∈ Y, then a ∈ Y ∪ Z by definition of union.

We chose our representative element, a, and showed that a ∈ X ∪ Y implies that a ∈ Y ∪ Z and this completes the proof.

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Troy has a price chart below for various ingredients he needs to order for his sandwich bar. Sandwich Ingredients Item Cost (per

shepuryov [24]

Answer:

$93.75

Step-by-step explanation:

The computation of the total cost of order is shown below:

The Cost of 8 pounds of Pepperoni is

= 8 × $3.15

= 25.2

The Cost of 15 pounds of cheese is

= 15 × $1.85

= $27.75

The Cost of 12 pounds of sausage is

= 12 × $3.40

= $40.8

So, The total cost is

= $25.2 + 27.75 + $40.80

= $93.75

4 0

2 years ago

In a certain town, 60 families own tv sets, 85 own scooters, 70th own refrigerators, and 95 own radio sets. One hundred and thir

Black_prince [1.1K]

Answer:

310

Step-by-step explanation:

The maximum possible number is obtained when each family owns one appliance only. That total is ...

60 + 85 +70 +95 = 310

The maximum possible number of families is 310.

5 0

2 years ago

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

1 year ago

How much heat is required to raise the temperature of

Elina [12.6K]

Answer:

The amount of heat required to raise the temperature of liquid water is 9605 kilo joule .

Step-by-step explanation:

Given as :

The mass of liquid water = 50 g

The initial temperature = $T_1$ = 15°c

The final temperature = $T_2$ = 100°c

The latent heat of vaporization of water = 2260.0 J/g

Let The amount of heat required to raise temperature = Q Joule

Now, From method

Heat = mass × latent heat × change in temperature

Or, Q = m × s × ΔT

or, Q = m × s × ( $T_2$ - $T_1$ )

So, Q = 50 g × 2260.0 J/g × ( 100°c - 15°c )

Or, Q = 50 g × 2260.0 J/g × 85°c

∴ Q = 9,605,000 joule

Or, Q = 9,605 × 10³ joule

Or, Q = 9605 kilo joule

Hence The amount of heat required to raise the temperature of liquid water is 9605 kilo joule . Answer

4 0

1 year ago

Question 1(Multiple Choice Worth 2 points)

earnstyle [38]

These are 3 questions and 3 answers.

1) Find

$\lim_{x \to \ 2^+} f(x)$

Answer: 4.

Explanation:

The expression means the limit as the function f(x) approaches 2 from the right.

Then, you have to use the function (the line) that comes from the right of 2 and gets as close as you want to x = 2.

That is the line that has the open circle around y = 4, and that is the limit searched.

2) Use the graph to determine the limit if it exists.

Answer:

$\lim_{x \to \ 2^-} f(x) = 3$

$\lim_{x \to \ 2^+} f(x)=-3$

To determine each limit you use the function from the side the value of x is being approached.

Note, that since the two limits are different it is said that the limit of the function as it approaches 2 does not exist.

3)
Answer: - 1

$\lim_{x \to \ 3^-} f(x) = -1$

To find the limit when the function is approached to 3 from the left you follow the line that ends with the open circle at (3, -1).

Therefore, the limit is - 1.

5 0

2 years ago

Read 2 more answers