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mixer [17]
2 years ago
8

HELP ME !!!!! Help me please !!!!

Mathematics
1 answer:
lora16 [44]2 years ago
8 0

Answer: 141.3cm^3

Step-by-step explanation:

Pi((3)^2)(-5)

Pi(9)(5)

Pi(45)

3.14×45

141.3

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Let A, B, C and D be sets. Prove that A \ B and C \ D are disjoint if and only if A ∩ C ⊆ B ∪ D
ANEK [815]

Step-by-step explanation:

We have to prove both implications of the affirmation.

1) Let's assume that A \ B and C \ D are disjoint, we have to prove that A ∩ C ⊆ B ∪ D.

We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

Therefore, x ∈ (A \ B) ∩ (C \ D), absurd!

It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

The absurd came from assuming that A ∩ C ⊄ B ∪ D.

That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that  A \ B ∩ C \ D is not empty. That means there is an element x that belongs to  A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

As x ∈ A \ B, x belongs to A but x doesn't belong to B.  

As x ∈ C \ D, x belongs to C but x doesn't belong to D.

With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

It's absurd because we were assuming that A ∩ C ⊆ B ∪ D, therefore every element of A ∩ C must belong to B ∪ D.

The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

7 0
3 years ago
Which inequalities are true? Select the four correct answers.
tiny-mole [99]

The correct anwer is option C and option E which are √4<√5<√√55 and √8<2.9<√√9.

<h3>What is inequality?</h3>

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The two inequalities √4<√5<√√55 and √8<2.9<√√9. are true.

√4<√5<√√55  → 2 < 2.23 < 7.41

√8<2.9<√√9    → 2.82 < 2.9 < 3

Therefore correct answers is option C and option E which are √4<√5<√√55 and √8<2.9<√√9.

To know more about inequality follow

brainly.com/question/24372553

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6 0
2 years ago
What is the first term of the geometric sequence below?
wlad13 [49]

Answer:

A. 2

Step-by-step explanation:

The common ratio between the terms listed is 2. Each term is being multiplied by 2, so to find the first term, you have to divide the first term listed by 2.

4/2 = 2

3 0
2 years ago
Read 2 more answers
Who want to help ???
Fiesta28 [93]
For a set of trials P_{desired}=\frac{desired}{total}. In this case our desired out come is all multiples of 3: 3,6,9 and 12. The total number of outcomes can be found as 100 by adding up all the frequencies. Thus our experimental probability is P_{x=3n}=\frac{6+14+12+1}{100}=\frac{33}{100}=33\%.
8 0
3 years ago
Qfind the product. Write the product in simplest form 1 2/3 x 4 2/5
Elan Coil [88]
1 2/3 = 5/3
4 2/5 = 22/5
5/3•22/5= 110/15
= 22/3
7 0
3 years ago
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