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Llana [10]
3 years ago
15

Match the following.

Mathematics
2 answers:
Temka [501]3 years ago
7 0
Match the following.

Given A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {1, 3, 5}

1. A ∪ B {1, 2, 3, 4, 5, 6}

2. A ∪ C {1, 2, 3, 4, 5}

3. A ∩ B {2, 4}
4. A ∩ C {1, 3, 5}
5. B ∩ C null, or empty set
Strike441 [17]3 years ago
4 0

Answer with Step-by-step explanation:

Intersection of two sets gives the element which is common in both the sets and union gives the elements of both the sets.

A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {1, 3, 5}

1. A ∪ B={1,2,3,4,5,6}

2. A ∪ C={1,2,3,4,5}

3. A ∩ B={2,4}  

4. A ∩ C={1,3,5}  

5. B ∩ C=null or empty set  

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A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E. There is a 10mi/h cross wind blowing due eas
Ksju [112]

Answer:

The actual speed = 27.12 mi/h

Direction = 36.5° in NE(north of east)

Step-by-step explanation:

As given , A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E.

⇒θ = 36°

Let v₀ be the constant speed, then v₀ = 20

Let vₓ be the speed in East direction

     v_{y} be the speed in North direction

So,

vₓ  = v₀ sin(θ) = 20 sin(36°) + 10 ( As given, There is a 10mi/h cross wind blowing due east.)

⇒vₓ  = 20(0.588) + 10 = 11.76 + 10 = 21.76 mi/h

and   v_{y}  = v₀ cos(θ) = 20 cos(36°) = 20(0.809) = 16.18 mi/h

Now,

the actual speed = √(vₓ)² + (v_{y})²

                            = √(21.76)² + (16.18)²

                            = √473.498 + 261.792

                            = √735.29 =  27.12

⇒The actual speed = 27.12 mi/h

Now,

Direction = θ = tan^{-1}(\frac{v_{y} }{v_{x} } ) = tan^{-1}(\frac{16.18 }{21.76 } ) =  tan^{-1}(0.74) = 36.5

⇒ Direction = 36.5° in NE(north of east)

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