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2 years 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]2 years 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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PLEASE HELP ASAP: A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of z

dimaraw [331]

1) $\frac{v(8)-v(0)}{8 - 0} = \frac{10-18}{8} = -1\frac{m}{s}$ .
2) $v(5) = 5^2-9*5+18 = 25-45+18 = -2\frac{m}{s}$ .
3) The particle is moving right when the velocity function is positive: $0\ \textless \ t\ \textless \ 3$ or $6\ \textless \ t\ \textless \ 8$ .
4) When $0\ \textless \ t\ \textless \ \frac{9}{2}$ the particle is slowing down because the acceleration is close to zero $\Rightarrow$ the particle is speeding up when acceleration is increasing away from zero: $\frac{9}{2}\ \textless \ t\ \textless \ 8$ .
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2 years ago

the diagonal of a tv is 26 inches long assuming that this diagonal forms a tv pair 30-60-90 right triangles what are the exact l

Alexxandr [17]

It is an application of Pythagorean Theorem

And it is clear that the lower angle is 30 and the apex angle is 60 (this is how always normal TVs look like) ... refer to the image I attached

So, to calculate the width and the length:

$\frac{length}{26} =cos(30)\\~\\length=26*cos(30)=13 \sqrt{3} ~~in$

$\frac{width}{26} =sin(30)\\~\\width=26*sin(60)=13~~in$

You can after that round the length to be 22.517 in

Hope you got the idea

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2 years ago

A softball pitcher throws a softball to a catcher behind home plate. The softball is 3 feet above the ground when it leaves the

Xelga [282]

The <em><u>correct answer</u></em> is:

h(t) = –16t² + 50t + 3

Explanation:

The general form of an equation such as this is h(t) = at² + v₀t + h₀, where a is the constant due to gravity, v₀ is the initial velocity and h₀ is the initial height.

We are given that the constant due to gravity is -16.

The initial velocity is 50, and the initial height is 3; this gives us the equation

h(t) = -16t² + 50t + 3

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1 year ago

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Amiraneli [1.4K]

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1 year ago

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2 years ago