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lukranit [14]
3 years ago
12

Question number 8. Prove that 3 + √5 is an irrational number.​

Mathematics
1 answer:
Marina86 [1]3 years ago
7 0

Answer :

Let's assume the opposite of the statement i.e., 3 + √5 is a rational number.

\\  \sf \: 3 +  \sqrt{5}  =  \frac{a}{b}   \\  \\   \qquad \: \tiny \sf{(where \:  \: a \:  \: and \:  \: b \:  \: are \:  \: integers \:  \: and \:  \: b \:  \neq \: 0)} \\

\\  \sf \:  \sqrt{5}  =  \frac{a}{b}  - 3 =  \frac{a - 3b}{b}  \\

Since, a, b and 3 are integers. So,

\\ \sf \:  \frac{p - 3b}{b}  \\  \\  \qquad \tiny \sf{ \: (is \:  \: a \:  \: rational \:  \: number \:) } \\

Here, it contradicts that √5 is an irrational number.

because of the wrong assumption that 3 + √5 is a rational number.

\\

Hence, 3 + √5 is an irrational number.

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Multiply by the conjugate and simplify.

1/2 + 5i/2

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You are at a coffee shop and notice that as the temperature of the room gets colder, more people order hot beverages. From this
mina [271]

Answer:

negative relationship.

Step-by-step explanation:

An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

Cause and effect can be defined as the relationship between two things or events in which an occurrence one (cause) leads to the occurrence of another (effect).

A negative relationship or correlation can be defined as the relationship between two variables in which there exist an inverse relationship between them i.e as one variable increases, the other decreases and vice-versa.

In this scenario, you are at a coffee shop and notice that as the temperature of the room gets colder, more people order hot beverages. From this observation, you conclude that there is a negative relationship between the temperature and hot beverage sales at this coffee shop because for the temperature to get colder it would decrease and for the hot beverages to be hot, its temperature must be increased.

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3 years ago
What are the chances of landing on heads when tossing one coin?
e-lub [12.9K]

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50%

Step-by-step explanation:

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Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation 2 h tt = − 16t^2+
tekilochka [14]

Answer:

It will take 5.61 seconds for the coin to reach the stream.

Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

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The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

h(t) = -16t^{2} + 72t + 100

-16t^{2} + 72t + 100 = 0

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Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

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4 years ago
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Answer:

800m

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