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2 years ago

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Describe a sequence

1 answer:

Evgen [1.6K]2 years ago

8 0

A rotation of 90 degrees counterclockwise followed by a dilation with a scale factor of 1/2.

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Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Ar

Veseljchak [2.6K]

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

$((a, b), (c, d))\in R$

Where $R$ is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

$\forall a \in A \Rightarrow (a,a) \in R$

Here we need to prove:

$\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R$

As per the given relation:

$((a,b), (a,b) ) \Rightarrow ab =ab$ which is true.

$\therefore$ R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

$\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R$

Here we need to prove:

$\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R$

As per the given relation:

$((a,b),(c,d)) \in R$ means $ad = bc$

$((c,d),(a,b)) \in R$ means $cb = da\ or\ ad =bc$

Hence true.

$\therefore$ R is symmetric.

3. R to be transitive, we need to prove:

$if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R$

$((a,b),(c,d)) \in R$ means $ad = cb$ .... (1)

$((c,d), (e,f)) \in R$ means $fc = ed$ ...... (2)

To prove:

To be $((a,b), (e,f)) \in R$ we need to prove: $fa = be$

Multiply (1) with (2):

$adcf = bcde\\\Rightarrow fa = be$

So, R is transitive as well.

Hence proved that R is an equivalence relation.

8 0

2 years ago

MATH ALGEBRA QUESTION

Alexxx [7]

Easy
remember
x^-m=1/(x^m)

so

f(-1)=4*7^-1=4*(1/(7^1))=4*(1/7)=4/7
f(2)=4*7^2=4*49=196

5 0

2 years ago

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What is the probability of rolling a six sided die and not landing on 3?

sineoko [7]

Answer: 5/6

Step-by-step explanation:

5 0

2 years ago

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Select the correct answer.

ICE Princess25 [194]

What are the choices, it’s blank.

4 0

2 years ago

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These tables of values represent continuous functions. In which table do the values represent an exponential function?

vichka [17]

Answer:

The correct option is B.

Step-by-step explanation:

A function is called an exponential function if it has common ratio.

A function is called an linear function if it has common difference.

In option A.

$\frac{f(2)}{f(1)}=\frac{6}{3}=2$

$\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}$

$2\neq \frac{3}{2}$

Since the given table has different ratio, therefore it is not an exponential function. Option A is incorrect.

In option B.

$\frac{f(2)}{f(1)}=\frac{6}{2}=3$

$\frac{f(3)}{f(2)}=\frac{18}{6}=3$

$3=3$

Since the given table has common ratio, therefore it is an exponential function. Option B is correct.

In option C.

$\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}$

$\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}$

$\frac{11}{5}\neq \frac{17}{11}$

Since the given table has different ratio, therefore it is not an exponential function. Option C is incorrect.

In option D.

$\frac{f(2)}{f(1)}=\frac{8}{7}$

$\frac{f(3)}{f(2)}=\frac{9}{8}$

$\frac{8}{7}\neq \frac{9}{8}$

Since the given table has different ratio, therefore it is not an exponential function. Option D is incorrect.

3 0

2 years ago

Read 2 more answers