Matemática discreta Exemplos

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{3}{2} \cdot (9 p + 1) + 1) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{3}{2} \cdot (9 p + 1) + 1) + 1) + 1$

Etapa 1

Simplifique cada termo.

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Etapa 1.1

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Etapa 1.1.1

Simplifique cada termo.

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Etapa 1.1.1.1

Aplique a propriedade distributiva.

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{3}{2} (9 p) + \frac{3}{2} \cdot 1 + 1) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{3}{2} (9 p) + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

Etapa 1.1.1.2

Multiplique

\frac{3}{2} (9 p)

$\frac{3}{2} (9 p)$ .

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Etapa 1.1.1.2.1

Combine

9

$9$ e

\frac{3}{2}

$\frac{3}{2}$ .

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{9 \cdot 3}{2} p + \frac{3}{2} \cdot 1 + 1) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{9 \cdot 3}{2} p + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

Etapa 1.1.1.2.2

Multiplique

9

$9$ por

3

$3$ .

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27}{2} p + \frac{3}{2} \cdot 1 + 1) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27}{2} p + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

Etapa 1.1.1.2.3

Combine

\frac{27}{2}

$\frac{27}{2}$ e

p

$p$ .

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} \cdot 1 + 1) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} \cdot 1 + 1) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

Etapa 1.1.1.3

Multiplique

\frac{3}{2}

$\frac{3}{2}$ por

1

$1$ .

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} + 1) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} + 1) + 1) + 1$

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} + 1) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} + 1) + 1) + 1$

Etapa 1.1.2

Escreva

1

$1$ como uma fração com um denominador comum.

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} + \frac{2}{2}) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} + \frac{2}{2}) + 1) + 1$

Etapa 1.1.3

Combine os numeradores em relação ao denominador comum.

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3 + 2}{2}) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3 + 2}{2}) + 1) + 1$

Etapa 1.1.4

Some

3

$3$ e

2

$2$ .

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{5}{2}) + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{5}{2}) + 1) + 1$

Etapa 1.1.5

Aplique a propriedade distributiva.

t = \frac{3}{2} \cdot (\frac{3}{2} \cdot \frac{27 p}{2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot \frac{27 p}{2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

Etapa 1.1.6

Multiplique

\frac{3}{2} \cdot \frac{27 p}{2}

$\frac{3}{2} \cdot \frac{27 p}{2}$ .

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Etapa 1.1.6.1

Multiplique

\frac{3}{2}

$\frac{3}{2}$ por

\frac{27 p}{2}

$\frac{27 p}{2}$ .

t = \frac{3}{2} \cdot (\frac{3 (27 p)}{2 \cdot 2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{3 (27 p)}{2 \cdot 2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

Etapa 1.1.6.2

Multiplique

27

$27$ por

3

$3$ .

t = \frac{3}{2} \cdot (\frac{81 p}{2 \cdot 2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{2 \cdot 2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

Etapa 1.1.6.3

Multiplique

2

$2$ por

2

$2$ .

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

Etapa 1.1.7

Multiplique

\frac{3}{2} \cdot \frac{5}{2}

$\frac{3}{2} \cdot \frac{5}{2}$ .

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Etapa 1.1.7.1

Multiplique

\frac{3}{2}

$\frac{3}{2}$ por

\frac{5}{2}

$\frac{5}{2}$ .

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{3 \cdot 5}{2 \cdot 2} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{3 \cdot 5}{2 \cdot 2} + 1) + 1$

Etapa 1.1.7.2

Multiplique

3

$3$ por

5

$5$ .

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{2 \cdot 2} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{2 \cdot 2} + 1) + 1$

Etapa 1.1.7.3

Multiplique

2

$2$ por

2

$2$ .

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + 1) + 1$

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + 1) + 1$

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + 1) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + 1) + 1$

Etapa 1.2

Escreva

1

$1$ como uma fração com um denominador comum.

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + \frac{4}{4}) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + \frac{4}{4}) + 1$

Etapa 1.3

Combine os numeradores em relação ao denominador comum.

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15 + 4}{4}) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15 + 4}{4}) + 1$

Etapa 1.4

Some

15

$15$ e

4

$4$ .

t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{19}{4}) + 1

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{19}{4}) + 1$

Etapa 1.5

Aplique a propriedade distributiva.

t = \frac{3}{2} \cdot \frac{81 p}{4} + \frac{3}{2} \cdot \frac{19}{4} + 1

$t = \frac{3}{2} \cdot \frac{81 p}{4} + \frac{3}{2} \cdot \frac{19}{4} + 1$

Etapa 1.6

Multiplique

\frac{3}{2} \cdot \frac{81 p}{4}

$\frac{3}{2} \cdot \frac{81 p}{4}$ .

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Etapa 1.6.1

Multiplique

\frac{3}{2}

$\frac{3}{2}$ por

\frac{81 p}{4}

$\frac{81 p}{4}$ .

t = \frac{3 (81 p)}{2 \cdot 4} + \frac{3}{2} \cdot \frac{19}{4} + 1

$t = \frac{3 (81 p)}{2 \cdot 4} + \frac{3}{2} \cdot \frac{19}{4} + 1$

Etapa 1.6.2

Multiplique

81

$81$ por

3

$3$ .

t = \frac{243 p}{2 \cdot 4} + \frac{3}{2} \cdot \frac{19}{4} + 1

$t = \frac{243 p}{2 \cdot 4} + \frac{3}{2} \cdot \frac{19}{4} + 1$

Etapa 1.6.3

Multiplique

2

$2$ por

4

$4$ .

t = \frac{243 p}{8} + \frac{3}{2} \cdot \frac{19}{4} + 1

$t = \frac{243 p}{8} + \frac{3}{2} \cdot \frac{19}{4} + 1$

t = \frac{243 p}{8} + \frac{3}{2} \cdot \frac{19}{4} + 1

$t = \frac{243 p}{8} + \frac{3}{2} \cdot \frac{19}{4} + 1$

Etapa 1.7

Multiplique

\frac{3}{2} \cdot \frac{19}{4}

$\frac{3}{2} \cdot \frac{19}{4}$ .

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Etapa 1.7.1

Multiplique

\frac{3}{2}

$\frac{3}{2}$ por

\frac{19}{4}

$\frac{19}{4}$ .

t = \frac{243 p}{8} + \frac{3 \cdot 19}{2 \cdot 4} + 1

$t = \frac{243 p}{8} + \frac{3 \cdot 19}{2 \cdot 4} + 1$

Etapa 1.7.2

Multiplique

3

$3$ por

19

$19$ .

t = \frac{243 p}{8} + \frac{57}{2 \cdot 4} + 1

$t = \frac{243 p}{8} + \frac{57}{2 \cdot 4} + 1$

Etapa 1.7.3

Multiplique

2

$2$ por

4

$4$ .

t = \frac{243 p}{8} + \frac{57}{8} + 1

$t = \frac{243 p}{8} + \frac{57}{8} + 1$

t = \frac{243 p}{8} + \frac{57}{8} + 1

$t = \frac{243 p}{8} + \frac{57}{8} + 1$

t = \frac{243 p}{8} + \frac{57}{8} + 1

$t = \frac{243 p}{8} + \frac{57}{8} + 1$

Etapa 2

Simplifique a expressão.

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Etapa 2.1

Escreva

1

$1$ como uma fração com um denominador comum.

t = \frac{243 p}{8} + \frac{57}{8} + \frac{8}{8}

$t = \frac{243 p}{8} + \frac{57}{8} + \frac{8}{8}$

Etapa 2.2

Combine os numeradores em relação ao denominador comum.

t = \frac{243 p}{8} + \frac{57 + 8}{8}

$t = \frac{243 p}{8} + \frac{57 + 8}{8}$

Etapa 2.3

Some

57

$57$ e

8

$8$ .

t = \frac{243 p}{8} + \frac{65}{8}

$t = \frac{243 p}{8} + \frac{65}{8}$

t = \frac{243 p}{8} + \frac{65}{8}

$t = \frac{243 p}{8} + \frac{65}{8}$