Can someone please help me with this?

Mathematics

1 answer:

Arada [10]3 years ago

4 0

Answer:

$x=14$

Step-by-step explanation:

Similar shapes have proportional corresponding sides. So,

$\dfrac{AB}{PQ}=\dfrac{BC}{QR}=\dfrac{CD}{RS}=\dfrac{DE}{ST}=\dfrac{EA}{TP}$

Substitute all lengths:

$\dfrac{4}{28}=\dfrac{3}{21}=\dfrac{5}{35}=\dfrac{3}{21}=\dfrac{2}{x}$

Therefore,

$\dfrac{2}{x}=\dfrac{1}{7}\\ \\x=14$

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Substituting (2) in above

$f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$