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3 years ago

WILL MAKR BRIANLIEST IF RIGTH!!!

Mathematics

1 answer:

kicyunya [14]3 years ago

5 0

Answer:

3 units

Step-by-step explanation:

By intersecting chords theorem:

$AE \times EB = CE \times ED$

$\therefore 3 \times 4= x \times (x+1)$

$\therefore 12= x^2 +x$

$\therefore x^2 +x-12=0$

$\therefore x^2 +4x-3x-12=0$

$\therefore x(x +4)-3(x+4)=0$

$\therefore (x +4)(x-3)=0$

$\therefore (x +4)=0, \: (x-3)=0$

$\therefore x=-4, \: x=3$

Since, the value of x can not be negative.

$\therefore x\neq - 4$

$\implies x = 3$

$\implies CE = 3$

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and so on. Continuing in this way we end up with

$a_n=\dfrac{a_1}{n!}$

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$y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x$

We also require the solution to satisfy $y(0)=a_0$ , which we can do easily by adding and subtracting a constant as needed:

$y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}$

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3 years ago

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Step-by-step explanation: