A circle has a circumference of 12. It has an arc of length 11.

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

7 0

Answer:

The central angle is 330 degrees

Step-by-step explanation:

The arc length is equal to the circumference time the fractional part of the circle

arc length = circumference * x/360

11 = 12 * x/360

Divide each side by 12

11/12 = 12/12 *x/360

11/12 = x/360

Multiply by 360

11*360/12 = x /360 *360

330 = x

The central angle is 330 degrees

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Determine the sum of the first 9 terms in the geometric series where r= -0.25 and a1= 256.

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$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=-0.25\\ a_1=256\\ n=9 \end{cases}$

$\bf S_9=256\left(\cfrac{1-(-0.25)^9}{1-(-0.25)} \right)\implies S_9=256\left( \cfrac{1+0.25^9}{1+0.25} \right) \\\\\\ S_9=256\left( \cfrac{52429}{65536}\right)\implies S_9=\cfrac{52429}{256}\implies S_9=204.80078125$