Application of Geometric Series

Mathematics

1 answer:

Gnoma [55]2 years ago

6 0

Answer:

7.2224

Step-by-step explanation:

The value of the summation is given by the formula ...

Sn = (a1)(1 -r^n)/(1 -r) . . . . . where a1 is the first of n terms, and r is the common ratio.

Your sum has first term and ratio ...

a1 = 2(0.6) . . . . . summation term for n=1

r = 0.6

So the sum is ...

$\displaystyle \sum_{n=1}^4{2(0.6^n)}=2(0.6)\dfrac{1-0.6^4}{1-0.6}=\dfrac{1.2}{0.4}(0.8704) = 2.6112$

Then the value of the entire given expression is ...

$\displaystyle 2+2\sum_{n=1}^4{}2(0.6^n)=2+2(2.6112)=\boxed{7.2224}$

_____

A calculator can help you find the value.

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aflati masurile a doua unghiuri complementare stiind ca masura unuia dintre ele este cu 18° mai mica decat triplul masurii celui

Ahat [919]

Answer:

The angle is "27 and 63".

Step-by-step explanation:

Let A and B are two angles, in which A is " $\frac{1}{2}$ " complementary angles and B be is another complementary angle.

Condition of complementary angle :

$A+B =90 ......(i)$

Solution:

$\ A = \ 3B - 18 \\\\ \ put \ the \ value \ of \ A \ in \ equation.....(i) \\\\ \ Equation: \\ \\\Rightarrow \ A\ +\ B \ =\ 90 \\\\\Rightarrow \ 3B\ -\ 18 \ + \ B \ = \ 90 \\\\\Rightarrow \ 4B \ = \ 90 +18 \\\\\Rightarrow \ 4B = 108 \\\\ \Rightarrow B = \frac{108}{4} \\\\ \Rightarrow B \ = \ 27\\$

$\ put \ the \ value \ of \ B \ in \ equation (i).\\\\ \ Equation: \\\\\Rightarrow A+B=90\\\\\Rightarrow A+27=90\\\\\Rightarrow A=90-27\\\\\Rightarrow A= 63$