Find the measure of

Mathematics

2 answers:

Molodets [167]3 years ago

8 0

Answer:

28 degrees

Step-by-step explanation:

since DBE is 90 degrees, ABE is 90 degrees as well

given that BEF is 62 degrees

you need to subtract 90 from 62

to get 28 degrees as your answer

Ghella [55]3 years ago

4 0

sorry been trying to find something to say but i don't have a answer for it wish i could help

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What is the sum of the geometric series

lbvjy [14]

If $S$ denotes the sum of the first $n$ terms of a geometric series with first term $a$ and common ratio $r$ , then

$S=a+ar+ar^2+\cdots+ar^{n-3}+ar^{n-2}+ar^{n-1}$
$rS=ar+ar^2+ar^3+\cdots+ar^{n-2}+ar^{n-1}+ar^n$
$\implies S-rS=a+(ar-ar)+(ar^2-ar^2)+\cdots+(ar^{n-1}-ar^{n-1})-ar^n$
$\implies (1-r)S=a(1-r^n)$
$\implies S=a=\dfrac{1-r^n}{1-r}$

Using summation notation, you have

$S=\displaystyle\sum_{x=1}^nar^{x-1}=\sum_{x=0}^{n-1}ar^x=a\dfrac{1-r^n}{1-r}$

In this case, you have $a=2$ , $r=\dfrac12$ , and $n=16$ . So the value of the sum is

$\displaystyle\sum_{x=0}^{15}2\left(\frac14\right)^x=2\dfrac{1-\left(\frac14\right)^{16}}{1-\frac14}\approx2.67$

Rounded to the nearest whole number, the answer would be 3.

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2 years ago

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