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2 years ago

URGANT!! Please help

Mathematics

1 answer:

Blizzard [7]2 years ago

7 0

Answer:

1464 square kilometers

Step-by-step explanation:

Understanding :

Since it decreases by 4.25%, we can say that each year, the area is 95.75% of the previous year
The function can be written as 1900(0.9575)ⁿ, where n is the number of years

Year 6 :

1900(0.9575)⁶
1900(0.77060655)
1464 square kilometers (nearest square kilometer)

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Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.

Arisa [49]

Answer: $S_n=5(1-\dfrac{1}{n+1})$ ; 5

Step-by-step explanation:

Given series : $[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]$

Sum of series = $S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]$

Consider $\dfrac{1}{n\cdot(n+1)}=\dfrac{n+1-n}{n(n+1)}$

$=\dfrac{1}{n}-\dfrac{1}{n+1}$

⇒ $S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]$

Put values of n= 1,2,3,4,5,.....n

⇒ $S_n=5(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+......-\dfrac{1}{n}+\dfrac{1}{n}-\dfrac{1}{n+1})$

All terms get cancel but First and last terms left behind.

⇒ $S_n=5(1-\dfrac{1}{n+1})$

Formula for the nth partial sum of the series :

$S_n=5(1-\dfrac{1}{n+1})$

Also, $\lim_{n \to \infty} S_n = 5(1-\dfrac{1}{n+1})$

$=5(1-\dfrac{1}{\infty})\\\\=5(1-0)=5$

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3 years ago

What is the area of the sector of the circle below, if the radius is 5 m. and the central angle < AOB measures 88 °. (round a

MariettaO [177]

Answer:

b 19.2

Step-by-step explanation:

a = $\pi$ $r^{2}$ for a circle. We do not want to find the area for a whole circle. We only want to find the area for part of a circle. a hole circle is 360 degrees.