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GenaCL600 [577]
3 years ago
12

Malia is planting a garden in her yard.The dimensions are represented by x+4 feet and x+8 feet. She needs fencing to go around t

he perimeter of the garden to keep animals out. Which expression represents the amount of fencing she will need in feet. 4x+24 2x+12 (x+8)+(x+4) x^2+12
Mathematics
1 answer:
Kobotan [32]3 years ago
4 0

Answer:

I think you would have to do 2(x+4)+2(x+8) because it it talking about perimeter and if you imagine a square or rectangle, there are four sides, so just adding x+4 and x+8 wont be the whole perimeter. So, if you solve the expression 2(x+4)+2(x+8) it will give you 4x+24 XD

Step-by-step explanation:

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So what is given is:

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This is done by dividing left and right by 1.9, so you get:

length/1.9 = 1.9*w/1.9, which simplifies to w = length/1.9

Another approach is to replace the multiplication with a simpler one in your head. So in stead of reading "length = 1.9 * width, what is width?", you read "6 = 2*3, what is 3?". You'll immediately realize 3 = 6/2, and that shows you how to change the real equation, ie., width = length/1.9.




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3 years ago
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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