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Schach [20]
3 years ago
15

Solve |x+1| + 7 = 31

Mathematics
1 answer:
MakcuM [25]3 years ago
5 0

Answer:

x1=-25,x2=23

Step-by-step explanation: hope it helps :)

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums
gtnhenbr [62]

I'm guessing the sum is supposed to be

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}

Split the summand into partial fractions:

\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}

1=a(5k+4)+b(5k-1)

If k=-\frac45, then

1=b(-4-1)\implies b=-\frac15

If k=\frac15, then

1=a(1+4)\implies a=\frac15

This means

\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}

Consider the nth partial sum of the series:

S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)

The sum telescopes so that

S_n=\dfrac2{14}-\dfrac2{5n+4}

and as n\to\infty, the second term vanishes and leaves us with

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17

7 0
3 years ago
At the baseball stadium there are 548 seats that are divided into 14 rows how many seats are in each row
tatyana61 [14]

Answer:

There are 39 seats I think.

Step-by-step explanation:

548 divided by 14 is a decimal but rounded it to the nearest full number.

5 0
3 years ago
Read 2 more answers
What is the solution to бn + 1 = 2n – 7
yawa3891 [41]

Answer:

n = -2

Step-by-step explanation:

6n = 2n-8

4n = -8

n = -2

8 0
4 years ago
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Mrs. Miller has a rectangular garden with a length of 20 feet long with an area of (20x-200) square feet. Write an expression th
krek1111 [17]

Perimeter = (20 + 2x) mm.

Step-by-step explanation:

The octopus pupil has length 20 mm and the expression for its area is given by (20x - 200) square mm.

If the width of the octopus pupil is w, then 20w = 20x - 200

⇒ w = (x - 10) mm.

Therefore, the expression for its perimeter is 2(Length + Width) = 2 ( 20 + x - 10) = 2( 10 + x) = (20 + 2x) mm. (Answer)

6 0
3 years ago
Point W has coordinates (4, -7). If it is reflected over the y -axis, what are the coordinates of its image?
Korolek [52]

Answer:

I thank it is D

Step-by-step explanation:

4 0
2 years ago
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