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3 years ago

Which function is represented by the graph

Mathematics

1 answer:

krek1111 [17]3 years ago

7 0

Answer: y = -2|x| + 1

Step-by-step explanation: it is an absolute value function, y = |x|, moved up one. then we see that it has been flipped. it has also been vertically stretched by a factor of 2.

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Determine determine whether the following geometric series converges or diverges. if the series converges find its sum.

Lilit [14]

For starters,

$\dfrac{3^k}{4^{k+2}}=\dfrac{3^k}{4^24^k}=\dfrac1{16}\left(\dfrac34\right)^k$

Consider the $n$ th partial sum, denoted by $S_n$ :

$S_n=\dfrac1{16}\left(\dfrac34\right)+\dfrac1{16}\left(\dfrac34\right)^2+\dfrac1{16}\left(\dfrac34\right)^3+\cdots+\dfrac1{16}\left(\dfrac34\right)^n$

Multiply both sides by $\frac34$ :

$\dfrac34S_n=\dfrac1{16}\left(\dfrac34\right)^2+\dfrac1{16}\left(\dfrac34\right)^3+\dfrac1{16}\left(\dfrac34\right)^4+\cdots+\dfrac1{16}\left(\dfrac34\right)^{n+1}$

Subtract $S_n$ from this:

$\dfrac34S_n-S_n=\dfrac1{16}\left(\dfrac34\right)^{n+1}-\dfrac1{16}\left(\dfrac34\right)$

Solve for $S_n$ :

$-\dfrac14S_n=\dfrac3{64}\left(\left(\dfrac34\right)^n-1\right)$

$S_n=\dfrac3{16}\left(1-\left(\dfrac34\right)^n\right)$

Now as $n\to\infty$ , the exponential term will converge to 0, since $r^n\to0$ if $0$ . This leaves us with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{k=1}^n\frac{3^k}{4^{k+2}}=\sum_{k=1}^\infty\frac{3^k}{4^{k+2}}=\frac3{16}$

8 0

3 years ago

Read 2 more answers

What is the slope of a line perpendicular to y = -3/7x + 1 (Answer as an improper fraction and not a mixed number or decimal)

Veseljchak [2.6K]

For lines to be perpendicular they would need to have opposite slopes, so for a slope of -3/7 the slope of a perpendicular line would be 7/3

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3 years ago

Can someone help this is division with remanders

Talja [164]

Not really good at that sorry but one remaders are left over from the problem

3 0

3 years ago

11 under 4 as a decimal

babymother [125]

Answer:

.36

Step-by-step explanation:

6 0

2 years ago

If (x+2,5)=(3y+2)find x and y

kozerog [31]

Answer:

X = 7

Step-by-step explanation:

because of you do 5+2 = 7 then you minus 3 which you get 4.

the. if you have a production of around 10 you will get 7.

or you can do.

3+2 which is 5 and then you multiply that by 2 which is 10 and then you comprised that number therefore you will get 6 but you have to find X so we youndelie (think that's how u spell it) X which will equal to 1 and 6+1 is 7. once you get it it's quite simple

4 0

3 years ago