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hoa [83]
3 years ago
10

Math help! 20 Points!

Mathematics
2 answers:
erastova [34]3 years ago
4 0
The anwer is 3 because it 3
Salsk061 [2.6K]3 years ago
3 0

Hello

here's your answer

_____________________

=》3

______________________

Thanks

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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 nth 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
I need help Plzzzzzzzzzzz.
Furkat [3]

Answer: 1st one is no solution

and then i cant see the question for the 2nd one

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The concert tickets for Saturday were reduced from $50 to $30. By what percentage was the concert tickets reduced?
marin [14]

Answer:

40% price reduction

Step-by-step explanation:

The tickets were reduced by 40% because 20 is 2/5 or 40% of 50 and that was the amount of the price reduction.

7 0
3 years ago
Read 2 more answers
A board 109 cm long has to be cut into two pieces so that the longer part is 10 cm more than twice as long as the shorter part.
11111nata11111 [884]
 x = longer section
y = shorter section

x + y = 109
x = 2y + 10

so we sub in eq 2 into eq 1
2y + 10 + y = 109
3y + 10 = 109
3y = 109 - 10
3y = 99
y = 99/3
y = 33 <=== shorter section is 33 cm

x = 2y + 10
x = 2(33) + 10
x = 66 + 10
x = 76 <=== longer section is 76 cm
4 0
3 years ago
Please help me ASAP!!
REY [17]
<h2>Hello!</h2>

The answer is: f(x) = 2x^{2}

<h2>Why?</h2>

Quadratic function describes the graph of a parabola and they are formed by a quadratic term (x^{2}) a linear term (bx) and a constant number (c). Quadratic terms have an exponent of 2 and linear terms have an exponent of 1.

For this situation, we have only the quadratic term (x^{2}) which is enough to know that there is a quadratic function.

Have a nice day!

8 0
4 years ago
Read 2 more answers
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