F(x) = (3.x4 + 1)2<br> Determine the total number of roots of each polynomial function

Graph y = 2x - 5 using the

borishaifa [10]

O The line increases from the left to right

O The line crosses the x-axis at 2.5

O The line does not enter quadrant II at all...

...Are your answers

7 0

3 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

$\displaystyle \large{r=\frac{a_{n+1}}{a_n}}$

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

Above should be applied for series that have common ratio not equal to 1.

$\displaystyle \large{S_n=a_1 \cdot n}$

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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7 0

3 years ago

A student spent 15 minutes getting a 2-foot by 3-foot bulletin board. To the nearest tenth of a minute, how long did it take the

Cerrena [4.2K]

Answer:

The student took 2.5 minutes to paint 1 square foot.

Step-by-step explanation:

In order to know how long the student took to paint each square foot we first need to know the total area of the bulletin board. Since it is a rectangle we can compute it's area by multiplying the width and the height. That is:

area = 2*3 = 6 square foot

Since the student took 15 minutes to paint the whole board the pace at which he was working can be calculated by dividing the total area of the board by the time he took to paint all of it. So we have:

pace = 6/15 = 0.4 foot/min

To find how long it took him to paint 1 square foot we can divide it by the pace he was painting. We have:

time = 1/0.4 = 2.5 minutes

The student took 2.5 minutes to paint 1 square foot.

3 0

4 years ago

Frank makes four bows to decorate a gift basket. Each bow uses7/8 yards of ribbon. The ribbon comes in spool of 3 yards, 5 yards

Alinara [238K]

7/8 yrds of ribbon per bow
if you need 4 bows
7/8 x 4 = 28/8 = 3 1/2 yards of ribbon needed

7 0

3 years ago

SOMEONE PLEASE HELP ME WITH THIS PROBLEM!!!

sasho [114]

Answer:the last one

Step-by-step explanation:

5 0

3 years ago

F(x) = (3.x4 + 1)2 Determine the total number of roots of each polynomial function