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1 year ago

Determine whether the series is convergent or divergent. [infinity] n = 1 1 n√9 the series is a ---select--- p-series with p =

Mathematics

1 answer:

inna [77]1 year ago

6 0

The series is a convergent p-series with p = 3

<h3>How to know it is a divergent or a convergent series</h3>

We would know that a series is a convergent p series when we have ∑ 1 np. Then you have to be able to tell if the series is a divergent p series or it is a convergent p series.

The way that you are able to tell this is if the terms of the series do not approach towards 0. Now when the value of p is greater than 1 then you would be able to tell that the series is a convergent series.

The value of $\sqrt{9}= 3$

The formular for this is

∑ $\frac{1}{n^p} \\$

where n = 1

we know it is convergent because p is greater than 1. 3>1

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Answer:

3/2

Step-by-step explanation:

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2 years ago

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Gina's literacy bucket weighs 6 pounds. Her novel weighs 1 4/6 pounds, and her chrome book weighs 2 1/6 how much would her bucke

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Answer:

$2\frac{1}{6}$ pounds.

Step-by-step explanation:

We have been given that Gina's literacy bucket weighs 6 pounds. Her novel weighs 1 4/6 pounds, and her chrome book weighs 2 1/6.

To find weight of bucket after taking out the two items, we will subtract weight of each item from 6 pounds as:

$\text{Weight of bucket}=6-1\frac{4}{6}-2\frac{1}{6}$

Let us convert mixed fractions into improper fractions as:

$1\frac{4}{6}=\frac{6\cdot 1+4}{6}=\frac{10}{6}\\\\2\frac{1}{6}=\frac{6\cdot 2+1}{6}=\frac{12+1}{6}=\frac{13}{6}$

$\text{Weight of bucket}=6-\frac{10}{6}-\frac{13}{6}$

$\text{Weight of bucket}=\frac{6\cdot 6}{6}-\frac{10}{6}-\frac{13}{6}$

$\text{Weight of bucket}=\frac{36}{6}-\frac{10}{6}-\frac{13}{6}$

Combine numerators:

$\text{Weight of bucket}=\frac{36-10-13}{6}$

$\text{Weight of bucket}=\frac{13}{6}$

$\text{Weight of bucket}=2\frac{1}{6}$

Therefore, the weight of the bucket is $2\frac{1}{6}$ pounds.

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3 years ago

For the polynomial function ƒ(x) = x4 − 12x3 + 46x2 − 60x + 25, find all local and global extrema.

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$\bf f(x)=x^4-12x^3+46x^2-60x+25\\\\
-------------------------------\\\\
\cfrac{df}{dx}=4x^3-36x^2+92x-60\implies 0=4x^3-36x^2+92x-60
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0=x^3-9x^2+23x-15\impliedby \textit{doing some synthetic division with 5}
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0=(x^2-4x+3)(x-5)\implies 0=(x-3)(x-1)(x-5)\\\\
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\begin{cases}
f(1)=0\leftarrow minimum&1,0\\
f(3)=16\leftarrow maximum&3,16\\
f(5)=0\leftarrow minimum&5,0
\end{cases}\impliedby \textit{3 extrema, locals and globals}$

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2 years ago

10. Mark built a fence around his clubhouse. The perimeter of the fence is 80 feet. The

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Answer:

if the clubhouse is 4 sided then the length would be 25 ft

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3 years ago

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The profit y (in dollars) for a business from selling x coats is represented by y=56x . Graph the equation.

Agata [3.3K]

Answer:

The graph of the equation is also attached.

From the graph, it is clear that at x = 0, the value of y = 0

Hence, the line passes through the origin with the y-intercept 0.

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

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<u>Determining the y-intercept</u>

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

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The equation y = 5x has:

The slope m = 56

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The graph of the equation is also attached.

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