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Iteru [2.4K]
3 years ago
14

Find the area of the composite figure:

Mathematics
2 answers:
geniusboy [140]3 years ago
4 0

Answer:

21

Step-by-step explanation:

5 x 3 = 15

3 x 2 = 21

-Dominant- [34]3 years ago
3 0

Answer:

The area is 21.

Step-by-step explanation:

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Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.
Aleks [24]

Answer:

It means \sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6} also converges.

Step-by-step explanation:

The actual Series is::

\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}

The method we are going to use is comparison method:

According to comparison method, we have:

\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}

\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}

Now:

\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty}  \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

\sum_{n=1}^{inf}\frac{1}{n^p}

if p>1 then series converges. In oue case we have:

\sum_{n=1}^{inf}b_n=\frac{1}{n^4}

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means \sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6} also converges.

5 0
3 years ago
ILL MARK YOU BRAINLIEST Factor completely 3ab(x + 1) − 2(x + 1).
Nuetrik [128]
Part one of answering how to factor

3 0
3 years ago
A rectangular stirp of asphalt paving is 5 meters longer than it is wide. its area is 300 square meters. find the length and wid
kow [346]
Let's call L the width of the rectangle and W its width. The area of the rectangle is the product between the length and the width, and we are also told that the area is 300 square meters, so we can write
A=L\cdot W=300
Moreover, we know that the length is 5 meters longer than the width:
L=W+5
We have a system of 2 equations in 2 unknown variables, L and W. If we substitute the second equation into the first one, we get
(W+5)\cdot W=300
W^2+5W-300=0
which has two solutions: W=-20 and W=15. We can discard the negative solution since it does not have physical meaning, and now we can substitute the value of W into the second equation to find L:
L=W+5=15+5=20
<span>Therefore, the rectangle has width 15 meters and length 20 meters.</span>
7 0
3 years ago
Read 2 more answers
What can you tell me about the vertex and line of symmetry? Where are they? How do you calculate them?
MA_775_DIABLO [31]

Answer:

Formula Of Vertex and Line of symmetry

Step-by-step explanation:

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a

Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex"

3 0
2 years ago
Sky bought $22.50 worth of paint supplies at a store that sells brushes for $1.50 each and tubes of paint for $2.50 each. Let b
expeople1 [14]

Answer:

b = 10 , t = 3

Step-by-step explanation:

6 0
2 years ago
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