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2 years ago

What is helpful Problem-solving

1 answer:

6 0

Helpful problem solving is handling all problems the same , weather big , small or complex you should always problem solve in a fair way that’s convenient to everyone’s needs

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Identify the following sequences as arithmetic, geometric, or neither. For the arithmetic and geometric sequences, identify the

Lapatulllka [165]

Hence,

a. 12, 144, 1728,.. => Geometric

b. 0,5, 10, 15, 20, 25,... => Arithmetic

c. 0,4, 16, 36, 64,... => Neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,... => Geometric

Step-by-step explanation:

In order to identify the sequence as geometric or arithmetic sequence, we find the common difference and common ratio of the sequence. If the common difference is same, it is an arithmetic sequence and if the common ratio is same the sequence is a geometric sequence

Common difference is the difference between consecutive terms of an arithmetic sequence and common ration is the ratio between two consecutive terms of a sequence

So,

a. 12, 144, 1728,..

Here,

$a_1=12\\a_2=144\\a_2=1728$

Common difference:

$d=a_2-a_1 = 144-12 = 132\\=a_3-a_2 = 1728-144=1584$

Common Ratio:

$r=\frac{a_2}{a_1} =\frac{144}{12} = 12\\=\frac{a_3}{a_2}=\frac{1728}{144} =12$

As the common ratio is same, the given sequence is a geometric sequence.

b. 0,5, 10, 15, 20, 25,...

Here,

$a_1 = 0\\a_2 =5\\a_3 =10$

Common difference:

$d=a_2-a_1 = 5-0 = 5\\d=a_3-a_2 = 10-5 = 5$

As the common difference is same, the given sequence is an arithmetic sequence

c. 0,4, 16, 36, 64,...

Here

$a_1 = 0\\a_2 =4\\a_3 = 16\\a_4 = 36$

Common Difference:

$d= a_2-a_1 = 4-0 = 4\\a_3-a_2 = 16-4 = 12$

Common Ratio:

$r=\frac{a_2}{a_1} = \frac{4}{0} = Doesn't\ exist$

Neither the common ratio nor common difference are same, so the given sequence is neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,...

Here

$a_1 = 1.5\\a_2 = 2.25\\a_3 = 3.375$

Common Difference:

$d=a_2-a_1 = 2.25-1.5 = 0.75\\a_3-a_2 =3.375-2.25 = 1.125[/tex]Common Ratio: [tex]r=\frac{a_2}{a_1} = \frac{2.25}{1.5}=1.5\\=\frac{a_3}{a_2} =\frac{3.375}{2.25}=1.5$

As the common ratio is same, given sequence is geometric

Hence,

a. 12, 144, 1728,.. => Geometric

b. 0,5, 10, 15, 20, 25,... => Arithmetic

c. 0,4, 16, 36, 64,... => Neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,... => Geometric

Keywords: Sequence, Ratio

Learn more about sequences at:

#LearnwithBrainly

4 0

3 years ago

What is the equation of the line that passes through the point (-4,4) and has a slope of -3

Arte-miy333 [17]

Answer: y-4=-3(x+4) or y=-3x-8

Step-by-step explanation:

To find the equation of the line with a given point and slope, we can fill them into the point-slope formula. The point-slope formula is y-y₁=m(x-x₁).

y-4=-3(x-(-4)) [multiply]

y-4=-3(x+4)

Another equation could be slope-intercept form. It is y=mx+b.

y-4=-3(x+4) [distribute]

y-4=-3x-12 [add both sides by 4]

y=-3x-8

Now, we know that the equation is y=-3x-8 or y-4=-3(x+4).

3 0

3 years ago

The second statement is the of the first. Foundations of Geometry

Elina [12.6K]

i think its c. contrapositive

5 0

3 years ago

Read 2 more answers

What is an equation of the line that passes through the points (0, 3) and (5,−3)?

g100num [7]

Answer:

y = -6/5x + 3

Step-by-step explanation:

y = mx + c (or b, depending on where you're from)

Slope = m = -6/5

y = -6/5x + c

You can sub (0, 3) and (5, -3) into y = -6/5x + c and they both have the same answer where c = 3

Therefore, the equation is y = -6/5x + 3

Hop this helps

5 0

2 years ago

Consider two vectors A and B A=14i and B= -4i+8j

DaniilM [7]

Assuming $\mathbf a,\mathbf b\in\mathbb R^3$ , you have

$\mathbf a\cdot\mathbf b=(14)(-4)+(0)(8)=-56$

so

$((\mathbf a\cdot\mathbf b)\,\mathbf i)\cdot\mathbf a=(-56\,\mathbf i)\cdot(14\,\mathbf i)=(-56)(14)=-784$

Next,

$\mathbf a+\mathbf b=(14\,\mathbf i)+(-4\,\mathbf i+8\,\mathbf j)=10\,\mathbf i+8\,\mathbf j$

Then

$(\mathbf a+\mathbf b)\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\10&8&0\\-4&8&0\end{vmatrix}=112\,\mathbf k$

$((\mathbf a+\mathbf b)\times\mathbf b)\times\mathbf k=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\0&0&112\\0&0&1\end{vmatrix}=\mathbf 0$

4 0

3 years ago