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1 year ago

Find the fifth term of the geometric sequence whose first term is 81 and whose common ratio is 1/3.(1 point)13

1 answer:

7 0

$n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{5}\\ a_1=\stackrel{\textit{first term}}{81}\\ r=\stackrel{\textit{common ratio}}{\frac{1}{3}} \end{cases}\implies a_5=81\left( \cfrac{1}{3} \right)^{5-1} \\\\\\ a_5=81\left( \cfrac{1}{3} \right)^4\implies a_5=81\cdot \cfrac{1}{81}\implies a=1$

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15 points. Please answer as soon as possible.

abruzzese [7]

Answer:

A. $\frac{(a-b)^{2} +b^{2} }{a^{2}}$

Step-by-step explanation:

So to get the area of a square, we need to find the length of one side.

We know the length of the larger square is a, so the area of the larger cube is $a^{2}$

We can find the length of a side of the smaller square by using pythagoreans theorem to find the hypotenuse of the triangle formed in the bottom left corner. The length of one side along the x axis is a - b, and the length of the other side, along the y-axis, is b.

We can plug it into pythagoreans theorem to get

$(a-b)^{2} +b^{2} = C^{2}$ (C represents the length of one side of the smaller square, and the hypotenuse of the triangle)

$C = \sqrt{ (a-b)^{2} +b^{2}}$

The area of the smaller triangle is C squared to the area of the smaller triangle is

$(a-b)^{2} +b^{2}$

To get the ratio of the smaller square in comparison to the larger square we divide the area of the smaller square by the area of the larger square.

So the ratio should be

$\frac{(a-b)^{2} +b^{2} }{a^{2}}$

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3 years ago

Jocelyn Clinton works for a company that uses a percentage method to compute income tax withheld. Jocelyn is single and claims o

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Jocelyn makes more than $195 but not over $645. The amount she has to pay is 15% of the excess of 196. Find this first via subtraction.

421 - 195 = $226 over

Take 15% of this

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The tax also includes a $14.4 addition to this 15%.

33.9 + 14.4 = $48.3 total income tax

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3 years ago

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Answer:

Step-by-step explanation:

Let's express all the given numbers as decimals:

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0.3

0.8

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two tenths- 0.2

Ordering them from least to greatest:

two tenths, 0.3, five tenths, 0.8, nine tenths

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2 years ago

Read 2 more answers

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r-ruslan [8.4K]

Answer:

Step-by-step explanation:

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3 years ago

B. Translate each word into algebraic eqaution. (Use any letter)

Paraphin [41]

Answer

1. 9

1. 13

1. 147

1. 7/3

1. 9

Step-by-step explanation:

Algebraic equations

1. 2x=18

2. x-5=8

3. (x/7)=21

4. 3x+5=12

5. 2x=18

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2 years ago