What is the explicit rule for this geometric sequence?



2, 6, 18, 54, …2, 6, 18, 54, …



an=2⋅3nan=2·3n

an=3⋅2n−1an=3·2n-1

an=2⋅3n−1an=2·3n-1

an=3⋅2n

Final answer:

To calculate the value of the car in 8 years with a constant yearly depreciation rate of 5.1%, we can use the formula for compound interest.

Explanation:

To calculate the value of the car in 8 years, we can use the formula for compound interest: A = P(1 - r/n)^(nt), where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the initial amount is $9,250, the interest rate is 5.1%, and the number of times interest is compounded per year is 1. Plugging these values into the formula, we get:

A = 9250(1 - 0.051/1)^(1*8) = $6630.27

Therefore, the car will be worth approximately $6,630.27 in 8 years.

The distance traveled by the ball until it stops bouncing is:

                                   18 meters

It is given that:

a ball bounces from a height of 2 meters and returns to 80% of its previous height on each bounce.

This means that the distance traveled by the ball is the distance it travels by going down as well as coming up on bouncing.

and is given as follows:

[tex]\text{Total Distance}=2+0.8\times 2\ up+0.8\times 2\ down+(0.8)^2\times 2\ up+(0.8)^2\times 2\ down+.....\\\\\text{Total distance}=2+4\times (0.8)+4\times (0.8)^2+4\times (0.8)^3+....\\\\\text{Total distance}=2+4\times [0.8+(0.8)^2+(0.8)^3+......]\\\\\text{Total distance}=2+4\times (\dfrac{0.8}{1-0.8})[/tex]

Since, the formula of infinite geometric progression is:

[tex]\sum_{n=1}^{\infty} ar^{n-1}=\dfrac{a}{1-r}[/tex]

i.e.

[tex]\text{Total distance}=2+4\times (\dfrac{0.8}{0.2})\\\\\text{Total distance}=2+4\times 4\\\\\text{Total distance}=2+16\\\\\text{Total distance}=18\ \text{meters}[/tex]

Answer: C) The image is along the same ray as the preimage but is closer to the center of dilation.

There are 840 seats in total in Cinema Hall.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

Given:

First term, [tex]a_1[/tex] = 22

second row = 22 + 3 = 25

Third row = 25 + 3 = 28

So, the Recursive Formula is

[tex]a_n[/tex] = a + (n-1)d

[tex]a_n[/tex] = 10 + (n-1)3

[tex]a_n[/tex] = 10 + 3n - 3

[tex]a_n[/tex] = 7 + 3n

In 21th rows the seats are

= 7 +3 (21)

= 7 + 63 = 70

Now, to find the number of seats in hall we have to find the sum of seats from row 1 to row 21 using Formula

= n×([tex]a_1[/tex]+ [tex]a_n[/tex])/2

= 21 x (10 + 70) /2

= 21 x 80 /2

= 21 x 40

= 840

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Answer: The value of x is 12.5°.

Step-by-step explanation:

Since we have given that

ΔLMN ≅ ΔHIJ

So, According to "Congruency rules":

∠L = ∠H  -------------------------------------(1)

∠M = ∠I

∠N = ∠J

∠M = 65° , ∠L = 35° and ∠H = (2x+10)°

From eq(1), we get that

[tex]2x+10=35^\circ\\\\2x=35-10\\\\2x=25\\\\x=\dfrac{25}{2}\\\\x=12.5^\circ[/tex]

Hence, The value of x is 12.5°.

For this case, the first thing we must do is define variables.

We have then:

x: time in minutes

y: distance traveled.

We then have the following equations:

For Kathleen:

[tex] y = (\frac{1}{15}) x + 5
[/tex]

For Arnob:

[tex] y = (\frac{2}{15}) x
[/tex]

By the time Arnob reaches Kathleen we have:

[tex] (\frac{1}{15}) x + 5 = (\frac{2}{15}) x
[/tex]

From here, we clear the value of x.

We have then:

[tex] (\frac{2}{15}) x - (\frac{1}{15}) x = 5
[/tex]

[tex] (\frac{1}{15}) x = 5

x = (15) * (5)

x = 75 min
[/tex]

Answer:

it takes Arnob to catch up to Kathleen 75 minutes:

d. 75

Answer:

Its false

Step-by-step explanation:

well first i pt the answer in and it came out correct.

Answer:

A=2000(1+0.05)^4=2,431.01

Step-by-step explanation:

Finding the rate of change in something with respect to something is known as differentiation. For Example, Change in y with respect to x is known as the derivative of y with respect to x.

(a) [tex]9{x}^2-{y}^2 = 1[/tex]

Differentiating equation with respect to x :

[tex]9*2x - 2y\frac{dy}{dx} = 0\\ 18x = 2y\frac{dy}{dx}\\9\frac{x}{y} =\frac{dy}{dx}[/tex]

(b)

[tex]9{x}^2-{y}^2 = 1\\9{x}^2-1 = {y}^2 \\\sqrt[2]{9{x}^2-1} = y\\[/tex]

differentiating with respect to x gives:

[tex]\frac{1}{2\sqrt{9{x}^2-1} } *(18x) = \frac{dy}{dx}\\\frac{1}{\sqrt{9{x}^2-1} } *(9x) = \frac{dy}{dx}[/tex]

(c) [tex]9\frac{x}{y} =\frac{dy}{dx}[/tex]

substituting value of y

[tex]\sqrt[2]{9{x}^2-1} = y\\\\\frac{9x}{\sqrt[2]{9{x}^2-1}} = \frac{dy}{dx}[/tex]

Hence the solution is consistent.

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d/dx (2 x^2 y + y = 2x + 13) 4xy + 2x^2 y' + y' = 2 4xy + y'(2x^2 + 1) = 2 y' = (2- 4xy)/(2x^2 +1)

ow we can use this in a linear equation for a slope Ty = -5x/8 +5(3)/8 +8/8 = -5x/8 +(15+8)/8 = -5x/8 +23/8 this will gives us an approximation at x=2.8 now

ANSWER:

y ≈ (-10/19)*(2.8 - 3) + 1 = 1 2/19 ≈ 1.105

STEP-BY-STEP EXPLANATION:

y = (2x+13)/(2x^2+1)

y' = ((2x^2+1)*(2) - (2x+13)(4x)) / (2x^2+1)^2

at x=3, this is

y'(3) = (19*2 - 19*12)/19^2 = -10/19

So, your linearization is

y ≈ (-10/19)*(x-3) + 1

At x=2.8, this is

y ≈ (-10/19)*(2.8 - 3) + 1 = 1 2/19 ≈ 1.105

Answer:

C

Step-by-step explanation:

I took test on Edg

The graph will show exponential decay and The domain will be the set of natural numbers.

Option C and D will apply.

A geometric sequence is a sequence of numbers obtained by either  multiplying or dividing by the same value.

The geometric sequence given is

640, 160, 40, 10, ...

Each number is divided by 4

So the nth term will be

[tex]\rm T_n = a_1 r^{n-1}[/tex]

where [tex]\rm a_1 \; is \; the \; first \; term[/tex]

and r is the common ratio

r =(1/4) for this sequence

The function is

[tex]\rm T_n = 640(\dfrac {1}{4})^{n-1}[/tex]

As from the function it can be understood , That The graph will show exponential decay and The domain will be the set of natural numbers.

Option C and D will apply.

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The sequence is a geometric sequence showing exponential decay with a factor of 0.25 (divisible by 4). The graph will show exponential decay and not appear linear. The domain is the set of natural numbers, while the range consists of specific values from the sequence, not all natural numbers.

The sequence given is 640, 160, 40, 10, ..., which is a geometric sequence. We can determine this because each term is obtained by multiplying the previous term by a constant factor.

In this case, each term is divided by 4 to get the next term (160 is 640 divided by 4, 40 is 160 divided by 4, and so on). Therefore, the common ratio r is ¼ or 0.25, which is less than 1.

Now, let’s evaluate the statements provided:

So, the correct statements are that the graph will show exponential decay and the domain will be the set of natural numbers.

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Answer:

[tex]3x+7[/tex]

Step-by-step explanation:

[tex]\frac{3x^2-14x-49}{x-7}[/tex]

before dividing this fraction , lets factor the numerator

[tex]3x^2-14x-49[/tex]

Product is -49 and sum is -14, lets break the middle term using factors

[tex](3x^2+7x)+ (-21x-49)[/tex]

Take out GCF from each group

[tex]x(3x+7)-7(3x+7)[/tex]

[tex](3x+7)(x-7)[/tex]

Now we replace the factors in the numerator

[tex]\frac{(3x+7)(x-7)}{x-7}[/tex]

We have (x-7) at the top and bottom , so we cancel it out

[tex]3x+7[/tex]

Answer:

the root of 13

Step-by-step explanation:

The result of dividing 4241 by 57 is approximately 74.40.

To divide 4241 by 57, we perform the division as follows:

       74

  ____________

57 | 4241

    - 3996

    _______

       245

      - 228

      ______

        170

       -  171

       ______

            -1

The quotient is 74 with a remainder of 1.

Therefore, [tex]\( \frac{4241}{57} = 74 \)[/tex].40 with a remainder of 1.

Complete question:

What is 4241 divided by 57?