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2 years ago

Find the 6th term of the geometric sequence whose common ratio is 3/2 and whose first term is 5

Mathematics

1 answer:

Fynjy0 [20]2 years ago

5 0

Answer:

a(6) = 37.97

Step-by-step explanation:

If the first term a(1) is 5 and the common ratio r is 3/2, then the general formula for this geometric sequence is

a(n) = 5*r^(n - 1).

Thus, the 6th term is a(6) = 5*(3/2)^(6 - 1), or a(6) = 5(3/2)^5 = 37.97

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Please help!! Xoxo! Appreciate it :)

Degger [83]

Answer:

B x = sqrt(41)

Step-by-step explanation:

Since the large triangle is isosceles, the smaller triangles on the right side and left side are congruent right triangles.

The base of each smaller right triangle is 4 units long (8/2 = 4).

The vertical leg is 5.

Use the Pythagorean theorem to find x.

a^2 + b^2 = c^2

4^2 + 5^2 = x^2

16 + 25 = x^2

x^2 = 41

x = sqrt(41)

Answer: B x = sqrt(41)

8 0

2 years ago

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Which equation could be used to create the graph?

Eva8 [605]

Answer:

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (9, 3) ← 2 points on the line

m = $\frac{3-0}{9-0}$ = $\frac{3}{9}$ = $\frac{1}{3}$ , thus

y = $\frac{1}{3}$ x

y = $\frac{x}{3}$ → C

6 0

3 years ago

Read 2 more answers

Ishaan is 222 times as old as Christopher. 353535 years ago, Ishaan was 777 times as old as Christopher.

klemol [59]

<h3><u>Question:</u></h3>

Ishaan is 2 times as old as Christopher. 35 years ago, Ishaan was 7 times as old as Christopher. How old is Christoper now?

<h3><u>Answer:</u></h3>

The present age of Christoper is 42 years old

<h3><u>Solution:</u></h3>

Given that Ishaan is 2 times as old as Christoper

Let the present age of Christoper be "x"

Then, Present age of Ishaan = 2 times as old as Christoper

present age of Ishaan = 2x

<em><u>35 years ago, Ishaan was 7 times as old as Christopher</u></em>

Age of Ishaan 35 years ago = Present age of Ishaan - 35

Age of Ishaan 35 years ago = 2x - 35

Similarly,

Age of christoper 35 years ago = Present age of christoper - 35

Age of christoper 35 years ago = x - 35

From given statement, 35 years ago, Ishaan was 7 times as old as Christopher

Age of Ishaan 35 years ago = 7 times the age of Christoper 35 years ago

(2x - 35) = 7(x - 35)

<em><u>Solve the above equation for "x"</u></em>

2x - 35 = 7x - 245

2x - 7x = -245 + 35

-5x = -210

Thus present age of Christoper is 42 years old

5 0

3 years ago

Four consecutive integer numbers add to 2. What are the numbers?

il63 [147K]

The numbers would be -1, 0, 1, 2.
Hope this helps

3 0

3 years ago

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Can you please help with this question about exponential equations?

RSB [31]

Since $t$ represents the number of years passed since 2005, in 2005 we have $t=0$ , and in 2015 we have $t=10$ . Let $P_J(y),P_D(y)$ represent the profits of Jones and Davis, respectively, at year y.

We have

$P_J(2005) = 10(0.99)^0 = 10,\quad P_J(2015) = 10(0.99)^{10}\approx 9$

$P_D(2005) = 8(1.01)^0 = 8,\quad P_D(2015) = 8(1.01)^{10}\approx 9$

Choosing the best company somehow depends on how much time you can wait: Jones start with a higher value (10 vs 8), but it has a descending trend, because the multiplicative factor $0.99^t$ goes to zero as t grows.

On the other hand, Davis starts with a smaller value, but $1.01^t$ tends to infinity as t grows.

So, if you need an immediate result, the most valuable company is Jones, otherwise you're certain can Davis will eventually become bigger.

More precisely, we have

$8\cdot 1.01^t = 10\cdot 0.99^t \iff 0.8 = \left(\dfrac{0.99}{1.01}\right)^t \iff t\approx 11$

So, after 11 years, Davis will overcome Jones.

3 0

2 years ago