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Roman55 [17]
3 years ago
9

A geometric sequence is shown on the graph below. What is the formula for the nth term of the sequence?

Mathematics
1 answer:
tia_tia [17]3 years ago
8 0

Answer:

aₙ = 40*(1/2)ⁿ⁻¹

Step-by-step explanation:

<u>As per graph we have:</u>

  • a₁ = 40, a₂ = 20, a₃ = 10, a₄ = 5, a₅ = 2.5

<u>So the first term is </u><u>40</u><u> and common ratio is </u>

  • 20/40= 10/20 = 5/10 = 2.5/5 = 1/2

<u>Formula for nth term is:</u>

  • aₙ = a₁rⁿ⁻¹
  • aₙ = 40*(1/2)ⁿ⁻¹

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C is the answer
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5 0
3 years ago
Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Suppose that the future populat
yulyashka [42]

Answer:

The population will reach 34,200 in February of 2146.

Step-by-step explanation:

Population in t years after 2012 is given by:

P(t) = 0.8t^{2} + 6t + 19000

In what month and year will the population reach 34,200?

We have to find t for which P(t) = 34200. So

P(t) = 0.8t^{2} + 6t + 19000

0.8t^{2} + 6t + 19000 = 34200

0.8t^{2} + 6t - 15200 = 0

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

0.8t^{2} + 6t - 15200 = 0

So a = 0.8, b = 6, c = -15200

Then

\bigtriangleup = 6^{2} - 4*0.8*(-15100) = 48356

t_{1} = \frac{-6 + \sqrt{48356}}{2*0.8} = 134.14

t_{2} = \frac{-6 - \sqrt{48356}}{2*0.8} = -141.64

We only take the positive value.

134 years after 2012.

.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.

So the population will reach 34,200 in February of 2146.

6 0
3 years ago
Look at picture below
geniusboy [140]

Answer:

I believe the answer you are looking for is C-√57

Mark brainliest :)

8 0
1 year ago
Read 2 more answers
Find the value of x: 7e(×/3)=14
velikii [3]
<span>7e^(×/3)=14
</span><span>e^(×/3)=14/7
</span>e^(×/3)=2
take ln of both sides;
lne^(×/3)=ln2
****You should be familiar that lne^x=x as ln is the inverse function of e and vice versa****
then;
x/3=ln2
x=3ln2
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6 0
3 years ago
Name a point that is between 50 and 60 units away from (7,-2) and state the distance between the two points.
laila [671]

Let the required point be (a,b)

The distance of (a,b) from (7,-2) is

= \sqrt{(a-7)^2+(b+2)^2}

But this distance needs to be betweem 50 & 60

So

50

Squaring all sides

2500 < (a-7)² + (b+2)² < 3600

Let a = 7

So we have

2500 < (b+2)² <3600

b+2 < 60    or  b+2 > -60   => b <58 or b > -62

Also

b+2 >50    or b + 2 < -50  => b >48 or B < -52

Let us take one value of b < 58 say b = 50

So now we have the point as (7, 50)

The other point is (7,-2)

Distance between them

= \sqrt{(7-7)^2+(50+2)^2}= \sqrt{(52)^2}=52

This is between 50 & 60

Hence one point which has a distance between 50 & 60 from the point (7,-2) is (7, 50)


6 0
3 years ago
Read 2 more answers
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