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3 years ago

15

the population of a type of local dragonfly can be found using an infinite geometric series where a1= 65 and the common ratio is

1/6. find the sum of this infinite series tht will be the upper limit of this population.

1 answer:

LiRa [457]3 years ago

7 0

Sum of infinite series of a GS is a1 / (1-r)

so here it is 65 / (1 - 1/6) = 65 / 5/6 = 65*6 / 5 = 78 answer

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Why do biologists have taxonomic systems?

Komok [63]

<span>To provide consistent ways to identify and classify organisms as they are being studied.</span>

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3 years ago

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Write the equation of the parabola that has its x-intercepts at (1+<img src="https://tex.z-dn.net/?f=%5Csqrt%7B5%7D" id="TexForm

VladimirAG [237]

Answer:

$y=2x^2-4x-8$

Step-by-step explanation:

<u>Factored form of a parabola</u>

$y=a(x-p)(x-q)$

where:

p and q are the x-intercepts.
a is some constant.

Given x-intercepts:

(1+√5, 0)
(1-√5, 0)

Therefore:

$\implies y=a(x-(1+\sqrt{5}))(x-(1-\sqrt{5}))$

$\implies y=a(x-1-\sqrt{5})(x-1+\sqrt{5})$

To find a, substitute the given point (4, 8) into the equation and solve for a:

$\implies a(4-1-\sqrt{5})(4-1+\sqrt{5})=8$

$\implies a(3-\sqrt{5})(3+\sqrt{5})=8$

$\implies4a=8$

$\implies a=2$

Therefore, the equation of the parabola in factored form is:

$\implies y=2(x-1-\sqrt{5})(x-1+\sqrt{5})$

Expand so that the equation is in standard form:

$\implies y=2(x^2-x+\sqrt{5}x-x+1-\sqrt{5}-\sqrt{5}x+\sqrt{5}-5)$

$\implies y=2(x^2-x-x+\sqrt{5}x-\sqrt{5}x+\sqrt{5}-\sqrt{5}+1-5)$

$\implies y=2(x^2-2x-4)$

$\implies y=2x^2-4x-8$

6 0

1 year ago

The amount of money in Nadia’s savings account is represented by the recursive formula an=1.025(an-1)+50 if a6=291.51 what are t

Elis [28]

Recursive formula is one way of solving an arithmetic sequence. It contains the initial term of a sequence and the implementing rule that serve as a pattern in finding the next terms. In the problem given, the 6th term is provided, therefore we can solve for the initial term in reverse. To make use of it, instead of multiplying 1.025, we should divide it after deducting 50 (which supposedly is added).
<span>
Therefore, we perform the given formula: A (n) = <span>1.025(an-1) + 50
</span></span>a(5) =1.025 (235.62) + 50 = 291.51

a(4) = 1.025 (181.09) + 50 = 235.62

a(3) = 1.025 (127.89) + 50 = 181.09

a(2) = 1.025 (75.99) + 50 = 127.89

a(1) = 1.025 (25.36) + 50 = 75.99

a(n) = 25.36

The terms before a(6) are indicated above, since a(6) is already given.

So, the correct answer is <span>A. $25.36, $75.99.</span>

3 0

3 years ago

10 people who build at the same rate can frame a house in 6 days. What fractional part of a house can 4 people frame a house in

Alina [70]

10 people who build at the same rate can frame a house in 6 days. That means it will take one person $10\times6=60$ days to finish the house.

Which means that it will take 4 people $\frac{60}{4}=15$ days to finish the house.

So, the fractional part of the house 4 people can frame in 3 days will be $\frac{3}{15}=\frac{1}{5}$

Thus, Option D is the correct answer.

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3 years ago

5 less the quotient of 14 times a number x and 9

AURORKA [14]

Answer:

$\frac{14x}{9}-5$

Step-by-step explanation:

14 times a number x : 14* x = 14x

Quotient of 14 times a number x an 9 : $\frac{14x}{9}$

5 less the quotient of 14 times a number x and 9 :

$\frac{14x}{9}-5$

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2 years ago