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2 years ago

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A math club had 4 members in its first year. It had 19 members in its fourth year and 29 members in its sixth year. Assuming a c

onstant rate of increase, how many members will the math club have in its thirteenth year?

1 answer:

IceJOKER [234]2 years ago

4 0

Here you go! It increases by 5 members each year.

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The answer is 3.65 x 10^5

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2 years ago

Please help me. these problems<br>

jeyben [28]

Answer:

1st problem:

Converges to 6

2nd problem:

Converges to 504

Step-by-step explanation:

You are comparing to $\sum_{k=1}^{\infty} a_1(r)^{k-1}$

You want the ratio r to be between -1 and 1.

Both of these problem are so that means they both have a sum and the series converges to that sum.

The formula for computing a geometric series in our form is $\frac{a_1}{1-r}$ where $a_1$ is the first term.

The first term of your first series is 3 so your answer will be given by:

$\frac{a_1}{1-r}=\frac{3}{1-\frac{1}{2}}=\frac{3}{\frac{1}{2}=6$

The second series has r=1/6 and a_1=420 giving me:

$\frac{420}{1-\frac{1}{6}}=\frac{420}{\frac{5}{6}}=420(\frac{6}{5})=504$ .

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2 years ago

Which expression represents the distance between the points (11, 4) and (5,8)?

antiseptic1488 [7]

Answer:

$\displaystyle d = 2\sqrt{13}$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right<u> </u>

<u>Algebra I</u>

Coordinates (x, y)

<u>Algebra II</u>

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

<u>Step 1: Define</u>

Point (11, 4) → x₁ = 11, y₁ = 4

Point (5, 8) → x₂ = 5, y₂ = 8

<u>Step 2: Find distance </u><em><u>d</u></em>

Simply plug in the 2 coordinates into the distance formula to find distance <em>d</em>

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(5-11)^2+(8-4)^2}$
[√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{(-6)^2+(4)^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{36+16}$
[√Radical] Add: $\displaystyle d = \sqrt{52}$
[√Radical] Simplify: $\displaystyle d = 2\sqrt{13}$

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Answer:

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Step-by-step explanation:

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