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4 years ago

Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula.

Mathematics

2 answers:

-BARSIC- [3]4 years ago

8 0

Answer:

The explicit formula for the sequence is

Step-by-step explanation:

The above sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 38

d = 32 - 38 = - 6 or 20 - 26 = - 6 or

14 - 20 = - 6

So the formula for the sequence is

A(n) = 38 + ( n - 1)-6

= 38 - 6n + 6

We have the final answer as

Hope this helps you

bogdanovich [222]4 years ago

4 0

Answer:

$\huge\boxed{a_n=-6n+44}$

Step-by-step explanation:

This is an arithmetic sequence:

32 - 38 = -6

26 - 32 = -6

20 - 26 = -6

14 - 20 = -6

The common difference d = -6.

The explicit formula of an arithmetic formula:

$a_n=a_1+(n-1)(d)$

Substitute:

$a_1=38;\ d=-6$

$a_n=38+(n-1)(-6)$ <em>use the distributive property</em>

$a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44$

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Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −

crimeas [40]

Solving quadratic equations, it is found that he needs to charge:

1. He needs to charge $40 to break even.

2. He needs to charge $30 for a profit of $600.

<h3>What is a quadratic function?</h3>

A quadratic function is given according to the following rule:

$y = ax^2 + bx + c$

The solutions are:

$x_1 = \frac{-b + \sqrt{\Delta}}{2a}$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a}$

In which:

$\Delta = b^2 - 4ac$

The profit equation in this problem is:

P(x) = -3x² + 150x - 1200.

He breaks even when P(x) = 0, hence:

-3x² + 150x - 1200 = 0.

The coefficients are a = -3, b = 150, c = -1200, hence:

$\Delta = 150^2 - 4(-3)(-1200) = 8100$

$x_1 = \frac{-150 + \sqrt{8100}}{-6}$

$x_2 = \frac{-150 - \sqrt{8100}}{-6} = 40$

He needs to charge $40 to break even.

For a profit of $600, we have that P(x) = 600, hence:

-3x² + 150x - 1200 = 600.

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The coefficients are a = -3, b = 150, c = -1800, hence:

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He needs to charge $30 for a profit of $600.

More can be learned about quadratic equations at brainly.com/question/24737967

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2 years ago

Twelve basketball players, whose uniforms are numbered 1 through 12, stand around the center ring on the court in an arbitrary a

Ksju [112]

Answer:

Shown

Step-by-step explanation:

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3 years ago

May runs around a 4 m track at a consistent speed of 250 m/min. how many minutes does it take me to complete for lapse of the tr

Nookie1986 [14]

Answer:

<u>It takes May 6 minutes and 24 seconds to run 4 laps and 1 minute and 36 seconds per lap</u>

Statement and question:

May runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take May to complete 4 laps of the track?

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Speed of May = 250 meters per minute

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2. How many minutes does it take May to complete 4 laps of the track?

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4 years ago