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3 years ago

7

On the first math exam, 16 students received an A grade. On the second math exam,12 students received an A grade.what percentage

decrease is that?

1 answer:

Neko [114]3 years ago

8 0

Answer:

25%

Step-by-step explanation:

(16-12)/16=0.25

0.25×100=25

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The result is 1/3 (-6 + x)

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3 years ago

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Express the terms of the following sequence by giving a recursive formula.

MAXImum [283]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

6 0

3 years ago

Amy purchased a brand-new mountain bike, which she's riding through

Neko [114]

Answer:

The Acceleration of bike after 3 minutes of ride is 14 meter² per minutes

Step-by-step explanation:

Given as :

The displacement of bike is the function of time

i.e s(t) = t³ - 2 t² + 3 meters

The Time of bike acceleration = t = 3 minutes

Let The Acceleration of bike = a meter² per minutes

Now, According to question

∵ <u>Acceleration is define as the rate of change of velocity</u>

i.e acceleration = $\dfrac{\textrm velocity}{\textrm time}$

or, a = $\dfrac{\textrm v}{\textrm t}$

And

<u>Velocity is define as rate of change of displacement</u>

i.e velocity = $\dfrac{\textrm displacement}{\textrm time}$

Or, v = $\dfrac{\textrm s}{\textrm t}$

Since here displacement is function of time

So , v = $\frac{\partial s(t)}{\partial t}$

Or, v = $\frac{\partial (t³ - 2 t² + 3)}{\partial t}$

Or, v = 3 t² - 4 t + 3

So, velocity is the function of time = v = 3 t² - 4 t + 3 meter per minutes

Now, Again

Acceleration = a = $\frac{\partial v}{\partial t}$

Or, a = $\frac{\partial (3 t² - 4 t + 3)}{\partial t}$

Or, a = 6 t - 4

∴ Acceleration is the function of time = a = 6 t - 4

Now, Acceleration of bike after 3 minutes

So, at t = 3 min

i.e a = 6 t - 4

Or, a = 6 × 3 - 4

Or, a = 18 - 4

∴ a = 14 meter² per minutes

Hence, The Acceleration of bike after 3 minutes of ride is 14 meter² per minutes . Answer

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3 years ago

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