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Nadusha1986 [10]
3 years ago
11

the derivative of the function f is given by f'(x)=x^2cos(x^2). How many points of inflection does the graph of f have on the op

en interval (-2,2)
Mathematics
1 answer:
Vsevolod [243]3 years ago
5 0
The point of inflection is calculated by equating the second derivative to zero and determining x from there.

f"(x) = -x²2xsinx² + cosx²(2x) = 0

2xcosx² - 2x³sinx² = 0
2x (cosx² - xsinx²) = 0

2x = 0   ⇒  x = 0
cosx² - xsinx² = 0   ⇒ x = 3.82 (if you use shift+solve in your scientific calculator)

Thus, the function only has 1 point of inflection and it is at x = 0.
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The formula for obtaining the value of a term of a sequence is given as a

as a recursive formula.

Responses:

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The amount of pocket money Smith gets = 2 × The amount he gets in the previous day

The amount Smith gets on the first day = R1

Required:

The given information expressed as a sequence.

Solution:

The amount of money smith gets can be expressed as follows;

Amount he gets on day 1 = R1

On day 2, R2 = 2·R1

On day 3, R3 = 2·R2 = 2·2·R1 = 4·R1

On day 4, R4 = 2·R3 = 2·2·2·R1 = 8·R1

On day 5, R5 = 2·R4 = 2·2·2·2··R1 = 16·R1

The information written as a sequence is therefore;

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  • The type of sequence is a<u> geometric sequence, or progression</u> where the first term is R1, and the common ratio, r = 2

Learn more about geometric sequence here:

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2 years ago
Find the value of each variable using sine and cosine round your answers to the nearest tenth​
Fudgin [204]

9514 1404 393

Answer:

  r ≈ 19.0

  s ≈ 17.7

Step-by-step explanation:

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

So, you have ...

  cos(43°) = r/26

  r = 26·cos(43°) ≈ 19.0

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  sin(43°) = s/26

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5 0
3 years ago
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits
kakasveta [241]
If the number only has 2 digits, it could only be 91, because since the tens digit is 8 more than the ones digit, the tens digit is greater than or equal to 8. it cannot be 10 or more, because that would make the number over 100, leaving only 8 and 9. If the tens digit is 8, the ones digit is zero, and since it cannot be zero, then the tens digit must be 9, leaving the ones digit to be 1. So, the final answer is 91.
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3 years ago
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The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student wil
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Solution :

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P (correct in the 4th attempt)

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So, $\sigma = \frac{\sqrt{k(1-p)}}{p}$

     $\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$

        = 1.6330

6 0
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