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3 years ago

F(x) =

Mathematics

1 answer:

Oksana_A [137]3 years ago

4 0

9514 1404 393

Answer:

f'(x) = (-6x² -14x -23)/(x² +5x +2)²

f''(x) = (12x³ +42x² +138x +202)/(x² +5x +2)³

Step-by-step explanation:

The applicable derivative formula is ...

d(u/v) = (v·du -u·dv)/v²

f'(x) = ((-x² -5x -2)(4x +4) -(2x² +4x -3)(-2x -5))/(-x² -5x -2)²

f'(x) = (-4x³ -24x²-28x -8 +4x³ +18x² +14x -15)/(x² +5x +2)²

f'(x) = (-6x² -14x -23)/(x² +5x +2)²

Similarly, the second derivative is the derivative of f'(x).

f''(x) = ((x² +5x +2)²(-12x -14) -(-6x² -14x -23)(2(x² +5x +2)(2x +5)))/(x² +5x +2)⁴

f''(x) = ((x² +5x +2)(-12x -14) +2(6x² +14x +23)(2x +5))/(x² +5x +2)³

f''(x) = (12x³ +42x² +138x +202)/(x² +5x +2)³

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a coin is flipped eight times where each flip comes up either heads or tails. how many possible outcomes: 1). are there in total

Ymorist [56]

There are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.

Consider the provided information.

A coin is flipped eight times where each flip comes up either heads or tails.

Part (a) How many possible outcomes are there in total?

Each time we flip a coin it comes up either heads or tail.

Therefore the total number of ways are: 2⁸ = 256

Hence, there are 256 ways in total.

Part (b) contain exactly three heads?

We want exactly 3 heads, therefore,

n=8 and r=3

According to the definition of combination:

To get exactly 3 heads,

n=8 and r=3

(⁸C₃ ) = 8! / 3!(5!) = 56.

Therefore, there are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.

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1 year ago

Simplyfy using appropiate properties 1/4×2/5+-1/6×3/2+3/7×2/5

Triss [41]

Answer:

-1/35

Step-by-step explanation:

* means multiply

because of pemdas you should do three multiplication parts first

(1/4×2/5)+(-1/6×3/2)+(3/7×2/5)

1/20 - 3/12 + 6/35

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-12/60 + 6/35

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3 years ago

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AVprozaik [17]

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ArbitrLikvidat [17]

Answer:

A) 8, 15, 17.

Step-by-step explanation:

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The Pythagorean theorem states that: $a^2+b^2=c^2$