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3 years ago

Derivative using chain rule of cosx/1+sinx

1 answer:

4 0

I am not sure how you would approach this using the chain rule, but I can use the quotient rule.

The derivative of cos(u)=-sin(u)
The derivative of sin(u)=cos(u)

The quotient rule states:

[f'(x)g(x)-f(x)g'(x)] / [g(x)]^2

f'(x)= -sin(x)
g(x)= [1+sin(x)]
f(x)= cos(x)
g'(x)= cos(x)

Plug in:

[-sin(x)*[1+sin(x)] - [cos(x)*cos(x)] / (1+sin(x))^2

Simplify by distributing

-sin(x) - sin^2(x) - [cos(x)*cos(x)] / (1+sin(x))^2

Multiply the cos(x)*cos(x)

-sin(x) - sin^2(x) - cos^2(x) / (1+sin(x))^2

That is the answer or the answer could be simplified further by pulling out the negative.

- [sin(x)+sin^2(x)+cos^2(x)] / (1+sin(x))^2

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How many five card hands consisting of 2 kings and 3 aces can be dealt from a deck of 52 playing cards?

m_a_m_a [10]

Answer:

24.

Step-by-step explanation:

In a standard deck of 52 cards, there are four kings and four aces.

Permutation $\displaystyle {n \choose k}$ gives the number of ways to choose $k$ items out of a pile of $n$ of these items. The equation for calculating

$\displaystyle {n \choose k} = \frac{n!}{(n - k)! \cdot k!}$ .

Consider: how many ways to choose two kings out of four? Assume that the order for choosing the two cards does not matter. The number of possible ways can be found using the following permutation:

$\displaystyle {4 \choose 2} = \frac{4!}{(4 - 2)! \cdot 2!} = \frac{4!}{2! \cdot 2!}=\frac{4 \times 3 \times 2 \times 1}{(2 \times 1) \times (2 \times 1)} = 6$ .

Similarly, find the number of ways to choose three aces out of four.

$\displaystyle {4 \choose 3} = \frac{4!}{(4 - 3)! \cdot 3!} = \frac{4!}{1! \cdot 3!}\frac{4 \times 3}{1 \times (3 \times 2 \times 1)} = 4$ .

Note that

No card other than the two kings and the three aces are involved in this choice of five cards.
The choice of the two kings is independent of the choice the choice of the aces. (Choosing some kings does not change the choices of aces, and vice versa for the choice of the kings.)

Therefore, multiply these two permutations to find the number of ways to choose these five cards:

$\displaystyle {4 \choose 2} \cdot {4 \choose 3}= 24$ .

6 0

4 years ago

Pedro had $14.90 in his wallet. He spent $1.25 on a drink. How much does he have left?

faust18 [17]

Answer:

589

Step-by-step explanation:

Pedro had $14.90 in his wallet. He spent $1.25 on a drink. How much does he have left?

(a) Estimate the answer by rounding to the nearest whole numbers before subtracting.

(b) Find the difference. Show your work (steps).

8 0

3 years ago

I need help please help

sveticcg [70]

Answer:

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What is the range of the data?

Zepler [3.9K]

Answer:

A. 21

Step-by-step explanation:

To find range you just take the highest number and subtracted by the lowest

4 0

3 years ago

Read 2 more answers

How to solve the problem <br> 5 1/4 X 3 =

Gennadij [26K]

You can multiply them both as fractions or turn the fraction into a decimal and multiply it like that.
5 1/4 will have to turn into an improper fraction which means you have to get rid of the whole number so. To do so you have to multiply the whole number by the denominator which would be 5x4 which is 20 then add it to the numerator so I’d be 21.
Next turn the 3 into a fraction since it’s a whole number it’d be 3/1
Finally multiply straight across 21/4 x 3/1 which is 63/4 and luckily it’s already In it’s simplified form

3 0

3 years ago