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tensa zangetsu [6.8K]
4 years ago
11

Find the interval in which f(x)=sinx−cosx is increasing or decreasing?

Mathematics
1 answer:
alisha [4.7K]4 years ago
3 0

Answer:

There is no short answer.

Step-by-step explanation:

To find to intervals which f(x) increases or decreases, we first need to find it's derivative.

f(x) = sinx - cosx\\f'(x) = cosx - (-sinx) = cosx + sinx

The function is increasing when it's value is  > 0 and decreasing when it's value is < 0.

If we take a look at this graph, cosx+sinx is positive when they are both positive or when cosx is greater then sinx on the negative part.

I hope this answer helps.

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Approximate the stationary matrix S for the transition matrix P by computing powers of the transition matrix P.
Scrat [10]

Answer:

S = [0.2069,0.7931]

Step-by-step explanation:

Transition Matrix:

P=\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]

Stationary matrix S for the transition matrix P is obtained by computing powers of the transition matrix P ( k powers ) until all the two rows of transition matrix p are equal or identical.

Transition matrix P raised to the power 2 (at k = 2)

P^{2} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]

P^{2} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right]

Transition matrix P raised to the power 3 (at k = 3)

P^{3} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]

P^{3} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]

  P^{3} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right]

Transition matrix P raised to the power 4 (at k = 4)

P^{4} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]

P^{4} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]

P^{4} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right]

Transition matrix P raised to the power 5 (at k = 5)

P^{5} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]

P^{5} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]

P^{5} =\left[\begin{array}{ccc}0.2069&0.7931\\0.2069&0.7931\end{array}\right]

P⁵ at k = 5 both the rows identical. Hence the stationary matrix S is:

S = [ 0.2069 , 0.7931 ]

6 0
4 years ago
Hue is arranging chairs. She can form 5 rows of a given length with 2 chairs left over, or 7 rows of that same length if she get
Andru [333]
I just took the 16 chairs and added 2 since thats how many are left over, then since adding these 16 chairs, you are creating 2 more rows, so (16+2)/2 =9 Therefore, each row must have nine chairs in it and Hue starts off with 5x9+2= 47 chairs
4 0
3 years ago
Please I need help the answer please
Volgvan

Answer:-72

Step-by-step explanation:

(6)*(-12)

-72

5 0
4 years ago
Read 2 more answers
4+ (-3) - 2*(-6)<br> What is the answer to
konstantin123 [22]

Answer:

13

Step-by-step explanation:

4+(-3)-2*(-6)

4-3-2*-6

1-(-12)

1+12

13

4 0
3 years ago
Read 2 more answers
A man is in a treehouse 10 feet above the ground. He is looking at the top of another tree that is 22 feet tall.The bases of the
Soloha48 [4]

Answer:

22 degrees.

Step-by-step explanation:

Please find the attachment.

We have been given that a man is in a tree-house 10 feet above the ground. He is looking at the top of another tree that is 22 feet tall.The bases of the trees are 30 feet apart.

To find the angle of elevation from the man's feet to the top of the tree, we will use tangent because we know adjacent side and opposite side to angle x.

\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}

\text{tan}(x)=\frac{12}{30}

Now, we will use arctan or inverse tan to solve for x as:

x=\text{tan}^{-1}(\frac{12}{30})

x=21.8014094^{\circ}

Upon rounding to nearest degree, we will get:

x\approx 22^{\circ}

Therefore, the angle of elevation from the man's feet to the top of the tree is approximately 22 degrees.

5 0
4 years ago
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