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3 years ago

Question is in picture please help!

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

6 0

Answer:

I’m not 100% sure but I think 120°.

Step-by-step explanation:

This is because, angles on a straight line add up to 180°. Because there is 60 degrees on one side of line B, this means the other section is 120° (120°+60°=180°) The angle labelled (3x) is alternate to the angle of 120°. Alternate angles are always equal, meaning that 3x is equal to 120°.

I hope this is right.

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13.10. Suppose that a sequence (ao, a1, a2, ) of real numbers satisfies the recurrence relation an -5an-1+6an-20 for all n> 2

Gwar [14]

a. This recurrence is of order 2.

b. We're looking for a function $A(x)$ such that

$A(x)=\displaystyle\sum_{n=0}^\infty a_nx^n$

Take the recurrence,

$\begin{cases}a_0=a_0\\a_1=a_1\\a_n-5a_{n-1}+6a_{n-2}=0&\text{for }n\ge2\end{cases}$

Multiply both sides by $x^{n-2}$ and sum over all integers $n\ge2$ :

$\displaystyle\sum_{n=2}^\infty a_nx^{n-2}-5\sum_{n=2}^\infty a_{n-1}x^{n-2}+6\sum_{n=2}^\infty a_{n-2}x^{n-2}=0$

Pull out powers of $x$ so that each summand takes the form $a_kx^k$ :

$\displaystyle\frac1{x^2}\sum_{n=2}^\infty a_nx^n-\frac5x\sum_{n=2}^\infty a_{n-1}x^{n-1}+6\sum_{n=2}^\infty a_{n-2}x^{n-2}=0$

Now shift the indices and add/subtract terms as needed to get everything in terms of $A(x)$ :

$\displaystyle\frac1{x^2}\left(\sum_{n=0}^\infty a_nx^n-a_0-a_1x\right)-\frac5x\left(\sum_{n=0}^\infty a_nx^n-a_0\right)+6\sum_{n=0}^\infty a_nx^n=0$

$\displaystyle\frac{A(x)-a_0-a_1x}{x^2}-\frac{5(A(x)-a_0)}x+6A(x)=0$

Solve for $A(x)$ :

$A(x)=\dfrac{a_0+(a_1-5a_0)x}{1-5x+6x^2}\implies\boxed{A(x)=\dfrac{a_0+(a_1-5a_0)x}{(1-3x)(1-2x)}}$

c. Splitting $A(x)$ into partial fractions gives

$A(x)=\dfrac{2a_0-a_1}{1-3x}+\dfrac{3a_0-a_1}{1-2x}$

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

so that for $|3x|$ and $|2x|$ , or simply $|x|$ , we have

$A(x)=\displaystyle\sum_{n=0}^\infty\bigg((2a_0-a_1)3^n+(3a_0-a_1)2^n\bigg)x^n$

which means the solution to the recurrence is

$\boxed{a_n=(2a_0-a_1)3^n+(3a_0-a_1)2^n}$

d. I guess you mean $a_0=2$ and $a_1=5$ , in which case

$\boxed{\begin{cases}a_0=2\\a_1=5\\a_2=13\\a_3=35\\a_4=97\\a_5=275\end{cases}}$

e. We already know the general solution in terms of $a_0$ and $a_1$ , so just plug them in:

$\boxed{a_n=2^n+3^n}$

8 0

3 years ago

Which properties does not belong with the other three?

Oksi-84 [34.3K]

Hi there!

»»————-　★　————-««

I believe your answer is:

$x - 6 = 5$

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

I am assuming that '3=x divided by 3' is supposed to be $3 = \frac{x}{3}$ .

⸻⸻⸻⸻

The first, second, and fourth equations have x divided by a number. To isolate x, we would have to use the multiplication property of equality.

⸻⸻⸻⸻

For the third one ( $x-6=5$ ), the variable 'x' is being subtracted by 6. We would have to use the addition property of equality to isolate x.

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

8 0

3 years ago

After Stan makes a 15% down payment on a $7,000<br> motorcycle, how much will he still owe?

Svetllana [295]

1,500 I thinkkkkkkkkk

3 0

3 years ago

PLEASE HELP! 25 POINTS <br><br> listen the question number then answer

frutty [35]

Answer: <

Explantion:

$8*4-2(4)=24$

$5(10-4)=30$ , because you factor the 5 into 10 and 4 so

$50-20=30$

The second one you want will be integers.

7 0

4 years ago

Read 2 more answers

MATH HOMEWORK HELP!! >> Solving systems by GRAPHING:

grin007 [14]

I dont know the coordinates because i dont feel like putting them in right now buttttt........

main street bus equation is y=2x+40

County bus line equation is y=3x+20

thats all i've got.

7 0

3 years ago