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Phantasy [73]
3 years ago
12

Simplify sin(3pi minus x)

Mathematics
1 answer:
Slav-nsk [51]3 years ago
8 0

Answer:

sinx

Step-by-step explanation:

hello :

note :

for all x in ℝ :   1) sin(x+2π) = sinx        2)  sin(π-x) = sinx

in this exercice :

3π - x = 2π+(π - x)

sin(3π - x) = sin(2π +(π - x)) =sin(π-x) = sinx

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You're trying to find constants a_0,a_1,a_2 such that \hat y=a_0+a_1\hat x+a_2{\hat x}^2. Equivalently, you're looking for the least-square solution to the following matrix equation.


\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}

To solve \mathbf{Ax}=\mathbf b, multiply both sides by the transpose of \mathbf A, which introduces an invertible square matrix on the LHS.

\mathbf{Ax}=\mathbf b\implies\mathbf A^\top\mathbf{Ax}=\mathbf A^\top\mathbf b\implies\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b

Computing this, you'd find that

\mathbf x=\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}\approx\begin{bmatrix}121.119\\-3.786\\-0.175\end{bmatrix}

which means the first choice is correct.
8 0
3 years ago
Khan academy Find the median of the data in the dot plot below. chocolate chips
Helga [31]

Answer:

Where's the picture?

Step-by-step explanation:

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Evaluate the expression. 1− 6P4/ 8P6
allochka39001 [22]
4p^2-3/4p^2. I hope that help..
6 0
3 years ago
Write using only positive exponents
eimsori [14]

Answer:

C

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Help if u do both I’ll mark Brainlynest
amm1812

Answer:

See step-by-step explanation

Step-by-step explanation:

16. C, <AOB = 20

The total angle (<AOC) is equal to the sum of the angles inside of it (<AOB and < BOC).

<AOC= <AOB + <BOC

47=<AOB+27

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17. 24

Area of a square = s^{2}

36= s^{2}

s= 6

One side is 6

The perimeter of a square is 4(s)

4(6) = 24

Word of encouragement:

Good luck!

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3 years ago
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