Prove the identity: cos(3x) + cos(x) = 2cos(2x)cos(x)I'm almost done with my homework, just got stuck on this one.

Answers

Answer 1

Answer: $cos \alpha +cos \beta =2\cdot cos ( \alpha + \beta )/(2) \cdot cos ( \alpha - \beta )/(2)\n-----------------\n\n \alpha =3x\ \ \ and\ \ \ \beta =x\n\n$

$L=cos \alpha +cos \beta =cos(3x)+cos(x)\n\n\Rightarrow\ \ \ 2\cdot cos ( \alpha + \beta )/(2) \cdot cos ( \alpha - \beta )/(2)=2\cdot cos (3x+x)/(2) \cdot cos (3x-x)/(2) =\n\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2\cdot cos (4x)/(2) \cdot cos (2x)/(2) =\n\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2\cdot cos(2x)\cdot cos (x)=R$

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Ten plus 8 to the third power divided by 16

Answers

Answer: 42

Step-by-step explanation:

10+8^3/10

Exponets first

8^3=512

Then Divide

512/16=32

Finally add

32+10=42

Use Order of Operations

There is a proportional relationship between the volume of a sample of helium in liters and the mass of that sample in grams. if the mass of a sample is 5 grams, its volume is 28 liters. (5, 28) is shown on the graph below. what is the constant of proportionality in this relationship, in this situation, what is the meaning of the number you found in question 1?(explain in the short answer) Add at least three more points to the graph above, and label with their coordinates.(Show your work)
Write an equation that shows the relationship between the mass of a sample of helium and its volume. Use m for mass and v for volume.(Please answer in v = form)

Answers

Answer:

v = 5.6m

Step-by-step explanation:

Proportional relationship equation:

y = kx, where k- constant of proportionality

Use the given point to work out the value of k:

28 = 5k
k = 28/5
k = 5.6

In our case the equation is:

v = 5.6m, where v- volume, m- mass

Answer:

Step-by-step explanation:

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Answers

3/5 of 60= 60 divided by 5= 1212 x 3= 36

Identify the coordinates of the vertices of the polygon.Identify the coordinates of the vertices of the polygon.A. (3,5), (–6,1), (–3,–4), (0,–5), (7,–3)
B. (–3,5), (–6,1), (–3,–4), (0,–5), (7,–3)
C. (3,5), (–6,1), (–3,–4), (–5,0), (7,–3)
D. (3,5), (6,1), (–3,–4), (0,–5), (7,–3)

Answers

Answer:

Step-by-step explanation:

The coordinates are (3,5),(7,-3),(0,-5),(-3,-4) and (-6,1). So the correct option is A

Show that (2.1) is a solution of the system of equations.Substitute (2, 1) into x + 3y = 5 to get -
Simplify the equation to get -
Substitute (2, 1) into y = -x+ 3 to get -
Simplify the equation to get -