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Studentka2010 [4]
3 years ago
5

Simplify the trigonometric expression sin(4x)+2 sin(2x) using Double-Angle

Mathematics
1 answer:
drek231 [11]3 years ago
8 0

Answer:

{ \bf{ =  \sin(4x)  + 2 \sin(2x) }} \\  = { \bf{2 \sin(2x) \cos(2x)   + 4 \sin(x)  \cos(x) }} \\  { \bf{ = 4 \sin(x) \cos(x) . ({ \cos }^{2}  x -  { \sin}^{2} }x) + 4 \sin(x) \cos(x)  }  \\  = { \bf{4 \sin(x) \cos(x)  ( { \cos }^{2}x -  { \sin }^{2}x + 1)  }} \\  = { \bf{4 \sin(x) \cos(x)  }(2 { \cos }^{2} x)} \\  = { \bf{8 \sin(x)  { \cos}^{3}x }}

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An algebra test contains 38 problems. Some of the problems are worth 2 points each. The rest of the questions are worth 3 points
Naily [24]

Let 'x' be the problems worth 2 points.

Let 'y' be the problems worth 3 points.

Since, there are 38 total problems.

So, x+y =38 (equation 1)

x = 38-y

Since, a perfect score is 100 points.

So, 2x+3y = 100 (equation 2)

Substituting the value of 'x', we get

2(38-y)+3y=100

76-2y+3y=100

76+y = 100

y = 24

x+y = 38

x = 38-24 = 14

So, 14 problems are worth 2 points and 24 problems are worth 3 points.

5 0
3 years ago
Read 2 more answers
1 point
Dimas [21]

Answer:

The simplest radical form is 9\sqrt{5} ⇒ (c)

Step-by-step explanation:

To simplify any square root;

  • Factorize the number under the root using prime numbers
  • Take out the root any number repeated twice as one number

<em><u /></em>

<em><u>Examples:</u></em>

1. Simplify \sqrt{8}

factorize 8 using prime numbers

8 = 2 × 2 × 2, then \sqrt{8}=\sqrt{(2)(2)(2)}

Take two of 2 out the root, then \sqrt{8}=2\sqrt{2}

2. Simplify \sqrt{18}

factorize 18 using prime numbers

18 = 2 × 3 × 3, then \sqrt{18}=\sqrt{(2)(3)(3)}

Take the two 3 out the root, then \sqrt{18}=3\sqrt{2}

Let us simplify 3\sqrt{45}

∵ 45 = 3 × 3 × 5

∴ 3\sqrt{45}=3\sqrt{(3)(3)(5)}

→ Take the two 3 out by one 3

∴  3\sqrt{45}=3(3)\sqrt{5}

→ Multiply the numbers out the root

∴ 3\sqrt{45}=9\sqrt{5}

∴ The simplest radical form is 9\sqrt{5}

8 0
3 years ago
your phone says that 14.5% is equivalent to the decimal 14.5 explain why your friend is incorrect by comparing the fraction -14.
Lelechka [254]
A percent is a proportion of something that can come from a variety of different numbers depending on what you are measuring. 14.5% is not the same as 14.5 because the 14.5% isn’t necessarily 14.5 of a certain amount. For example, $14.50 of the $100 you have could be from your grandparents; making 14.5% of your money from your grandparents but a deposit of $145 into a bank account that already has $855 would mean that 14.5% of the money in that bank account was from that deposit but $145 does not equal $14.50. They just have the same proportion just different on different scales.

Hope this is what you were looking for.
4 0
3 years ago
Find sin D sin E cos D and cos E
Andrew [12]

9514 1404 393

Answer:

  sin(D) = cos(E) = (√3)/2

  cos(D) = sin(E) = 1/2

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and right triangle sides.

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

For this diagram, this means ...

  sin(D) = cos(E) = (13√3)/26 = (√3)/2

  cos(D) = sin(E) = 13/26 = 1/2

5 0
3 years ago
1.) What is the mode of the data ? Show work ( A.3, B.5, C.8, D.10 )
ArbitrLikvidat [17]
Hey there.

1.) The mode is the number that's most frequent in a given list.
In our list, we have 2, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 10.
Our most frequent number is 6; therefore, our mode is 6.

2.) The median is the number in the middle of a list organized from least to greatest.
2, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 10;
4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9;
4, 5, 5, 5, 6, 6, 6, 6, 7;
5, 5, 5, 6, 6, 6, 6;
5, 5, 6, 6, 6;
5, 6, 6;
6.
6 is our median.

I hope this helps, despite your answer choices not providing the correct answer.
6 0
3 years ago
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