Which expression is equivalent to cos(3x) sin x?

Mathematics

2 answers:

ArbitrLikvidat [17]2 years ago

7 0

Answer:

Step-by-step explanation: I tried all the other options and this was the only correct one for me on Edmentum.

LuckyWell [14K]2 years ago

4 0

Answer:

$\frac{1}{2} [sin(4x)-sin(2x)]$

Step-by-step explanation:

Use the Product-Sum identity to turn cos(3x) sin x into a sum.

Formula: cos(u) + sin(v) = $\frac{1}{2}[sin(u+v)-sin(u-v)]$

Plug 4x and 2x for u and v into the formula: $\frac{1}{2}[sin(3x+x)-sin(3x-x)]$

Simplify: $\frac{1}{2}[sin(4x)-sin(2x)]$

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What does 312,819 round to, to the nearest ten thousand?

Paha777 [63]

Answer:

310,000

Step-by-step explanation:

3 0

2 years ago

What is the sum if the first 22 terms of the following series? 86 + 79 + 72 + 65 +58+...

Arturiano [62]

Seems to be an arythmetic sequence
Sn=[n(a1+an)]/2
where
Sn means sum of all terms up the nth term
n=number of terms
a1=first term
an=nth term

so from 86 to the 22th term is from a1 to a22

find teh sequence
miknus 7 each time
an=a1+d(n-1)
an=87-7(n-1)
find 22n term
a22=87-7(22-1)
a22=87-7(21)
a22=87-147
a22=-60

S22=[22(87-60)]/2
S22=[22(27)]/2
S22=594/2
S22=297

the sum is 297

5 0

3 years ago

a street light is at the top of a 18 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a s

shutvik [7]

The most appropriate choice for similarity of triangles will be given by -

Speed of tip of the shadow of woman = 6 ft/s

What are similar triangles?

Two triangles are said to be similar, if the corrosponding angles of the triangles are same and the corrosponding sides of the triangles are in the same ratio.

Here,

The diagram has been attached here

Let the distance of woman from the pole be x ft and the distance of tip of the shadow to the pole be y ft.

Height of street light = 18 ft

Height of woman = 6ft

The two triangles are similar [As height of woman is parallel to the height of pole]

$\frac{y - x}{6}=\frac{y}{18}\\18y - 18x = 6y\\18y - 6y = 18x\\12y = 18x\\y = \frac{18}{12}x\\y = \frac{3}{2}x\\$