Helpppppp its a test

Sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0

andreev551 [17]

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0

sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2

sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ

… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π

… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5

sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ

… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π

… … … … … ==> x = nπ or x = (2n + 1)π/2

cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ

… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ

… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ

(where n is any integer)

5 0

3 years ago

Marine biologists have been studying the effects of acidification of the oceans on weights of male baluga whales in the Arctic O

PSYCHO15rus [73]

Answer:

c. 61.25 kg

Step-by-step explanation:

The margin of error in estimating the true mean weight of male baluga whales in the Artic Ocean.

a. 15.31 kg

b. 51.40 kg

c. 61.25 kg

d. 80.49 kg

Margin of Error Formula= z × Standard deviation/√n

95% confidence interval = 1.96

Standard deviation = 125kg

n = 16 samples

Margin of error= 1.96 × 125/√16

= 1.96 × 125/4

= 245/4

= 61.25kg

The margin of error in estimating the true mean weight of male baluga whales in the Artic Ocean is 61.25kg

6 0

3 years ago

4 people are on the team. Members will be chosen randomly to serve as chairperson, treasurer, secretary, or timekeeper . Noor is

aliina [53]

Answer:

Step-by-step explanation:

Given that four people are on the team. Members will be chosen randomly to serve as chairperson, treasurer, secretary, or timekeeper

Since one person cannot serve two posts we have total number of ways

= 4(3)(2)(1) = 24

If Noor is chair person and Qu treasurer then remaining 2 can take two posts in 2 different ways

So probability that Noor is selected to be chairperson and Qu is selected to be treasurer

=favourable outcomes/total outcomes

= $\frac{2}{24} \\=0.083$

8 0

4 years ago

A rectangular yard has area 96 square feet. If the width of the yard is 4 ft less than length, what is the perimeter,in feet, of

marusya05 [52]

Area of the rectangular yard = 96 square feet
Let us assume the length of the yard = x feet
Width of the yard = x - 4 feet
Then
Area of the yard = length * width
96 = x(x - 4)
96 = x^2 - 4x
x^2 - 4x - 96 = 0
x^2 - 12x + 8x - 96 = 0
x(x - 12) +8(x - 12) = 0
(x - 12)(x + 8) = 0
As the value of length cannot be negative so
x - 12 = 0
x = 12
So
Length of the yard = 12 feet
Width of the yard = x - 4 feet
   = 12 - 4 feet
   = 8 feet
Then
Perimeter of the yard = 2 (length + width)
   = 2(12 + 8)
   = 2 * 20 feet
   = 40 feet.
So the perimeter of the yard is 40 feet.

6 0

3 years ago

I need help understanding how to solve this problem.

LUCKY_DIMON [66]

Answer:

D. (-5/13, -12/13)

Explanation:

It is indicated to find the coordinates of the point T (5/13, 12/13) at a distance π + x.

π is an arc of half a circle, i.e. 180º.

Then, the distance π+ x means that the point T is rotated 180º.

The rule for the rotation of a point 180º around the origin is:

(x, y) → (-x, - y)

Applying that rule to the point T:

(5/13, 12/13) → (-5/13, - 12/13) ← answer

6 0

4 years ago

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