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Anton [14]
3 years ago
11

Prove that sin^4x - cos^4x = 2sin^2x - 1

Mathematics
1 answer:
Liula [17]3 years ago
5 0

Step-by-step explanation:

Step 1: From the given equation, taking the Left Hand Side (LHS) of the equation

Step 2: Simplify the LHS to make it equal to the Right Hand Side (RHS)

LHS = sin^4x - cos^4x = (sin²x)² - (cos²x)²

       = (sin²x - cos²x)(sin²x + cos²x)

       = sin²x - (1 - sin²x)  since sin²x + cos²x = 1

       = 2 sin²x - 1

       = RHS

Hence proved.

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Which expression is equivalent to –3(u+7)<br> PLEASE ANSWER THE QUESTION
Andreyy89

Answer: (u+7) x -3

I like to use substitution, for example u=2

(2+7) x -3 = -27

-3(2+7) = -27

5 0
3 years ago
Nathan is out rafting. He rafts 16 miles with the river current. At the end of 16 miles, he turns around and rafts the same dist
Novosadov [1.4K]
S = d/t

st = d

t = d/s

The time going is t1.
The time returning is t2.
The total time is 4 hours, so we have t1 + t2 = 4

The speed of the current is c.
The speed going is 9 + c.
The speed returning is 9 - c.

t1 = 16/(9 + c)

t2 = 16/(9 - c)

t1 + t2 = 16/(9 + c) + 16/(9 - c)

4 = 16/(9 - c) + 16/(9 + c)

1 = 4/(9 - c) + 4/(9 + c)

(9 + c)(9 - c) = 4(9 - c) + 4(9 + c)

81 - c^2 = 36 - 4c + 36 + 4c

81 - c^2 = 72

c^2 = 9

c^2 - 9 = 0

(c + 3)(c - 3) = 0

c + 3 = 0   or   c - 3 = 0

c = -3   or   c = 3

We discard the negative answer, and we get c = 3.

The speed of the current is 3 mph.
7 0
4 years ago
Read 2 more answers
a cylinder has a volume of 18 Pi cubic inches the radius of the cylinder is 3 in what is the height of the cylinder
Lera25 [3.4K]
<span>Cylinder Volume   =   </span><span>π <span>• r² • height
</span></span>
18 PI = PI * 9 * height
height = 18 PI / PI * 9
height = 2 inches


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6 0
4 years ago
Expenses that are incurred directly or entirely in connection with the selling of merchandise are classified as
zubka84 [21]
Cost of goods sold (COGS)

I’m not entirely sure, but I believe this is the answer.
6 0
3 years ago
PLEASE HURRY NEED ANSWER+ BRAINLIEST &amp; 15 POINTS<br><br>QUESTION IN ATTACHMENT
Jobisdone [24]

Answer:

Initial value is 5, Growth, 7%

Initial value is 60, Decay, 7%

Step-by-step explanation:

Growth and decay are given respectively by A=P(1+r)^x\\or\\A=P(1-r)^x. Growth adds to 1 by its percent. Decays subtracts from one its percent.

Since the left has a rate greater than 1 it is growth and the amount above is it's percent as a decimal. We convert by multiplying 0.07 by 100 which equals 7%. The right has a rate less than 1 and is decay. The amount below 1 has been found by subtracting the rate. So we subtracted -0.07 to get 093. Then 0.07 is our rate and we multiply by 100 to get -7%.

The initial value is P and is always P. On the left, 5 is in the P position. On the right, 60 is in the P position.

5 0
3 years ago
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