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antoniya [11.8K]
3 years ago
10

Hi please help me with this math question​

Mathematics
1 answer:
Natasha2012 [34]3 years ago
7 0

Step-by-step explanation:

cos(3x) = sin(2x)

Use reflection.

sin(π/2 − 3x) = sin(2x)

π/2 − 3x = 2x

π/2 = 5x

x = π/10

Instead, use multiple angle formulas.

cos(3x) = sin(2x)

4 cos³x − 3 cos x = 2 sin x cos x

4 cos³x − 3 cos x − 2 sin x cos x = 0

cos x (4 cos²x − 3 − 2 sin x) = 0

cos x (4 (1 − sin²x) − 3 − 2 sin x) = 0

cos x (4 − 4 sin²x − 3 − 2 sin x) = 0

-cos x (-4 + 4 sin²x + 3 + 2 sin x) = 0

-cos x (4 sin²x + 2 sin x − 1) = 0

If t = sin(π/10), then:

4t² + 2t − 1 = 0

Solve with quadratic formula:

t = [ -2 ± √(2² − 4(4)(-1)) ] / 2(4)

t = [ -2 ± √(4 + 16) ] / 8

t = (-2 ± 2√5) / 8

t = (-1 ± √5) / 4

Since π/10 is in the first quadrant, sin(π/10) is positive.

sin(π/10) = (-1 + √5) / 4

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Answer:

|–2| |5| |–8| |11| |–12|

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3 years ago
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jamie and emily are married and make a total annual gross pay of 91,500. Use the table below to calculate their total and federa
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Their total income tax is $10,980.

<h3><u /></h3><h3><u>Percentages</u></h3>

Given that Jamie and Emily are married and make a total annual gross pay of $91,500, to determine their total income tax at 12% rate, the following calculation must be performed:

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8 0
2 years ago
F(x) = -1/3 x + 7 determine the input that would give an output value of 2/3
-BARSIC- [3]
Ur output value is f(x).....so to do this problem u need to sub in 2/3 for f(x) and solve for the input value which is x

f(x) = -1/3x + 7
2/3 = -1/3x + 7 ...multiply everything by 3
2 = -x + 21
2 - 21 = - x
- 19 = -x
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7 0
3 years ago
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Given f (x ) = x^2 + 3x + 2 and g (x ) = x + 1, perform the indicated operations.
Nana76 [90]

Answer:

(i) (f - g)(x) = x² + 2·x + 1

(ii) (f + g)(x) = x² + 4·x + 3

(iii) (f·g)(x) = x³ + 4·x² + 5·x + 2

Step-by-step explanation:

The given functions are;

f(x) = x² + 3·x + 2

g(x) = x + 1

(i) (f - g)(x) = f(x) - g(x)

∴ (f - g)(x) = x² + 3·x + 2 - (x + 1) = x² + 3·x + 2 - x - 1 = x² + 2·x + 1

(f - g)(x) = x² + 2·x + 1

(ii) (f + g)(x) = f(x) + g(x)

∴ (f + g)(x) = x² + 3·x + 2 + (x + 1) = x² + 3·x + 2 + x + 1 = x² + 4·x + 3

(f + g)(x) = x² + 4·x + 3

(iii) (f·g)(x) = f(x) × g(x)

∴ (f·g)(x) = (x² + 3·x + 2) × (x + 1) = x³ + 3·x² + 2·x + x² + 3·x + 2 = x³ + 4·x² + 5·x + 2

(f·g)(x) = x³ + 4·x² + 5·x + 2

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change into improper fraction then do the problem then turn back into mixed number

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