4sin²(x) = 5 - 4cos(x)
4{¹/₂[1 - cos(2x)]} = 5 - 4cos(x)
4{¹/₂[1] - ¹/₂[cos(2x)]} = 5 - 4cos(x)
4[¹/₂ - ¹/₂cos(2x)] = 5 - 4cos(x)
4[¹/₂] - 4[¹/₂cos(2x)] = 5 - 4cos(x)
2 - 2cos(2x) = 5 - 4cos(x)
- 2 - 2
-2cos(2x) = 3 - 4cos(x)
-2[2cos²(x) - 1] = 3 - 4cos(x)
-4cos²(x) + 2 = 3 - 4cos(x)
- 2 - 2
-4cos²(x) = 1 - 4cos(x)
-4cos²(x) + 4cos(x) - 1 = 0
4cos²(x) - 4cos(x) + 1 = 0
[2cos(x) - 1]² = 0
2cos(x) - 1 = 0
+ 1 + 1
2cos(x) = 1
2 2
cos(x) = ¹/₂
cos⁻¹[cos(x)] = cos⁻¹(¹/₂)
x = 60, 300
x = π/3, 5π/3
[0, 2π) = 0 ≤ x < 2π
[0, 2π) = 0 ≤ π/3 ≤ 2π or 0 ≤ 5pi/3 < 2π
The picture is extremely blurry, could you write out some of the answers?
This is a system of equation:
7y - 5x = 31
x = 4 - 2y
Plug in 4 - 2y for x
7y - 5(4 - 2y) = 31
Distribute -5 to both 4 and -2y
7y - 20 + 10y = 31
Simplify
17y - 20 = 31
Isolate the y. Note the equal sign. What you do to one side you do to the other. Do the opposite of PEMDAS.
Add 20 to both sides
17y - 20 (+20) = 31 (+20)
17y = 51
Divide 17 from both sides to isolate the y
17y/17 = 51/17
y = 51/17 or 3
y = 3
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Plug in 3 for y in one of the equations.
x=4−2y
x = 4 - 2(3)
Simplify.
x = 4 - 6
x = -2
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x = -2, y = 3 is your answer, or B)
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hope this helps
Answer:
Rounding out we have that 15 liters equals 3.96 gallons
Step-by-step explanation:
I hope this halp
Answer:
1,470.265 (or about 1,470.3 when rounded to nearest tenth) feet cubed
Step-by-step explanation:
May this bring you more knowledge
