Which equation shows the quadratic formula used correctly to solve 7x^2 = 9 + x for x?
1 answer:
To use the quadratic formula properly, you first would want to set your quadratic equation equal to zero by moving all terms to one side and combining like terms. That would look like: 
. Now, you can use the quadratic formula: 
; note the "+" after the "-b" term should actually be a +/- as there are 2 answers to a quadratic. Last, plug in the correct numbers for a, b, and c to get your answer. 
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The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)
<h3>How to solve the trigonometric equations?</h3><u>Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)</u>
The equation can be split as follows:
y = 1 - cos(x)
y = 2 - 2sin²(x)
Next, we plot the graph of the above equations (see graph 1)
Under the domain interval (-π, π), the curves of the equations intersect at:
(-π/3, 0.5) and (π/3, 0.5)
Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)
<u>Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)</u>
The equation can be split as follows:
y = 4cos⁴(x) - 5cos²(x) + 1
y = o
Next, we plot the graph of the above equations (see graph 2)
Under the domain interval [0, 2π), the curves of the equations intersect at:
(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)
Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)
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Answer:
C. 5.2 cm
Step-by-step explanation:
Arc length formula:
where s = arc length
n = central angle of arc
r = radius of circle
diamter = d = 10 cm
r = d/2 = 10 cm/2 = 5 cm
n = 60 deg
Answer: 5.2 cm