Question 837577: Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)
12 cos(x) − 6 = 0
Find the solutions of the equation in [0, 2π). (Enter your answers as a comma-separated list.)
sin 2x = 1
Use the fundamental identities to simplify the expression. There is more than one correct form of the answer.
3 sec2 x(1 − sin2 x)
Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer.
3 sin2 x csc2 x − 3 sin2 x
A sample of a radioactive substance decayed to 96.5% of its original amount after a year. (Round your answers to two decimal places.)
(a) What is the half-life of the substance?
yr
(b) How long would it take the sample to decay to 55% of its original amount?
yr
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
Trigonometry-basics/837577 (2014-02-04 21:00:13): Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)
12 cos(x) − 6 = 0
cos(x) = 1/2
x = pi/3, -pi/3
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Find the solutions of the equation in [0, 2π). (Enter your answers as a comma-separated list.)
sin(2x) = 1
2x = pi/2
x = pi/4
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Use the fundamental identities to simplify the expression. There is more than one correct form of the answer.
3 sec^2(x)(1 − sin^2 (x))
= 3sec^2(x)(cos^2(x))
= 3*1 = 3
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Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer.
3 sin2(x) csc2 x − 3 sin2 x
= 3 - 3sin^2(x)
= 3(1-sin^2(x)
= 3*cos^2(x)
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A sample of a radioactive substance decayed to 96.5% of its original amount after a year. (Round your answers to two decimal places.)
(a) What is the half-life of the substance?
A(t) = 0.965^t*Ao
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(1/2)Ao = 0.965^t*Ao
0.965^t = 1/2
t = log(1/2)/log(0.965)
t = 19.46 years
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(b) How long would it take the sample to decay to 55% of its original amount?
t = log0.55/log(1/2)
t = log(1/2)/log(0.55) = 1.1594
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Cheers,
Stan H.
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