Answer:
sin(2x)=cos(π2−2x)
So:
cos(π2−2x)=cos(3x)
Now we know that cos(x)=cos(±x) because cosine is an even function. So we see that
(π2−2x)=±3x
i)
π2=5x
x=π10
ii)
π2=−x
x=−π2
Similarly, sin(2x)=sin(2x−2π)=cos(π2−2x−2π)
So we see that
(π2−2x−2π)=±3x
iii)
π2−2π=5x
x=−310π
iv)
π2−2π=−x
x=2π−π2=32π
Finally, we note that the solutions must repeat every 2π because the original functions each repeat every 2π. (The sine function has period π so it has completed exactly two periods over an interval of length 2π. The cosine has period 23π so it has completed exactly three periods over an interval of length 2π. Hence, both functions repeat every 2π2π2π so every solution will repeat every 2π.)
So we get ∀n∈N
i) x=π10+2πn
ii) x=−π2+2πn
iii) x=−310π+2πn
(Note that solution (iv) is redundant since 32π+2πn=−π2+2π(n+1).)
So we conclude that there are really three solutions and then the periodic extensions of those three solutions.
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Answer:
The probability that exactly one switch is good is
Step-by-step explanation:
The probability that a switch is defective is:
The probability that a switch is not defective is
Therefore, if two switches are selected, the probability that exactly 1 is good is:
-5, -4 -1, 3, 5, if i am correct
We know that Larry has AT LEAST 3 more books than Pat, and we also know that Pat has AT MOST 3 LESS books than Larry.
Answer:
Step-by-step explanation:
Cost at the rate 6 for $15.24:
Cost of 
bottles
Cost of 
bottle
Cost of 
bottles
Cost at the rate 4 for $11.16:
Cost of 
bottles
Cost of bottle
Cost of bottles
Hence 
is less expensive.
Total saving
