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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Related Questions (More Answers Below)
Ok, what is $0.1369 rounded to the nearest cent?
100 cents make a dollar which means the most possible cents not making a dollar is 99 cents
So that means you leave the first two decimals alone and focus on the last two.
What is 69 closer to? 70 or 60? Well, its larger than 65 which is the halfway point so its closer to 70
Is 70 closer to 0 or 100? Well, since 70 is past the halfway point which is 50, its closer to 100.
Think of 3 as 0 and the next number up which is 4 as 100, well, since 70 is closer to 100 than 0, its closer to 4.
So That means that 0.1369 rounded to the nearest cent is $0.14
Your answer rounded is $0.14
Answer:
<h3><u>Cylinder</u></h3>
Given:
<h3><u>Cube</u></h3>
Given:
<h3><u>Volume available to be filled with water</u></h3>
Volume of cylinder - volume of cube
= 684π - 512
= 1532.75204 cm³
1 litre = 1000 cm³
⇒ 1.5 litres = 1000 × 1.5 = 1500 cm³
As 1500 < 1532.75204, the volume of water poured into the container is smaller than the empty space available in the cylinder. Therefore, the water will <u>not</u> come over the top of the container.
The next score is 90 because 85+91+92+92=360/4= 90 average.
Answer: 36 degrees
Step-by-step explanation:
subtract 5 from 30=25
add 11 to 25
25+11=36
