anonymous
  • anonymous
Find the values of p so that the function 8sin^3(x)=p-7cos2x would not have any solutions.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
experimentX
  • experimentX
8sin^3(x) will always be less or equal than 8 and greater than or equal to -8, since sine function will always generate less than 7cos2x will always be less than or equal to 7 and greater than or equal to -7, so, if p < -15 then it will not have any solution and also if p > 15, same is the case.
anonymous
  • anonymous
But I've given the answer and it's supposed to be p=(-inf;-15)u(7;inf)
anonymous
  • anonymous
How do you get the 7 to infinity part?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Got it. Thanks!
experimentX
  • experimentX
(-inf;-15)u(15;inf) is my answer
anonymous
  • anonymous
Yes, mine must be wrong.
experimentX
  • experimentX
incase cos part is -7 and the sin part is 8, than p must be 15, if p is greater than 15, then no solution exist.
anonymous
  • anonymous
Yes.
experimentX
  • experimentX
Oo... wait, maximize and minimize the following function, you will get a lot better answer f(x) = 8sin^3(x)-7cos2x
anonymous
  • anonymous
How do you do that?
experimentX
  • experimentX
take first derivative ... and equate it to zero. and solve for x. for now!! and alert me
anonymous
  • anonymous
Okay. I'll let you know.
anonymous
  • anonymous
x=nPi , x=2nPi , x=(-1)^n+nPi
anonymous
  • anonymous
Second one is wrong.
anonymous
  • anonymous
+-Pi/2+2nPi.
experimentX
  • experimentX
let's see http://www.wolframalpha.com/input/?i=+y+%3D+8sin%5E3%28x%29-7cos2x+
experimentX
  • experimentX
http://www4c.wolframalpha.com/Calculate/MSP/MSP43821a11302d5f30bd4f00001ghb080f5h89969g?MSPStoreType=image/gif&s=54&w=372&h=36
anonymous
  • anonymous
Yes, got those already.
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=solve+14%28sin2x%29%2B24+%28sinx%29%5E2+cosx
experimentX
  • experimentX
in these points you either get maximum value or minimum value
anonymous
  • anonymous
And then?
experimentX
  • experimentX
the best way would be to put these values in our function and check which gives maximum value and which gives minimum value
experimentX
  • experimentX
beyond greatest maximum value, solution does not exist .... and same goes to minimum value
anonymous
  • anonymous
Alright. I try to write it all down. Thank you!
experimentX
  • experimentX
and your answer is p<-7 and p>15
experimentX
  • experimentX
thats from graph
anonymous
  • anonymous
Oh, okay.
experimentX
  • experimentX
http://www4c.wolframalpha.com/Calculate/MSP/MSP66131a112fh7c8a5gf7b00006276ff9g8beb6fif?MSPStoreType=image/gif&s=56&w=299&h=128&cdf=RangeControl

Looking for something else?

Not the answer you are looking for? Search for more explanations.