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.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

this should say for what value of x on the interval... Sorry!

deriving trig...aint had to do this yet :)

Dx(-7.2 sin(.3x)) = -7.2(.3) cos(.3x)

lol .... I was getting there :)

sorry! lol

lets multiply by 100 to get rid of some of those decimals

-54 sin(.3x) - 216(cos.3x) = 0

can we factor out anything from 54 and 216? I know 2 comes out...

you can take out a 9 i think

54/216 = 27/108..try 3 now 9/36 try 3 again 3/12 and 3 again 1/4

looks like 54 factors out completely...
216/54 = anything useful? 4 yay!!

-54(sin(.3x) + 4cos(.3x)) this look right to you so far?

yeah I'm following I think. lol, that's what I have when I do the same work on my calculator. :)

so, lets see what sin(.3x) + cos(.3x) gets us to equal 0

they gotta be opposites of each other, so lets throw one to the other side

and dont forget that 4 that I left out lol

yeah i was going to ask why we weren't using it, lol but nevermind

4cos(.3x) = - sin(.3x)
now picture these graphs for a minute

the cos is just stretched 4 tall, so the 4 doesnt matter
the sin is flipped over upside down

.3 = the frequency of the graphs

these cross points at 2 places every time they go thru one frequency...does that make sense?

once in Q2 and another in Q4

the only angle that has sin and cos equal is 45 degrees

right.. I put them in my graphing calculator. lol so that means I have more than one answer right?

yes... more than one answer, and it will have something to do with 45 degrees

-9.65 and 11.28 is our interval

.3(sqrt(2)/2) = ?

.2121320344

I might be wrong about the 45 tho :)

derive it again to see if we can get some useful information...

derive the original f(x) or take the second derivative?

second derivative will give us a better picture....

64.8 sin(0.3 x)-16.2 cos(0.3 x)

I got:
y'' = .648 sin(.3x) - .162 cos(.3x)

oh, yeah I just had it multiplied by 100 still

it might be helpful, but im still "stuck" :)

lets go back to the original..
sin(.3x) + 4cos(.3x)

Is there a way for us to write them both in the same terms, like a way for us to make cos to sin?

there can be a square root involved, or a phase shift....

sin = sqrt(1-cos^2)

sin^2 = 1-cos^2

oww...my eyes.....

then:
17cos^2(.3x) -1 = 0 right?

i believe you're correct.

cos^2(.3x) = 1/17

cos(.3x) = sqrt(17)/17 then ....if that helps :)

okay so x ends up being like 4.419392212

cos-1(sqrt(17)/17) is?

cos-1(sqrt(17)/17) is 1.325817664 i think

25.32 is what I get for that x :) does that make any sense?

25.32 radians of course

ohh.. so why am I getting a different number, is my calculator just in the wrong mode?

maybe; and I used 1/sqrt(17) to be simple

lets plug that in to see what we get:
sin(.3(25.32)) + 4cos(.3(25.32)) :=: 0 ??

I'm not getting zero. :\

0.1321 + 3.9648 = .... ack!!!
lol.

need someone smarter than me I guess :)

oh no. lol what do I do now? Do you have any ideas of where else I can get help b y midnight?

how many points it take off if it is wrong?

I'm not sure.. there are only 4 sections and this one is technically two parts.

let me review our stuff for a few minutes and see what I can deduce...

I don't know how they're getting tangent though.

What if we divided both sides by cos(0.3x) and then had tan(0.3x)=4.. does that work?

tan(a) = 4
tan-1(4) = what?

i was getting to it.... :)

75.96 degrees is a divide that by.3

so we have 253.212=x ?

that sounds large. lol

remember that tan-1 spits out an angle between -90 and 90

(75.96 + 180) /.3 ?? maybe

(75.96 - 90)/.3?

that one gives us -46.8

i see that..... maybe our interval itself gives us a max or min at the end points?

if you put those in.. for -9.65, we get 0.0119783705 and for 11.28, we get -0.190832377

.3x gives us one cycle every 20pi/3 does that helps us out?

6 and 2/3 pi

x = 20/3 (pi n+tan-1(1/4 (1+sqrt(17))))

What is the value of our interval in terms of pi?

x(pi) = -9.65
x = pi/-9.65

-.325 pi to .279 pi right?

okay.. I'm just lost at this point. lol I really don't even know how to get any further in this.

im at a loss for the moment as well :) its all those decimals that are messing me up