What is the value of 6/x+2x^2, when x=3

Find all solutions of the equation: 2cos^2x-cosx=1

Art [367]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3166243

——————————

Solve the trigonometric equation:

$\mathsf{2\,cos^2\,x-cos\,x=1}\\\\ \mathsf{2\,cos^2\,x-cos\,x-1=0}$

Make a substitution:

$\mathsf{cos\,x=t\qquad (-1\le t\le 1)}$

and the equation becomes

$\mathsf{2t^2-t-1=0}$

Rewrite conveniently – t as + t – 2t, and then factor the left-hand side by grouping:

$\mathsf{2t^2+t-2t-1=0}\\\\ \mathsf{t\cdot (2t+1)-1\cdot (2t+1)=0}$

Factor out 2t + 1:

$\mathsf{(2t+1)\cdot (t-1)=0}\\\\ \begin{array}{rcl} \mathsf{2t+1=0}&~\textsf{ or }~&\mathsf{t-1=0}\\\\ \mathsf{2t=1}&~\textsf{ or }~&\mathsf{t=1}\\\\ \mathsf{t=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{t=1} \end{array}$

Substitute back for t = cos x:

$\begin{array}{rcl}\mathsf{cos\,x=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{cos\,x=1}\\\\ \mathsf{cos\,x=cos\,60^\circ}&~\textsf{ or }~&\mathsf{cos\,x=cos\,0} \end{array}$

Therefore,

$\begin{array}{rcl} \mathsf{x=\pm\,60^\circ+k\cdot 360^\circ}&~\textsf{ or }~&\mathsf{cos\,x=0+k\cdot 360^\circ} \end{array}$

where k is an integer.

Solution set:

$\mathsf{S=\left\{x\in\mathbb{R}:~~x=-\,60^\circ+k\cdot 360^\circ~~or~~x=60^\circ+k\cdot 360^\circ~~or~~x=k\cdot 360^\circ,~~k\in\mathbb{Z}\right\}}$

I hope this helps. =)

3 0

2 years ago

The weekly cost (c) of manufacturing (x) number of remotes is given by the equation below. what is the cost to manufacture 2500

IRISSAK [1]

C= 2000 + 3(2500)
C= 2000 + 7,500
C= $9,500

6 0

2 years ago

Quick please! Which best describes the triangle? 1.Acute and isosceles 2.Acute and scalene 3. Right isosceles 4.Obtuse and isosc

rjkz [21]

Answer:

hey there!!!

Step-by-step explanation:

i think the best option is acute and isosceles from my view

hope it helps you...

4 0

2 years ago

Sara is 9 years younger than her brother, Michael. The sum of their ages is 47 years. How old is Sara and how old is her brother

kotykmax [81]

Answer:

Michael is 38 and Sara is 29

Step-by-step explanation:

Because it says the sum of their age is 47 you do 47-9=38 so that would be Michael's age and than because Sara is 9 years younger than him and then you would do 38-9=29

7 0

2 years ago

If 332 students brought shirts and there are 830 students at the school what percents of the student brought shirts

Anika [276]

Answer: 40%

Step-by-step explanation: What I like doing with problems like this is work backward, so that is how this explanation is going to work.

830*0.40=332 so that is how I got 40% now lets dig a little deeper.

How to find percent is take the whole and times it by the decimal of percent you want (eg. if 400 is my whole I want to find out what 30% of it is I would do 400*0.30)

So then we take our 830 times it by what we think best fits and that's how I solved it!

If you need any further help let me know!

6 0

2 years ago