Answer:
-36
Step-by-step explanation:
R=-2
M=12
12(-2)= -24-12=
Solve cos(4x)-cos(2x)=0 ∀ 0<=x<=2pi ..............(0)
Normal solution:
1. use the double angle formula to decompose, and recall cos^2(x)+sin^2(x)=1
cos(4x)=cos^2(2x)-sin^2(2x)=2cos^2(2x)-1 .................(1)
2. substitute (1) in (0)
2cos^2(2x)-1-cos(2x)=0
3. substitute u=cos(2x)
2u^2-u-1=0
4. Solve for x
factor
(u-1)(u+1/2)=0
=> u=1 or u=-1/2
However, since cos(x) is an even function, so solutions to
{cos(2x)=1, cos(-2x)=1, cos(2x)=-1/2 and cos(-2x)} ...........(2)
are all solutions.
5. The cosine function is symmetrical about pi, therefore
cos(-2x)=cos(2*pi-2x),
solution (2) above becomes
{cos(2x)=1, cos(2pi-2x)=1, cos(2x)=-1/2, cos(2pi-2x)=-1/2}
6. Solve each case
cos(2x)=1 => x=0
cos(2pi-2x)=1 => cos(2pi-0)=1 => x=pi
cos(2x)=-1/2 => 2x=2pi/3 or 2x=4pi/3 => x=pi/3 or 2pi/3
cos(2pi-2x)=-1/2 => 2pi-2x=2pi/3 or 2pi-2x=4pi/3 => x=2pi/3 or x=4pi/3
Summing up,
x={0,pi/3, 2pi/3, pi, 4pi/3}
Answer:
9 cm
Step-by-step explanation:
hope it helps<3
Answer:
-5/4
Step-by-step explanation:
formula
y2-y1=x2-x1
0-5 over 2+2=-5/4
Answer:
-44
Step-by-step explanation:
first term is -4, second -9, third -14, fourth -19, etc.
there is constant difference (-5) between each two neighbor terms
you can use calculator by pushing the following buttons: -4-5========
the method is:
1) insert first term (-4)
2) insert a difference (-5)
3) push the "=" button 1 time less than the desired term number
So, if you must find 9th term, you push "=" button 8 times
after pushing buttons -4-5======== you get a result -44 on a calc