Answer:
Yes
Step-by-step explanation:
The angles are identical, so they are congruent.
Hope I helped! Plz leave a comment and a rating!
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:
1 = 40%
2= 4%
3= 2.5
4= 1/4
5= 220%
Step-by-step explanation:
hope this helps
Answer:
y = 4x - 1
Step-by-step explanation:
The slope of the line (m) is 4. The line crosses the y-axis at a y-value of -1, so b = -1.
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Answer:
$96 spent.
Step-by-step explanation:
Set up a proportion to determine the amount spend for 72 sheets. Express it in sheets/amount spent:
Cross multiply:
6 · x = 8 · 72
6x = 576
Divide:
x = $96 spent for 72 sheets.
