Sin(2θ)+sin(<span>θ)=0
use double angle formula: sin(2</span>θ)=2sin(θ)cos(<span>θ).
=>
2sin(</span>θ)cos(θ)+sin(<span>θ)=0
factor out sin(</span><span>θ)
sin(</span>θ)(2cos(<span>θ)+1)=0
by the zero product property,
sin(</span>θ)=0 ...........(a) or
(2cos(<span>θ)+1)=0.....(b)
Solution to (a): </span>θ=k(π<span>)
solution to (b): </span>θ=(2k+1)(π)+/-(π<span>)/3
for k=integer
For [0,2</span>π<span>), this translates to:
{0, 2</span>π/3,π,4π/3}
Answer:
Roughly 18,000
Step-by-step explanation:
When you need to do rough mental math, you can do something like 720 vs 25 or 30 which is pretty simple to do in your head.
If you are very proficient in mental math, you can do something like 720 * 25, which is harder, but if you know the tricks, you can do this quickly.
720 * 25
Multiply 25 by 7.
175
Add two zeros.
17,500
Multiply 25 by 2
50
Add a zero.
500.
17500 + 500 = 18000
Answer:
C. 13 gallons
Step-by-step explanation:
150 divided by 6 is 25. 325 divided by 25 is 13.
Explanation:
Conversion of a quadratic equation from standard form to vertex form is done by completing the square method.
Assume the quadratic equation to be 
where x is the variable.
Completing the square method is as follows:
- send the constant term to other side of equal
- divide the whole equation be coefficient of
, this will give 
- add
to both side of equality 
- Make one fraction on the right side and compress the expression on the left side
- rearrange the terms will give the vertex form of standard quadratic equation
Follow the above procedure will give the vertex form.
(NOTE : you must know that 
. Use this equation in transforming the equation from step 3 to step 4)
First you set f(x) and h(x) equal to each other. So 1/x+1=2x+3. Next, you multiply each side by 1 to cancel out the fraction. So now the answer is x+1=2x+3. Now subtract 1 from each side. X=2x+2. Subtract 2x from each side now. -2x=2. Divide by -2x and get the answer x= -1
