I'll write "x" instead theta.
sin x + 1 = cos(2x)
formula: cos(2x) = 1 - 2sin²x
sin x + 1 = 1 - 2sin²x
2sin²x + sin x = 0
sin x (2sin x + 1) = 0
sin x = 0 or sin x = -1/2
x1 = πk and x2 = -π/6 + 2πk and
x3 = 5π/6 + 2πk
for domain 0≤x<2π :
x1 = 0 (for k=0 in x1)
x2 = π (for k=1 in x1
x3 = 11π/6 (for k=1 in x2)
x4 = 5π/6 (for k=0 in x3).
k is an integral.
Answer:
x = 
, y = 
Step-by-step explanation:
1. Isolate for x in one of the equations:
2x = 9x - 14y
2x-9x = 9x-9x -14y
-7x = -14y
-7x/-7 = -14y/-7
x = 2y
2. Substitute 2y in for x in the second equation:
9(2y) = 40 - 14y
3. Simplify:
18y = 40 - 14y
4. Isolate for y:
18y+14y = 40 -14y+14y
32y = 40
32y/32 = 40/32
y =
5. Substitute the new y-value into the simplified expression x = 2y:
x = 2(5/4)
x =
hope this helps!
Answer: ∛v
Step-by-step explanation:
Since we know volume is measured height x width x length, we know the equation we'd use here would be:
___ x ___ x ___ = v in³
If this was area, we would have ___ x ___ = v in², and it would be easy to find each blank. You would just find the square root of "v", making your answer √v.
When you have 3 things multiplied by each other (that are exactly the same, which is the situation here since this is a cube), you will want to find ∛x (if x is our unknown variable). This means that we are finding ONE-THIRD of the number ... sort of. So if x was equal to 8, then ∛x = 2, because 2 x 2 x 2 = 8.
In our situation here, x = v, and since we don't know the actual number, we will keep it as a square root, so the answer to your question is ∛v.
I really hope I was able to explain easy enough, feel free to ask anything else!
Step-by-step explanation:
In Kate's equation, 20 is the total number of tickets, 4 is number of tickets per ride, r is number of rides already ridden, and 4r is the number of tickets used
in Brian's equation, 5 is total number of rides Katie can ride and 5 - r is the number of rides left to ride
It would be 7lbs, you divide the total amount by the amount per pound and you get the weight.
