Answer:
y=4 sin(4x)
Step-by-step explanation:
So you are given y(0)=0. This means when x=0, y=0.
So plug this in:
0=c1 cos(4*0)+c2 sin(4*0)
0=c1 cos(0) +c2 sin(0)
0=c1 (1) +c2 (0)
0=c1 +0
0=c1
So our solution looks like this after applying the first boundary condition:
y=c2 sin(4x).
Now we also have y(pi/8)=4. This means when x=pi/8, y=4.
So plug this in:
4=c2 sin(4*pi/8)
4=c2 sin(pi/2)
4=c2 (1)
4=c2
So the solution with the given conditions applies is y=4 sin(4x) .
Testing:
y'=16 cos(4x)
y''=-64 sin(4x).
y''+16y=0
-64 sin(4x)+16(4 sin(4x))
-64 sin(4x)+64 sin(4x)
0
So the solution still works.
Answer: x=11
Step-by-step explanation:
First, since angle A and angle B are vertical angles, that means that they are congruent. If they are congruent, then the m of angle A equals the measure of angle B. So, (3x+3)=(4x-8). Simplify using algebra so that in the end, you will find that x=11.
3x+3=4x-8
3=x-8
11=x
The additive property of zero states that when you have any number and add zero to it, your answer will always equal the original number
Answer:
36 miles.
Step-by-step explanation:
If you look, each time can be divided by 5 to get the miles. 180/5 is 36, so the answer is 36 miles.
you would need to make 0.03 a whole number 1st, so you take the decimal point and move it 2 places, and you do that to 8.4.
Now, divide the way you would usually do. If there is a remainder, keep adding 0's until you get the answer with no remainder. If the 0 keeps going on and on just stop after 2 0's.
