c2*sin(wt)+c1*cos(wt)= A*Sin(wt+phi), where c2=Acos(Phi) and c1=Asin(Phi). They ask me to find the amplitude of the function 2 sin(4pi*t)+5 cos(4pi*t), in terms of A sin(wt+phi). How do i do this?

The amplitude of is the absolute value of . So first you need to condense the given function into one sine expression.

Recall that

so you need to choose and accordingly.

If we line up the terms of the given function with the expanded one above, we should have

Now, using the Pythagorean identity,

so the amplitude is √29.

Just for completeness, we also get

where is any integer.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.