Since we don't have a figure we'll assume one of them is right and we're just being asked to check if they're the same number. I like writing polar coordinates with a P in front to remind me.
It's surely false if that's really a 3π/7; I'll guess that's a typo that's really 3π/4.
P(6√2, 7π/4) = ( 6√2 cos 7π/4, 6√2 sin 7π/4 )
P(-6√2, 3π/4) = ( -6√2 cos 3π/4, -6√2 sin 3π/4 )
That's true since when we add pi to an angle it negates both the sine and the cosine,
cos(7π/4) = cos(π + 3π/4) = -cos(3π/4)
sin(7π/4) = sin(π + 3π/4) = -sin(3π/4)
Answer: TRUE
A (-5, 6)
B (-5, 2)
C (-9, 2)
D (-9, 6)
As it is just a rotation around the origin by 180, you can just change the sign in front of the numbers :)
If you can find an explicit formula for a sequence, you will be able to quickly and easily find any term in the sequence simply by replacing n with the number of the term you seek. An explicit formula designates the nth term of the sequence, as an expression of n (where n = the term's location).
100 divided by 10 is ten, so they would give you ten bottles!
A. $40, because you would do 1,000 × 1.04 = $1,040, and then subtract the original $1,000.
b. $81.60, because 1,000 × 1.04² = 1,081.6
c. $480.24, because 1,000 × 1.04^10 = 1,480.24.
I have used the formula for compound interest presuming you were aware of it, but I will be happy to explain what I did if you want :).
I hope this helps!
