Answer: price of soda (a) = $2 and price of popcorn (b) = $0.5
Step-by-step explanation:
Let's denote soda = a and popcorn = b
Kaylin bought a soda and two popcorn, writing out an equation for this would be
a + 2b = $3...........equation (i)
And her brother bought 3 sodas and 1 popcorn.
3a + b = $6.50..........equation (ii)
From equation (i),
a + 2b = 3
Making a the subject of formula,
a = 3 - 2b......equation (iii)
Using substitution reaction, put equation (iii) into equation (ii)
3(3 - 2b) + b = $6.50
9 - 6b + b = 6.50
9 - 5b = 6.50
Collecting like terms,
5b = 9 - 6.50
Divide both sides by 5,
b = 5.
Put b = 5 into equation (i)
a + 2(0.5) = 3
a + 1 = 3
a = 2
Therefore, the price of soda is $2 per one and $0.5 for each popcorn.
Rotating the steering wheel left 300 degrees is the same as turning it right 60 degrees. Well, not if you're driving, but the same as far as where the points on the wheel end up.
In polar coordinates X is P(8, 90°), which is how I'll write magnitude 8, angle 90 degrees. In rectangular coordinates that's (8 cos 90°, 8 sin 90°) = (0,8) as we're told.
After rotation by 300° the angle of X is 90° + 300° = 390° so our coordinates are
P(8, 390°) = (8 cos 390°, 8 sin 390°) = (8 cos 30°, 8 sin 30°)
= (8 (√3/2), 8 (1/2)) = (4√3, 4)
Answer: (4√3, 4)
I'll leave the rounding to you; I hate ruining a nice exact answer with an approximation.
As we see we would have reached the same 30° point if we had rotated -60° instead of 300°.
