Ok so parentheses first, 143*5 which is 715. Then you take 715+67 which is 782.Finally you take 782^5 which makes the answer 292437973214432.
Solve for cos(t) and sin(t):
x = 2 + 3 cos(t) ⇒ cos(t) = (x - 2)/3
y = 1 - sin(t) ⇒ sin(t) = 1 - y
Recall the Pythagorean identity,
sin²(t) + cos²(t) = 1
It follows that
((x - 2)/3)² + (1 - y)² = 1
or
(x - 2)²/9 + (y - 1)² = 1
12 hours..........
+ - = 1
Multiply by 12 to clear the fractions
3t + 2t - 4t = 12
t = 12 hrs to fill the pool
Answer:
y = 2sin(x/2 - pi/4) + 1
Step-by-step explanation:
The normal sine has a range of [-1, 1]. This one has a range of [-1, 3], so the amplitude is 2 times higher (4 vs 2).
After that, 2sin(x) has a range of [-2, 2], but this one has a range of [-1, 3], so we need to shift it upwards by 1.
We now know that the answer is 2sin(____)+1.
A normal sine has it's middle point while rising at x = 0, but this one has it at x = pi/2 - so we need to shift a sine to the right by pi/2.
Lastly, a sine has a cycle of length 2pi, but this one has a cycle of length 4pi. We can achieve that by dividing the argument 2.
We now know that the answer is 2sin(x/2 - pi/4) + 1. We can plot it to verify.
You would do (12 ÷ 8)6 or 12 ÷8 ×6