Answer:
31/6
Step-by-step explanation:
I got it right on my quiz
Answer:
1/3
Step-by-step explanation:
for every 1 part of water there is 3 parts juice so if there's only 1 part juice it would be a 1/3
Answer:
5.25 gallson
Step-by-step explanation:
Answer:
$1.21
Step-by-step explanation:
Start by finding the total amount spent on shirts. Do this by multiplying $3.65 and 4 together. You will get 14.6. So, he spent $14.60 on 4 shirts. Take this amount and subtract it from the total amount paid for shirts and socks. $23.07 minus $14.60. This will give you $8.47 left to spent on socks. $8.47 divided by 7 is $1.21. Therfore, James paid $1.21 per pair of socks.
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)