Step-by-step explanation:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ)
Multiply by the reciprocal:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)
(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]
(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]
Distribute and simplify:
(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)
[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)
(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)
Use Pythagorean identity:
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)
(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)
Factor:
(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))
(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))
(1 + sin θ) / cos θ
The miles per hour is 84 kilometers per 60 minutes (7:5 ratio) so if we take seven kilometers times the ratio 5/7 we get 5 minutes
You may find it easiest if you convert all the fractions to decimal form:
5.433...
5.166...
5.756
Now reorder these from smallest to largest.
Note: I had to guess that by "68,90," you actually meant "68/90."
Answer:
B. 14 ⁴⁄₁₀
Step-by-step explanation:
I say its b because all u have to do it multiply 6 ⅕ but not the 6, just the 1 and the 5, just multiply by two and both fractions will have the same total amount which is 10 and 6 ⅕ will turn to 6 with 2/10 so all u have to do now is add that fraction to 8 ²⁄₁₀
