Csc a - sin a = cos a cot a
1/sin a - sin a = cos a (cos a / sin a)
(1 - sin^2 a)/sin a = cos^2 a/sin a
cos^2 a/sin a = cos^2 a/sin a
Therefore, the given equation is an identity.
For No. 13 you need to calculate the distance each girl travels and compare to see whose distance is greater. The formula for distance is rate x time or d=rt. The rate is just how fast they consistently go.
Mia
d = r x t
d = 14 x 3/2
d = 21 miles
Chloe
d = r x t
d = 35 x 3/4 (btw 3/4 is just 45/60 simplified)
d = 105/4 = 26 1/4 miles
Final Answer: Chloe traveled further
For No. 14 we will recalculate Mia's distance but replace 1/5 hours with 2 hours because it says she will bike 30 minutes after Chloe had stopped. Afterwards we will compare Mia's new distance with Chloe's old distance.
Mia
d = r x t
d = 14 x 2
d = 28 miles
Final Answer: Yes Mia would be able to catch up to Chloe, and even surpass her in 30 minutes if Chloe stopped.
The answer is e, 3 3/4
if you add 3/4+3/4+3/4+3/4+3/4 (five times for the five batches), or did 3/4 * 5, you would get 15/4, which simplifies to 3.75, or 3 3/4
