Questions in pre-calculus , HELP me Plz !?

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1- A salesman traveled a total distance of 530 km. In the first part of the journey, he took a
bus traveling at 100 km/h and in the second part he took a taxi traveling at a speed of 120 km/h. If
the total time of the journey was 5 hours, how much distance did the salesman travel on the taxi?


2-Verify the identity:

sin(sin^-1x + cos^-1x) =1


3- Find the period and phase shift of the function h(x) = 2 tan[pi/4 (x+1)]

4- A radioactive substance has a half-life of 29 years. How long will it take for 80% of the given
sample to decay?
 
1st question,
you know that speed = distance /time, therefore d=st
530km must equal the distances in both cars added togeather. (t=time spent in taxi) therefore: 5hrs-t= time spent in bus
therefore, 530= 120t+ 100(5-t), expand 100(5-t) = 120t + 500 -100t (-500 to both sides: 530-500= 120t-100t +500 -500)
which simplifies to 30 = 20t
so t= 30/20 = 1.5 hours in the taxi. d=st so distance in the taxi = 120 * 1.5hrs =180km
just to check, distance in bus = 100* (5-1.5) = 350
350+180 =530
 
1st question,
you know that speed = distance /time, therefore d=st
530km must equal the distances in both cars added togeather. (t=time spent in taxi) therefore: 5hrs-t= time spent in bus
therefore, 530= 120t+ 100(5-t), expand 100(5-t) = 120t + 500 -100t (-500 to both sides: 530-500= 120t-100t +500 -500)
which simplifies to 30 = 20t
so t= 30/20 = 1.5 hours in the taxi. d=st so distance in the taxi = 120 * 1.5hrs =180km
just to check, distance in bus = 100* (5-1.5) = 350
350+180 =530
 
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