The slope formula:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m - a slopeb - y-intercept
We have:
![m=-\dfrac{2}{3}](https://tex.z-dn.net/?f=m%3D-%5Cdfrac%7B2%7D%7B3%7D)
and point
![(0;-1)\to b=-1](https://tex.z-dn.net/?f=%280%3B-1%29%5Cto%20b%3D-1)
Substitute:
Answer: A.
The value of t is:
a) when v = 15 then t = 3 hours
b) when v = 18 then t = 2.52 hours
<h3><u>Solution:</u></h3>
The relation between speed and time taken is given as:
![\text {time taken}=\frac{\text {distance}}{\text {speed}}](https://tex.z-dn.net/?f=%5Ctext%20%7Btime%20taken%7D%3D%5Cfrac%7B%5Ctext%20%7Bdistance%7D%7D%7B%5Ctext%20%7Bspeed%7D%7D)
It is given that for first 30 km, the speed of bicyclist is v km/hour
<em><u>
Time taken to cover first 30 km is given by:</u></em>
![t_1 = \frac{v}{30}](https://tex.z-dn.net/?f=t_1%20%3D%20%5Cfrac%7Bv%7D%7B30%7D)
For next 17 km the speed of bicyclist is 2 km/hour greater than his original speed
so the speed to cover next 17 km = v + 2
<em><u>
Time taken to cover next 17 km is given by:</u></em>
![t_{2} =\frac{17}{v+2}](https://tex.z-dn.net/?f=t_%7B2%7D%20%3D%5Cfrac%7B17%7D%7Bv%2B2%7D)
Now total time t spent by the bicyclist to cover entire trip is given by
---- eqn 1
We have to find value of "t" for a) v = 15 and b) v = 18
<u><em>a) value of t when v = 15</em></u>
Substitute v = 15 in eqn 1
![t=\frac{30}{v}+\frac{17}{v+2}=\frac{30}{15}+\frac{17}{15+2}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B30%7D%7Bv%7D%2B%5Cfrac%7B17%7D%7Bv%2B2%7D%3D%5Cfrac%7B30%7D%7B15%7D%2B%5Cfrac%7B17%7D%7B15%2B2%7D)
t = 2 + 1 = 3
So t = 3 hours
<u><em>b) value of t when v = 18</em></u>
![\begin{array}{l}{t=\frac{30}{v}+\frac{17}{v+2}=\frac{30}{18}+\frac{17}{18+2}=1.67+0.85} \\\\ {t=2.52}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Bt%3D%5Cfrac%7B30%7D%7Bv%7D%2B%5Cfrac%7B17%7D%7Bv%2B2%7D%3D%5Cfrac%7B30%7D%7B18%7D%2B%5Cfrac%7B17%7D%7B18%2B2%7D%3D1.67%2B0.85%7D%20%5C%5C%5C%5C%20%7Bt%3D2.52%7D%5Cend%7Barray%7D)
Thus t = 2.52 hours
Answer:
just ignore this whole thing
1 1/6 probability.
2
1st. 3 2nd. 1/2 even =odd
4
5
6
1/6 x 1/2 =1/12
Answer: C) 3/4x
Step-by-step explanation: