Answer:
(a)In the attachment
(b)The road of length 35.79 km should be built such that it joins the highway at 19.52km from the perpendicular point P.
Step-by-step explanation:
(a)In the attachment
(b)The distance that enables the driver to reach the city in the shortest time is denoted by the Straight Line RM (from the Ranch to Point M)
First, let us determine length of line RM.
Using Pythagoras theorem

The Speed limit on the Road is 60 km/h and 110 km/h on the highway.
Time Taken = Distance/Time
Time taken on the road 
Time taken on the highway 
Total time taken to travel, T 
Minimum time taken occurs when the derivative of T equals 0.

Square both sides

The road should be built such that it joins the highway at 19.52km from the point P.
In fact,

Answer:18
Step-by-step explanation: She gave 3 children 3 pieces each. 3*3=9. She also took 9 pieces for herself. 9+9=18
On Venus the person is 153 lbs and on Mars it is 102 lbs.The difference is 51 lbs
Answer:
Keith scored 70% on the History test.
Step-by-step explanation:
We have been given that for History test, Keith had to answer 40 questions. Of these 40 questions, Keith answered 28 of them correctly.
To find the percentage Keith got on History test, we will have to figure out 28 is what percent of 40.



Therefore, Keith scored 70% on the History test.