Connect with a global community of knowledgeable individuals on IDNLearn.com. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.
Sagot :
Answer:
a)DL/dt is positive then L s increasing
b) L still increasing
Step-by-step explanation:
Let´s call O the place for the gas station, A the location point of police car ( at 5 miles east from the gas station ), and B the location point of the truck ( 12 miles south from a gas station.
The three points shape a right triangle with L (distance between police car and truck) then
L² = OA² + OB² at the point police car is 5 miles east and truck 12 miles south ( both from gas station)
L² = ( 5)² + (12)²
L = √ 25 + 144
L = √169
L = 13 miles
Pitagoras theorem establishes in a right triangle hypotenuse L is:
L² = a² + b² a and b are the legs then
In general
L² = x² + y ² x and y the legs over distance police-car/gas station and truck/gas station
Differentiation on both sides of the equation with respect to time give us:
2*L*DL/dt = 2*x*Dx/dt + 2*y*Dy/dt
Where Dx/dt = 130 m/h West Dy/dt = 100 m/h south
L = 13 m x = 5 m y = 12
Then by substitution
2*13*DL/dt = 2*5*130 + 2*12*100
DL/dt = (1300+ 2400) / 26
DL/dt = 142 m/h
DL/dt is positive then L s increasing
b) If truck speed is 70 m/h
DL/dt still positive but with smaller module, then L still increasing but at smaller speed
DL/dt = 1300 + 2*12*70
DL/dt = (1300 + 1680)/ 26
DL/dt = 114,6 m
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.