Students are voting on the color of T-shirts to wear on their field trip. There are 160 students-65 boys and 95 girls-going on
2 answers:
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The Lagrangian for this function and the given constraints is
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
and 
, and at the same time we find only one critical point at 
.
Check the Hessian for
, given by
is positive definite, since 
for any vector 
, which means 
attains a minimum value of 
at 
. There is no maximum over the given constraints.
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
Check the Hessian for
Answer:
The average speed of the car, in miles per hour, from 17:30 to 19:42, is 119.167 meters per second.
Step-by-step explanation:
Physically speaking, average speed (), measured in miles per hour, is the distance travelled (
), measured in miles, divided by time (
), measured in hours. That is:
(1)
The time needed by the vehicle is:
If we know that and
, then the average velocity of the car is:
The average speed of the car, in miles per hour, from 17:30 to 19:42, is 119.167 meters per second.