The Lagrangian is
with partial derivatives (all set equal to 0)
for 
, and
Substituting each 
into the second sum gives
Then we get two critical points,
or
At these points we get a value of 
, i.e. a maximum value of 
and a minimum value of 
.
Answer:
D. 108.25 sq in
Step-by-step explanation:
Area of triangle = bh/2
Area of bottom triangle = 4.3(5)/2 = 10.75
Area of a lateral triangle = 13(5)/2 = 32.5
Area of 3 lateral triangles = 3(32.5) = 97.5
Total surface area = 10.75 + 97.5 = 108.25
Given a data set consisting of 33 unique whole number observations, its five-number summary is: [19,32,47,61,77] how many observations are strictly less than 32?
Solution: The five number summary denotes:
Minimum = 19
First Quartile = 32
Median = 47
Third Quartile = 61
Maximum = 77
Since there are an odd number of observations (33) in the data set, the First Quartile (32) must be at the (33+1)/4 = 8.5th position, meaning there are 7 numbers less than 32.
Therefore, there are 7 observations that are strictly less than 32
180-(180-49-48)
180-(83)
97
180-((180-141)+(180-76))
180-(39+104)
180-143
137
180-((180-101)+60)
180-(79+60)
180-139
41
360-147-79
213-79
139
180-(360-109*2)
180-(360-218)
180-142
38
(180-118)/2
62/2
31
Hope this helps :)
