If the length, breadth and height of the box is denoted by a, b and h respectively, then V=a×b×h =32, and so h=32/ab. Now we have to maximize the surface area (lateral and the bottom) A = (2ah+2bh)+ab =2h(a+b)+ab = [64(a+b)/ab]+ab =64[(1/b)+(1/a)]+ab.
We treat A as a function of the variables and b and equating its partial derivatives with respect to a and b to 0. This gives {-64/(a^2)}+b=0, which means b=64/a^2. Since A(a,b) is symmetric in a and b, partial differentiation with respect to b gives a=64/b^2, ==>a=64[(a^2)/64}^2 =(a^4)/64. From this we get a=0 or a^3=64, which has the only real solution a=4. From the above relations or by symmetry, we get b=0 or b=4. For a=0 or b=0, the value of V is 0 and so are inadmissible. For a=4=b, we get h=32/ab =32/16 = 2.
Therefore the box has length and breadth as 4 ft each and a height of 2 ft.
Question:
Evaluate the expressions 3x - 2 and 4x + 4 for the following values of x. When you have found the value for each expression, write a statement using <, >, or = that shows how the two values are related. a. x = 0 b. x = -6 c. x = 5 d. x = -2
Answer:
Part a: 
Part b: 
Part c:
Part d:
Explanation:
Part a: Substituting 
, we get,
The value of 
is less than 
Thus,
Part b: Substituting 
, we get,
The value of and are equal.
Thus,
Part c: Substituting 
, we get,
The value of is less than
Thus,
Part d: Substituting 
, we get,
The value of is less than
Thus,
Bundle (31 , 40) has 40 bananas.
So 40 - 28 = 12 bananas
These 12 banana give the consumer negative utility which will be balance one for one apple.
So we have to need 12 apple to balance it.
So the final utility of apples and banana is 28 + (31 - 12) = 28 + 19 = 43
In second bundle (X , 23) has 23 bananas. We need to get the same utility 43.
Which we will get from 43 - 23 = 20 apples.
So X equal to 23.
Hi,
to find out the answer you need to divide 89 by 10 than by 5. Add those two answers together which is 23.73. That answer is dimes so 89-23.73=65.27..:) you could round the number up. I hope it helps!!!
Answer: B) 24
Step-by-step explanation:
Find the cabbage percent by adding all of the percentages it gives you together and subtracting from 100.
the cabbage percent is 15%.
So 15% of the garden is cabbages, the garden is 160 sq ft.
Turn into the percentage into a decimal. 15% = .15
Multiply 160x.15
The answer is 24.
