Answer:
The maximum volume of the box is:
Step-by-step explanation:
Given
Required
The maximum volume of the box
Let
The surface area of the box is:
So, we have:
Divide both sides by 2
Make b the subject
The volume of the box is:
Substitute:
Spit
Differentiate V with respect to a
Set to calculate a
Collect like terms
Multiply both sides by 2
Solve for a
Recall that:
Apply law of indices
So:
The four-fifths of a number, in this case, z is four times the number divided by z. That is 4z/5. When we add six to the product and equate the expression to 8, we get,
4z/5 = 8
The value of z from the equation is 10.
Answer:
117
Step-by-step explanation:
The average of all 7 people is the total weight of the original 6 people, plus the weight of the 7th person, all divided by 7.
For problems like this involving an average of numbers that are "close" together, here is a different strategy for solving the problem that you might like to try.
The original 6 people have an average weight of 173, which is 8 pounds more than the average of all 7 people. So all together, the weight of those 6 people is 6*8=48 pounds over the 165 average. That means the 7th person's weight must be 48 pounds below the 165 average.
So the weight of the 7th person is 165-48 = 117 pounds.
Answer:
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