A model of a skyscraper is made so that 1 inch represents 75 feet. Whar is the height of the actual building if the height of th
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Answer:
Step-by-step explanation:
Given
Required
The dimension that minimizes the cost
The volume is:
This gives:
Substitute
Make H the subject
The surface area is:
Area = Area of Bottom + Area of Sides
So, we have:
The cost is:
Substitute: and
To minimize the cost, we differentiate
Then set to 0
Rewrite as:
Divide both sides by W
Rewrite as:
Solve for
Take cube roots
Recall that:
Hence, the dimension that minimizes the cost is:
It's easy once you spot the ones that can cross cancel!
Say we have the fractions 8/10 and 20/23. (it's easier to see on top of each other)
If you look diagonally , so 8 and 23 and 10 and 20, you can see that 10 and 20 have a common factor. So we divide it by the highest common factor to reduce those numbers, making it easier to multiply. 10 and 20 can become 1 and 2, dividing by 10. So now we are left with 8/1 and 2/23, and now we multiply normally going across so 16/23.
This works going both diagonals and simplifying both, but in that case it would be easier to try and simplify the fractions before cross multiplying them.
Basically: look for those diagonals and if they can be divided down by the highest common factor, go for it to make it easier to multiply normally afterwards.
Hope I helped!