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Answer:
If all the dimensions of the rectangular pyramid are multiplied by 1/5, the volume will be 125 times smaller.
Step-by-step explanation:
A rectangular pyramid has the following dimensions:
length(l), height(h) and width(w)
The volume is:
If all the dimensions of the rectangular pyramid are multiplied by 1/5
Then we have that:
The modified volume will be:
So
If all the dimensions of the rectangular pyramid are multiplied by 1/5, the volume will be 1/125 of the original, that is, 125 times smaller.
Answer:
Graph B
No
Inside
Step-by-step explanation:
Let, the number of apples = x and number of peaches = y.
It is given that the farmer can afford maximum of 54 acres.
Thus, x + y ≤ 54.
Also, apples require 3000 gallons of water and peaches require 800 gallons of water each day.
Since, maximum amount of water is 80,000 gallons per day,
We get, 3000x + 800y ≤ 80,000.
It is required to maximize the profit given by z = 3400x + 1600y.
Thus, the system of equations becomes,
z = 3400x + 1600y
3000x + 800y ≤ 80,000.
x + y ≤ 54.
Plotting these equations gives the following graph.
We can see that the graph obtained is equivalent to Graph B.
Further, we know that the maximum value of the objective function z = 3400x + 800y is obtained at the boundary point of the solution region.
Thus, any point inside the solution region will give a feasible solution not maximum solution.
Hence, ( 30,20 ) will not maximize the profit as it lies inside the solution region.
