Sue the T-Rex grows cabbage in a square shaped garden. Each cabbage takes #1 ft^2# of area in the garden. This year, she increased her output by 211 cabbages compared to last year, If the shape remains a square how many cabbages did she grow this year?

Answer 1

Sue the T-Rex grew #11236# cabbages this year.

Squares of numbers follow the series #{1,4,9,16,25,36,49,......}#

and difference between consecutive squares is the series

#{1,3,5,7,9,11,13,15,.......}# i.e. each term #(2n+1)# times the previous one.
Hence if output has increased by #211=2*105+1#, it should be #105^2# last year i.e. #11025# last year and #11236# this year, which is #106^2#.
Hence, she grew #11236# cabbages this year.
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Answer 2

To find the number of cabbages Sue grew this year, we need to determine the area of her garden and then calculate how many cabbages can fit in that area. Since the garden is square-shaped, we can find the area by squaring the length of one side of the square.

Let's denote the number of cabbages Sue grew last year as ( x ). Since each cabbage takes up 1 ft(^2) of area, the area of the garden last year would have been ( x ) ft(^2).

This year, Sue increased her output by 211 cabbages, so the total number of cabbages grown this year is ( x + 211 ).

To find the area of the garden this year, we can set it equal to the number of cabbages grown this year, since each cabbage takes up 1 ft(^2) of area.

Therefore, ( x + 211 = \text{area of the garden this year} ).

Since the garden is square-shaped, the area is equal to the length of one side squared. So, if we take the square root of the area, we'll get the length of one side of the square garden.

After finding the length of one side of the square garden, we can square it to find the area. This will give us the total number of cabbages Sue grew this year.

So, the total number of cabbages Sue grew this year is ( (\sqrt{x + 211})^2 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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