A square has a side of 6.25 feet. What is the area in square feet? Round to the correct significant digits.

Mathematics

1 answer:

Hunter-Best [27]2 years ago

7 0

The solution to this question is 39.0625.

This is because you will need to multiply the width by height. As this is in square feet it will be irrespective of which two sides we choose.

The calculation that will need to be done is the following :

6.25ft X 6.25ft which will equal 39.0625.

6.25 has three significant digits so rounding 39.0625 off to three significant digits is 39.1 square feet

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The given statement is which we have to prove by the principal of Mathematical Induction

$2^{n}>n$

1.→For, n=1

L H S =2

R H S=1

2>1

L H S> R H S

So,the Statement is true for , n=1.

2.⇒Let the statement is true for, n=k.

$2^{k}>k$

---------------------------------------(1)

3⇒Now, we will prove that the mathematical statement is true for, n=k+1.

$\rightarrow 2^{k+1}>k+1\\\\L H S=\rightarrow 2^{k+1}=2^{k}\times 2\\\\\text{Using 1}\\\\2^{k}>k\\\\\text{Multiplying both sides by 2}\\\\2^{k+1}>2k\\\\As, 2 k=k+k,\text{Which will be always greater than }k+1.\\\\\rightarrow 2 k>k+1\\\\\rightarrow2^{k+1}>k+1$