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kondaur [170]
3 years ago
9

Find the rate of change of the following table.

Mathematics
1 answer:
Serjik [45]3 years ago
7 0

Answer:

\frac{1}{3}

Step-by-step explanation:

The rate of change is measured by the slope of the line in this linear table.

Calculate the slope m using the slope formula

m = \frac{y_{3}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (3, 2) ← 2 ordered pairs from the table

m = \frac{2-0}{3+3} = \frac{2}{6} = \frac{1}{3} ← rate of change

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Hoochie [10]

Answer with explanation:

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

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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

Hence it is true for, n=k+1.

So,we have proved the statement with the help of mathematical Induction, which is

      2^{k}>k

                 

   

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3 years ago
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Step-by-step explanation:

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fgiga [73]

Answer:

<h3>-4≤y≤7</h3>

Step-by-step explanation:

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Combining both solutions

-4≤y≤7

<em>Hence the range of values of y that satisfies both inequalities is -4≤y≤7</em>

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