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ZanzabumX [31]
3 years ago
14

Use induction to prove that 2? ?? for any integer n>0 . Indicate type of induction used.

Mathematics
1 answer:
Hoochie [10]3 years ago
3 0

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

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

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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if there are 90 calories in 3/4 cuo of yogurt how man calories are in 3 cups of yogurt 30 calories 202 calories 270 calories 360
Debora [2.8K]
Hello!

To find how many calories in three cups we can use the proportion below.

\frac{calories}{cups} = \frac{90}{3/4} = \frac{c}{3}

To find our answer we can say, "How many times does 3/4 go into 3," and then multiply that number by 90 as shown below.

3÷3/4=4
90(4)=360

Just to verify, we will cross multiply and check our answer 

90(3)÷3/4
270÷3/4=360

Therefore, our answer is D) 360 calories.

I hope this helps!

6 0
3 years ago
Read 2 more answers
Need math help please!!
s2008m [1.1K]
Just by looking at it, 2 seems to be the correct answer. I mean if you think about it, when the triangle is split in two smaller triangles, side LN is longer than LP so that means x needs to be a small number. I could either be 2 or 1. Well if you look at the big picture, side LM is longer than LN so it’s gonna need to be bigger. If you say x=1 then you are saying 2(1) +4 = 6 (therefore LM is 6) but if you say x=2 then you are saying 2(2) +4 = 8 which makes more sense


If x=2 then you can use the Pythagorean’s theorem

a2 + b2 = c2
4^2 + b^2 = 5^2
16 + b^2 = 25
25-16= 9
b^2= 9
b= 3


Now that we know what NP is we can do Pythagorean’s theorem to figure out what side LP is (we already know it but you can do it again to check lol)

So the answer is 2
5 0
3 years ago
An ice cream shop has a sign in their window that says, "We sell 12,000 scoops per month." The number of scoops has been rounded
dsp73

Answer:

B - 12,111

C - 11,589

Step-by-step explanation:

Here are the options

A - 10, 999

B - 12,111

C - 11,589

In order to round off to the nearest thousand, look at the hundred figure, if the number is greater or equal to 5, add 1 to the thousand figure. If this is not the case, add zero. Replace all the figures before the thousand figure with zero. i.e. the hundred ten, unit

Rounding off 10,999 to the nearest thousand is 11,000

the hundred figure is greater than 5, so one is added to the thousand figure. The

Rounding off 12,111 to the nearest thousand is 12,000

the hundred figure is less than 5, so zero is added to the thousand figure.

Rounding off 11,589 to the nearest thousand is 12,000

the hundred figure is equal to 5, so one is added to the thousand figure.

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2 years ago
Which products are greater than 256? Choose all that apply.
Novay_Z [31]
257 is the answer to this question
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Answer:

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Step-by-step explanation:

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Symptoms may include

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Swelling of the knee

Please go to your doctor...ik it hard with cov id and everything

7 0
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