All categories

3 years ago

Linear, exponential or neither f(1) = 13, f(n)=6f(n-1)

Mathematics

1 answer:

NikAS [45]3 years ago

8 0

↓The correct answer is here↓

brainly.com/question/7666093

You might be interested in

Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u> $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

6 0

3 years ago

How do you get the perimeter of a triangle, all side are 28 cm?

Alisiya [41]

Perimeter of the triangle, a+b+c

In this case, a=b=c=28

So, perimeter would be 28*3 = 84 cm

7 0

3 years ago

Mrs.Ramirez bought 2 qt of orange juice. If the juice is served in 6-oz glasses,how many glasses can be completely filled?

alekssr [168]

Hey there!

<span>There is 32 oz per qt. 2qts=64oz. Divide 64 by 6. </span><span> 6 goes evenly into 64 10 times with a remainder. So the answer is 10 glasses.
</span>
Hope this helps!

4 0

3 years ago

−20=−4x−6x Find the value of x

xeze [42]

Answer:

$\huge\boxed{x=2}$

Step-by-step explanation:

$-20=-4x-6x\qquad|\text{combine like terms}\\\\-20=-10x\qquad|\text{divide both sides by (-10)}\\\\\dfrac{-20}{-10}=\dfrac{-10x}{-10}\\\\2=x\to x=2$

4 0

3 years ago

If there are 400 cubic centimeters of a chemical in 1 liter of solution, how many cubic centimeters of water must be added to di

mars1129 [50]

$1l=1dm^3\\1dm=10cm\to1dm^3=(10cm)^3=1000cm^3\\\\1l=1000cm^3\\-------------\\ \begin{array}{ccc}400cm^3&-&25\%\\1000cm^3+x&-&100\%\end{array}\\cross\ multiply\\25(1000+x)=400\times100\\25000+25x=40000\ \ \ \ \ |subtract\ 25000\ from\ both\ sides\\25x=15000\ \ \ \ |divide\ both\ sides\ by\ 25\\\boxed{x=600\ (cm^3)}\\\\Answer:Must\ be\ added\ 600cm^3\ of\ water.$

5 0

3 years ago