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2 years ago

What is the image of A(8,2) under R90 ? A. (-2,8) B. (2,8) C.( 8,-2) D.(-8,2)

Mathematics

1 answer:

swat322 years ago

5 0

Answer: A. (-2,8)

Step-by-step explanation:

We know that the rule for rotation of $R_{90}$ is given by :-

$(x,y)\rightarrow(-y,x)$ , where (x,y) is the point of pre-image and (-y,x) is a point of image.

The given point of pre-image : A(8,2)

Then after rotation of $R_{90}$ , we have the image point as :-

$(8,2)\rightarrow(-2,8)$

Hence, the image point of A(8,2) is (-2,8) .

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Show that the Fibonacci numbers satisfy the recurrence relation fn = 5fn−4 + 3fn−5 for n = 5, 6, 7, . . . , together with the in

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Answer with step-by-step explanation:

We are given that the recurrence relation

$f_n=5f_{n-4}+3f_{n-5}$

for n=5,6,7,..

Initial condition

$f_0=0,f_1=1,f_2=1,f_3=2,f_4=3$

We have to show that Fibonacci numbers satisfies the recurrence relation.

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Apply this

$f_n=(f_{n-2}+f_{n-3})+f_{n-2}=2f_{n-2}+f_{n-3}$

$f_n=2(f_{n-3}+f_{n-4})+f_{n-3}=3f_{n-3}+2f_{n-4}$

$f_n=3(f_{n-4}+f_{n-5})+2f_{n-4}=5f_{n-4}+3f_{n-5}$

Substitute n=2

$f_2=f_1+f_0=1+0=1$

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Now, we have to show that $f_{5n}$ is divisible by 5 for n=1,2,3,..

Now replace n by 5n

$f_{5n}=5f_{5n-4}+3f_{5n-5}$

Apply induction

Substitute n=1

$f_5=5f_1+3f_0=5+0=5$

It is true for n=1

Suppose it is true for n=k

$f_{5k}=5f_{5k-4}+3f_{5k-5}$ is divisible 5

Let $f_{5k}=5q$

Now, we shall prove that for n=k+1 is true

$f_{5k+5}=5f_{5k+5-4}+3f_{5k+5-5}=5f_{5k+1}+3f_{5k}=5f_{5k+1}+3(5q)$

$f_{5k+5}=5(f_{5k+1}+3q)$

It is multiple of 5 .Therefore, it is divisible by 5.

It is true for n=k+1

Hence, the $f_{5n}$ is divisible by 5 for n=1,2,3,..

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2 years ago

Suppose that a system of linear equations has 3×5 augmented matrix whose 5th column is a pivot column. Is the system consistent?

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No, the system is inconsistent.

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2 years ago

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Answer:

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