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3 years ago

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Mathematics

1 answer:

viva [34]3 years ago

4 0

Answer:

Step-by-step explanation:

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Can somebody prove this mathmatical induction?

Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

$\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2$

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

3 step:

Check for n=k+1 whether the statement

$\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)$

is true.

Start with the left side:

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)$

According to the 2nd step,

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

Substitute it into the $\ast$

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)$

So, you have proved the initial statement

4 0

3 years ago

How many zeros in x^4 + 3x2 + 12

barxatty [35]

Answer:

We know that ,

Number of zeroes in a polynomial = degree of the polynomial

( degree of polynomial = the highest power in the polynomial )

therefore ,

$\bold\blue{number \:of \:zeroes \:of\: the \:given} \\\bold\blue{polynomial\: = \:4}$

hope helpful~

3 0

2 years ago

What is the image of the point (5, -3) after a reflection over the line y = x?

Musya8 [376]

Answer:

(-3,5)

Step-by-step explanation:

If the slope of y=x is 1, then you have to reflect over that line with a negative slope. It should reflect over to be (-3,5).

4 0

2 years ago

You are asked to draw a triangle with side lengths of 3 inches, 4 inches, and 1 inch. How many triangles like this can you draw?

marishachu [46]

I think you can draw two of them.

As you walk around the triangle in the clockwise direction,
you can run into the sides in the order of

   3 ==> 4 ==> 1

or in the order of

   3 ==> 1 ==> 4 .

Those are mirror images of each other. So they're not congruent,
and I think they're considered different triangles.

6 0

3 years ago

2a+b=15.7 what’s the possible values of b

Fiesta28 [93]

Answer:

b = 15.7 -2a

Step-by-step explanation:

You are asking us to solve for b

2a +b = 15.7

Subtract 2a from each side

2a-2a+b = 15.7 -2a

b = 15.7 -2a

4 0

3 years ago