Solve for x. x = ln 1 x =

Use mathematical induction to prove that for each integer n > 4,5" > 2^2n+1 + 100.

Flura [38]

Answer:

The inequality that you have is $5^{n}>2^{2n+1}+100,\,n>4$ . You can use mathematical induction as follows:

Step-by-step explanation:

For $n=5$ we have:

$5^{5}=3125$

$2^{(2(5)+1)}+100=2148$

Hence, we have that $5^{5}>2^{(2(5)+1)}+100.$

Now suppose that the inequality holds for $n=k$ and let's proof that the same holds for $n=k+1$ . In fact,

$5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.$

Where the last inequality holds by the induction hypothesis.Then,

$5^{k+1}>(2^{2k+1}+100)\cdot (4+1)$

$5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100$

$5^{k+1}>2^{2k+3}+100\cdot 4$

$5^{k+1}>2^{2(k+1)+1}+100$

Then, the inequality is True whenever $n>4$ .

3 0

3 years ago

My brother is wondering what 100÷1,000,000 equals.

alexandr402 [8]

Answer:

0.0001

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A circle with radius 3 has a sector with a central angle of 1/9 pi radians

Art [367]

The area of sector is 1.57 m²

Explanation:

Given:

Radius, r = 3 m

Central angle of a sector = 1/9π radians

Area of sector, A = ?

We know:

Area of sector, A = $\frac{1}{2} r^2 \alpha$

where,

α is the central angle in radians

On substituting the value we get:

$A = \frac{1}{2} X(3)^2 X \frac{1}{9}X 3.14\\ \\A = 1.57 m^2$

Therefore, the area of sector is 1.57 m²

5 0

3 years ago

What affect does h = -2 have on the parent function y=1/x Graph moves 2 units up Vertical stretch by a factor of |-2| Graph move

Marat540 [252]

Y = 1/(x - -2)
y = 1/(x + 2)
I moves the graph 2 units to the left

3 0

3 years ago

In the figure below the y-axis points north, the x-axis points east, and the xy-plane corresponds to the surface of the water. S

Sergeeva-Olga [200]

So the question ask to find the displacement vector and the distance from the submarine to the boat. Base on my calculation the displacement value of the given data you give is <(5-3),(1-4)(-5-0)>. I hope you are satisfied with my answer and feel free to ask for more

4 0

3 years ago