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3 years ago

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Consider the sequence Two-fourths, three-fifths, four-sixths, StartFraction 5 Over 7 EndFraction, ellipsis Which statement descr

ibes the sequence? The sequence diverges. The sequence converges to 0. The sequence converges to 1. The sequence converges to [infinity].

1 answer:

Phoenix [80]3 years ago

6 0

Answer:

The sequence converges to 1

Step-by-step explanation:

Given

$\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},...$

Require

Description of the sequence

The given sequence follows:

$\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},... \frac{n+1}{n+3}$

i.e.

$T_n = \frac{n+1}{n+3}$

For every term,

$\frac{n+1}{n+3} < 1$

In other words,

as the value of n increases, $\frac{n+1}{n+3}$ approaches 1

<em>Hence, (c) is true</em>

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Please put the explanation!

BaLLatris [955]

Answer:

60

Step-by-step explanation:

In order to get this answer, we must know that a triangle's angles add up to exactly 180. Also, Angles that intersect will have congruent, opposite sides. The last thing is that a line is = 180 degrees. So, the triangle with the 94 and the 142, you can use that. the angle next to the 142 is going to be 180-142 which is 38 and since the other angle is opposite 94, as well. when you add those up u get 132 and 180-132= 48 which is the missing angle for the far right triangle. then, you get the opposite of that angle, put that in the other triangle, do the same with the 72, and add those up to get 120 and since a triagle adds up to 180, 180-120 = 60. So, 60 is your missing angle. Cheers

5 0

2 years ago

A boat sails 20 miles wast of the port and then 15 miles south to an island how far is the boat from the port if you measure thr

sweet-ann [11.9K]

Answer:

25 miles

Step-by-step explanation:

Given: A boat sail 20 miles west of the port and then 15 miles south to an island.

Picture attached.

The distance from port to island could be measured in a straight line. It will form a hypotenous.

∴ we can use Pythogorean theorem to find the distance.

$h^{2} = a^{2} +b^{2}$

Where, "a" is adjacent= 20 miles and "b" is opposite= 15 miles.

$h^{2} = 20^{2} +15^{2}$

⇒ $h^{2} = 400+225= 625$

⇒ $h^{2} = 625$

⇒ $h= \sqrt{625}= \sqrt{25^{2} }$

We know $\sqrt{x^{2} } = x$ .

∴ $h= 25\ miles$

∴ Distance of Port from the Island is 25 miles.

6 0

3 years ago

Please help me A.S.A.P.

Vikentia [17]

Answer:

700 Dollars

Step-by-step explanation:

The expression for solving this is I = prt

So lets start with P, that is our principal or amount of money we start with, and we want to multiply it by our rate, or r , which is 3.5, so we would do 5000 x 0.035 to get 175, then we multiply that by our time or t, which is 4 years, so 175 x 4 = 700 dollars :D

5 0

2 years ago

Read 2 more answers

Lana71 [14]

Step-by-step explanation:

<h3>Appropriate Question :-</h3>

Find the limit

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

On substituting directly x = 1, we get,

$\rm \: = \: \sf \dfrac{1-2}{1 - 1}-\dfrac{1}{1 - 3 + 2}$

$\rm \: = \sf \: \: - \infty \: - \: \infty$

which is indeterminant form.

Consider again,

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

can be rewritten as

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 3x + 2)}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 2x - x + 2)}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( x(x - 2) - 1(x - 2))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ {(x - 2)}^{2} - 1}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 2 - 1)(x - 2 + 1)}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)(x - 1)}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)}{x(x - 2)}\right]$

$\rm \: = \: \sf \: \dfrac{1 - 3}{1 \times (1 - 2)}$

$\rm \: = \: \sf \: \dfrac{ - 2}{ - 1}$

$\rm \: = \: \sf \boxed{2}$

Hence,

$\rm\implies \:\boxed{ \rm{ \:\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right] = 2 \: }}$

$\rule{190pt}{2pt}$

7 0

2 years ago

Read 2 more answers

Is there some people who dont wear there retainer and still have straight teeth? cause mine still is

RideAnS [48]

Answer:

I Think Yes!

Step-by-step explanation:

Cause I Also Have A Straight Teeth and Also I Don't Wear Retainer!!

5 0

2 years ago