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3 years ago

Does this sum converge: show steps

Mathematics

1 answer:

ehidna [41]3 years ago

6 0

Answer:

Yes

Step-by-step explanation:

$\sum_{n=1}^{\infty} e^{-\sqrt{n} } \\\sum_{n=1}^{\infty} (\frac{1}{e})^{\sqrt{n} }$

If we say u = √n, then:

$\sum_{u=1}^{\infty} (\frac{1}{e})^{u}$

This is a geometric series. Since |1/e| < 1, the series converges.

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Find the area of the figure.

mel-nik [20]

Answer:

192+128+112+36=468 not really sure if this is the answer

4 0

3 years ago

Read 2 more answers

Help pls .!!!!!!!!!!!

Igoryamba

A and C are the answer

4 0

3 years ago

Read 2 more answers

#2 is the one I need help with

sleet_krkn [62]

Step-by-step explanation:

By arc sum Postulate of a circle:

2 x + 3x + 4x = 360°

9x = 360°

x = 360°/9

x = 40°

3x = 3* 40° = 120°

By inscribed angle theorem:

$m\angle 1= \frac {1}{2} \times 3x\\\\\therefore m\angle 1= \frac {1}{2} \times 120°\\\\\huge \red {\boxed {\therefore m\angle 1= 60°}}$

By tangent secant theorem:

$m\angle 2 = \frac {1}{2} \times 3x\\\\\therefore m\angle 2 = \frac {1}{2} \times 120°\\\\\huge \purple {\boxed {\therefore m\angle 2 = 60°}}$

Since, measure of central angle is equal to the measure of its corresponding minor arc.

$m\angle 3 = 3x\\\\\huge \pink {\boxed {\therefore m\angle 3 = 120°}}$

By angle sum Postulate of a triangle:

$m\angle 3 + 2 m\angle 4 = 180°\\\\120° + 2 m\angle 4 = 180° \\\\2 m\angle 4 = 180°- 120° \\\\2 m\angle 4 = 60° \\\\m\angle 4 = \frac {60°}{2} \\\\\huge \orange {\boxed {m\angle 4 =30°}}$

3 0

3 years ago

Find y.<br> Help me please thanks

valina [46]

Answer:

Step-by-step explanation:

Discussion

First draw FH

<FOH and <FGH share the end points of the chord FH

<FOH is a central angle.

<FGH touches the circumference of the circle in the on the same side of the point of angle <FOH is closest to

Therefore <FGH is 1/2 <FOH. That is always true of central angles and the smaller angle touching the circumference that <FOH points to

Conclusion

<FGH = 1/2 < FOH

58 = 1/2 <FOH

Therefore <FOH = 2 * 58 = 116

y = < FOH

Answer

y = 116

7 0

2 years ago

Just help me out with this polynomial i need help <br> { -m^{2} + 6} + { -4m^{2} + 7m + 2} =

PolarNik [594]

Answer:

$-5m^2+7m+8$

Step-by-step explanation:

Here, we add up two polynomials shown.

The polynomials are:

$[-m^2 + 6]+[-4m^2 +7m + 2]$

In order to add up the 2 polynomials shown, we have to see the "like terms" and add them up.

We add up the " $m^2$ " terms and the constant (number) terms. There is one term with "m", so we leave it like that. Let's add up. Shown below:\

$[-m^2 + 6]+[-4m^2 +7m + 2]\\=-m^2-4m^2+6+2+7m\\=-5m^2+7m+8$

This is the sum of the 2 polynomials shown: $-5m^2+7m+8$

7 0

3 years ago