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2 years ago

X∞n=0 (2 n + 1) x 2 n

Mathematics

1 answer:

Black_prince [1.1K]2 years ago

6 0

Answer:3

If x=0 or x=1 it is trivial, so 0<x<1. Define a=1−x2, then 0<a<1.

Step-by-step explanation:

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3 years ago

Please find the answer

Serggg [28]

Answer:

x^3 + 1/x^3 = 488

Step-by-step explanation:

x^2 + 1/x^2 = 62
x^2 + 1/x^2 + 2 = 64
( adding 2 in both sides )
(x + 1/x ) ^2 = 64
x + 1/x = 8

now,

( x+ 1/x ) ^ 3 = 512
x^3 + 1/x^3 + 3 × x × 1/x ( x + 1/x )
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2 years ago

A hot air balloon is flying at an altitude of 800 feet. A passenger takes a picture of the top of a tree and estimates that the

nalin [4]

The height of the tree given the depression angle to the top and the base

is given by the tangent relationship of the two given angles.

Correct response:

The height of the tree is approximately <u>79.58 feet</u>

<h3 /><h3>Methods used for the calculation of the height of the tree</h3>

Given:

Altitude of the hot air balloon = 800 feet

Angle of depression to top of tree = 43°

Angle of depression to base of tree = 46°

Required:

Height of tree

Solution:

The horizontal distance of the balloon from the tree is given as follows;

$\displaystyle tan(46^{\circ}) = \frac{Altitude \ of \ balloon}{Horizontal \ distance \ from \ tree} = \mathbf{\frac{800 \, feet}{Horizontal \ distance \ from \ tree}}$

Therefore;

$\displaystyle Horizontal \ distance \ of \ balloon \ from \ tree = \frac{800 \ feet}{tan(46^{\circ})}$

$\displaystyle tan(43^{\circ}) = \mathbf{\frac{Height \ of \ balloon \ above \ tree}{\dfrac{800 \, feet}{tan(46^{\circ})} }}$

Therefore;

$\displaystyle Height \ of \ balloon \ above \ tree = tan(43^{\circ}) \times \frac{800 \, feet}{tan(46^{\circ})}$

Height of tree = Altitude of balloon - Height of balloon above tree

Therefore;

$\displaystyle Height \ of \ tree = 800 \, feet - tan(43^{\circ}) \times \frac{800 \, feet}{tan(46^{\circ})} \approx \underline{ 79.58 \, feet}$

Learn more about angle of elevation and depression here:

brainly.com/question/1978238

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2 years ago