Afireplace arch is to be constructed in the form of a semiellipse. the opening is to have a height of 3 feet at the center and a width of 8 feet along the base. the contractor cuts a string of a certain length and nails each end of the string along the base in order to sketch the outline of the semiellipse. a.) what is the total length of the string? b.) how far from the center should the string be nailed into the base?

The distance between two points is the number of units between them.

The given parameters are:

(a) The total string length

The total string length is the length along the base.

Hence, the total string length is 8ft

(b) How far from the center should the string be nailed

The position of the string should be at the focus (f).

This is calculated as:

Where:

---- 1/2 the length of the string

---- eccentricity

Where

So, we have:

So, we have:

The focus is then calculated as:

Hence, the string should be positioned at a distance of from the center.

Read more about semiellipse at:

link

Step-by-step explanation:

Given

Fireplace is in the form of semi-ellipse  with height of 3 ft from center

Length of base=8 ft

if the arch is in the form of ellipse then it can be considered as horizontal ellipse with 2 a and 2 b be length of major and minor axis

2 a =8

a=4 ft

If contractor cover the whole base

then total length of string=2a =8 ft

(b)String should be nailed at focus

focus of ellipse is a e

where e=eccentricity

Focus

Thus string should be nailed at 2.64 m from center

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

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1

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$

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in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

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so technically the answer is  

→

$

72.6

(

1

+

20

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$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

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=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

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related questions

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: