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Annette [7]
2 years ago
8

A steep mountain is inclined 75 degree to the horizontal and rises 3900 ft above the surrounding plain. A cable car is to be ins

talled by connecting a cable from the top of the mountain to a spot on the plain that is 910 ft from the base of the mountain. Find the shortest length of cable needed.
Mathematics
1 answer:
maria [59]2 years ago
7 0

Answer: 4004.76\ ft

Step-by-step explanation:

Given

inclination is \theta=75^{\circ}

Mountain is h=3900\ ft high

Cable is tied x=910\ ft from the base of the mountain

From the figure, length of the shortest path is l

It is given by using Pythagoras theorem

\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=\sqrt{(3900)^2+(910)^2}\\\Rightarrow l=4004.76\ ft

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andriy [413]
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Since parabola passes through the point (2,−15) then 
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Since parabola passes through the point (-5,-29), then
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Since parabola passes through the point (−3,−5), then 
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Thus, we obtained following system:
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Solving it we get that 
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Thus, equation of parabola is
y = −2x²− 4x + 1

____________________

Rewriting in the form of 
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i) -2x² - 4x + 1 = y

ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)

iii) -3x² - 7x - 49/36 = y - 1 - 49/36
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v) -3(x + 7/6)² = y - 445/36 

vi) (x + 7/6)² = -⅓(y - 445/36) 
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So, after rewriting the equation would be - 

(x + 7/6)² = 4(-⅛)(y - 445/36)

__________________

I hope this is what you wanted.

Regards,
Divyanka♪
__________________
6 0
3 years ago
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Step-by-step explanation:

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