<span>1 PIE = 0.3048 METROS, Saludos!</span>
Answer:
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Step-by-step explanation:
Answer:
20 m
Step-by-step explanation:
Given:
- Length in mud = ¹/₂ its length
- Length in water = ¹/₃ its length
- Length above water = 3 ¹/₃ m
Let x be the length of the lamp post.
Convert 3 ¹/₃ to an improper fraction:
![\sf \implies 3 \frac{1}{3}=\dfrac{3 \times 3+1}{3}=\dfrac{10}{3}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%203%20%5Cfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B3%20%5Ctimes%203%2B1%7D%7B3%7D%3D%5Cdfrac%7B10%7D%7B3%7D)
The total length of the lamp post (x) is the sum of the three given lengths:
![\implies \sf mud+water+above\: water=x](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20mud%2Bwater%2Babove%5C%3A%20water%3Dx)
![\sf \implies \dfrac{x}{2}+\dfrac{x}{3}+\dfrac{10}{3}=x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7Bx%7D%7B2%7D%2B%5Cdfrac%7Bx%7D%7B3%7D%2B%5Cdfrac%7B10%7D%7B3%7D%3Dx)
Multiply both sides by 6:
![\sf \implies \dfrac{6x}{2}+\dfrac{6x}{3}+\dfrac{6 \cdot 10}{3}=6x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B6x%7D%7B2%7D%2B%5Cdfrac%7B6x%7D%7B3%7D%2B%5Cdfrac%7B6%20%5Ccdot%2010%7D%7B3%7D%3D6x)
![\sf \implies 3x+2x+20=6x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%203x%2B2x%2B20%3D6x)
![\sf \implies 5x+20=6x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%205x%2B20%3D6x)
Isolate x:
![\sf \implies 20=6x-5x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%2020%3D6x-5x)
![\implies \sf x=20](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20x%3D20)
Therefore, the whole length of the post is 20 m.
Equation of a line passing through point (x1, y1) with slope m is given by y - y1 = m(x - x1)
For perpendicular lines, the slope of the required line is given by -1 divided by the slope of the given line.
5x + 3y = 0
3y = -5x
y = -5/3x
slope of the given line is -5/3.
Thus, the slope of the required line = -1/(-5/3) = 3/5
y - 3/4 = 3/5(x - 7/8)
5(y - 3/4) = 3(x - 7/8)
5y - 15/4 = 3x - 21/8
40y - 30 = 24x - 21
24x - 40y = -30 + 21 = -9
24x - 40y = 9.