Moved Lighthouses
moved lighthouses
SOS Any math genius come in PLZ~ about calculus?
I think we have to use the "related rule" which involves derivatives to do this question.Like to find out dthita/dt.
A lighthouse is located on a small island 2 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
yay! only just now did i understand the question.
let x be the distance from P along the shoreline.
and r the length of beam to shoreline (from lighthouse)
r^2 = 2^2 + x^2 = x^2 + 4
2r * (dr/dt) = 2x * (dx/dt)
r^2 = 1 + 4 = 5
r = sqrt(5)
2/r = cos y, 2 = rcos y
0 = (dr/dr) * cos y - sin y * (dy/dt) * r
dr/dt
= r(dy/dt)tan y
= sqrt(5) * (8pi) * (1/2)
= 4sqrt(5) pi
2r * (dr/dt) = 2x * (dx/dt)
dx/dt
= sqrt(5) * 4sqrt(5) pi / 1
= 20 pi km / minute
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Lighthouses of the Great Lakes Sale Price: $1.99  |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $5.99 |
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15. Historic American Buildings Survey H. C. White, Photographer Dec. 6, 1934 SECOND FLOOR, STAIRS TO TOWER ROOM - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $8.99 |
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1. Historic American Buildings Survey (copy) Early Eighties EAST FRONT OF LIGHTHOUSE - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $16.99 |
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5. Historic American Buildings Survey (copy) Taken 3rd Decade of Present Century NORTH END AND EAST FRONT OF LIGHTHOUSE - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $8.99 |
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16. Historic American Buildings Survey H. C. White, Photographer Dec. 6, 1934 HATCHWAY FROM TOWER ROOM TO LANTERN - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $8.99 |
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14. Historic American Buildings Survey H. C. White, Photographer Dec. 6, 1934 SECOND FLOOR, STAIRS TO FIRST FLOOR - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $8.99 |
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3. Historic American Buildings Survey C. E. Peterson, Photographer c. 1934 GENERAL VIEW - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $16.99 |
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6. Historic American Buildings Survey H. C. White, Photographer Dec. 6, 1934 APPROACH TO POINT LOMA LIGHT, LOOKING SOUTH. - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $8.99 |
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9. Historic American Buildings Survey H. G. Fowler, Photographer Sept. 12, 1934 REAR ELEVATION, WEST - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
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Historic Photo Point Loma Lighthouse No. 355 (moved), San Diego, CA Sale Price: $5.99 |
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4. Historic American Buildings Survey (copy) 20th Century Picture EAST FRONT OF LIGHTHOUSE - Point Loma Lighthouse No. 355, (moved), San Diego, San Diego County, CA |
