Roil Call A e https://lmath.nku.edu/assessment/showtest.php?action- skip&to; 9 N

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Roil Call A e https://lmath.nku.edu/assessment/showtest.php?action- skip&to; 9 Nate.. G Google Forums Calendar Gradebook Log Out ulus I Fall 2017> Assessment iation and Related Rates NKU Imath Google Translate ) YouTube / NKU Home Pape: N- Owien are on Hamad Almarr This assignment is past the original due date of Tue 10/03/2017 5:00 pr . You have use auth Due in 4 hours, 24 minutes. Due Thu 10/05/2017 5:00 pm Show Intro/Instructiors A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speod of 6 tusec along a shadow moving when she is 50 ft from the base of the pole? straight path. How fast is the ip of her Previewsec Box 1: Enter your answer as a number (like 5,-3, 2.2172) or as a calculation (like 5/3, 23, 5+4) Enter DNE for Does Not Exist, oo for Infinity Points possible: 10 Unlimited attempts. Message instructor about this question Post this question to forum Submit

Explanation / Answer

Height of Pole, p = 15 ft.
Height of Woman, w = 6 ft.
Distance Between Woman and Pole, s = 50 ft.
Speed of Woman, ds/dt = 4 ft./sec
Length of Shadow = L
Distanc Between Woman and End of Shadow = x

Find dL/dt:
p / (s + x) = w / x
15 / (50 + x) = 6 / x
15x = 6(50 + x)
15x = 300 + 6x
15x - 6x = 300
9x = 300
x = 300 / 9
x = 33.3334

L = s + x
L = 50 + 33.3334
L = 83.3334

p / L = w / (L - s)
15 / L = 6 / (L - s)
15(L - s) = 6L
15L - 15s = 6L
15L - 6L = 15s
9L = 15s

Differentiate Implicitly:

9(dL/dt) = 15(ds/dt)
9(dL/dt) = 15(4)
9(dL/dt) = 60
dL/dt = 60 / 9
dL/dt = 6.66667

The tip of the shadow is moving at a rate of 6.66667 ft./sec.

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