a) Draw a diagram. At time t, A is 50t km south of the line which joined the ships at noon. B is 30t km north of that line, which is 150km long.
So, the distance d is such that
d^2 = 150^2 + (80t)^2
at 4:00,
d^2 = 150^2 + 320^2 = 124900
d = 353.4
2d dd/dt = 12800t
dd/dt = 12800t/2d
At 4:00, t=4
dd/dt = 12800*4/706.8 = 72.44
This makes sense, since the farther apart the two ships get, the closer their separation speed gets to just plain 50+30 = 80 km/hr
__________________________
b) Using similar triangles, when the woman is x meters from the light, the height h on the wall satisfies:
2/x = h/10
xh = 20
h dx/dt + x dh/dt = 0
Now, when she's 5m from the building, she's 5m from the light, so x=5 and
2/5 = h/10
h = 4
4*.75 + 5 dh/dt = 0
dh/dt = -3/5 = -0.6 m/s
_____________________________
c)*whew*
The length grows at a rate
dL/dt = 15cm/10^6 yrs
W = .12L2.53
B = .007W2/3
= .007(.12L2.53)2/3
= 0.00168L1.69
So, when L = 21
dB/dt = .00168*1.69L.69dL/dt
= .00284*21.69*15/10^6 = 0.000000348129
= 348.13 ng/yr
Answers to any of these questions would be of great help! (:
1 a) At noon, ship A is 150km west of ship B. Ship A is sailing south at 50km/h and ship B is sailing north at 30km/h. How fast is the distance between the ships changing at 4:00pm?
b) A spotlight on the ground is shining on a wall 10m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 0.7m/s, how fast is the length of her shadow on the building decreasing when she is 5m from the building?
c) Brain weight B as a function of body weight W in fish has been modeled by the power function B=0.007W^(2/3), where B and W are measured in grams. A model for body weight as a function of body length L (measured in cm) is W=0.12L^2.53. If, over 10 million years, the average length of a certain species of fish evolved from 15cm to 30cm at a constant rate, how fast was the species' brain growing when the average length was 21cm? Round your answer to the nearest hundredth. (in nanograms per year)
Thank you in advance! Help is much appreciated!
3 answers
thank you steve!
For question a), how did you get 12800? Where'd that come from?
1 answer