Chris - I answered this a few days back. Be sure to check my work for errors.
________
"ship passes lighthouse" tells me that the ship (at that instant) is on a straight line that is perpendicular to the shoreline and 10km from the lighthouse, moving parallel with the shoreline.
a) initially (at time t=0, the instant of the ship's passing at 11am) k = 10km and d = 0.
The ship continues to move parallel with the shoreline at 35km/h.
You can see that (for example) after 1 hour the ship will have traveled 35km from its earlier point (now d = 35km). The distance from the lighthouse, k, will now be the hypotenuse of the right triangle that has one of its two shorter sides equal to d=35km and the other equal to 10km. (sorry I can't draw a diagram with this tool)
After 1 hour: k = sqrt[(35km)^2 + (10km)^2] = 36.4km at 12noon (here d = 35km)
After 2 hours: k = sqrt[(70km)^2 + (10km)^2] = 70.7km at 1pm (here d = 70km)
In general: k (as a function of d) = sqrt[d^2 + (10km)^2], where d is in km
b) d as a function of t:
d = (35km/h) * t, where t is in hours
c) recall that (k o d) just means k(d(t))
you’re just putting one function into another function as the independent variable
you end up with k as a function of t
so just embed the function d(t) above into the function k(d) above
it’s as though t becomes the independent variable inside the function k so you get
k(d(t)) = k(t) = sqrt[(35km/h * t)^2 + (10km)^2], where t is in hours
the function is now k as a function of t instead of k as a function of d
Someone answer all of this clearly, I don't get it at all.
Suppose a ship is sailing at a rate of 35km/h parellel to a straight shoreline. The ship is 10km from shore when it passes a lighthouse at 11am.
Question 6 options:
a)
Let k be the distance between the lighthouse and the ship. Let d be the distance from the ship has travelled since 11am. Express k as a function of d. Please include a diagram.
b)
Express d as a function of t, the time elapsed since 11am.
c)
Find k∘d . What does this function represent?
6 answers
Good grief!
The wording of this question is an illustration why some students find Mathematics difficult and confusing.
How about this:
Let the time passed since 11:00 am be t hrs.
then d, the horizontal distance the ship has covered :
d = 35t km
and k, the distance from the lighthouse is
k = √(10^2 + (35t)^2)
or
k = √(1225t^2 + 100)
or
k = √(100 + d^2)
take your pick
from here you can find out anything about the situation.
btw, what jolly ranger stated is perfectly correct
The wording of this question is an illustration why some students find Mathematics difficult and confusing.
How about this:
Let the time passed since 11:00 am be t hrs.
then d, the horizontal distance the ship has covered :
d = 35t km
and k, the distance from the lighthouse is
k = √(10^2 + (35t)^2)
or
k = √(1225t^2 + 100)
or
k = √(100 + d^2)
take your pick
from here you can find out anything about the situation.
btw, what jolly ranger stated is perfectly correct
Thank you guys both of you!
So b) i would just say d=35km *t
your instructor may prefer that you write it explicitly as
d(t) = 35km * t, where t is in hours
just so all your i's are dotted
I don't know how picky they are
and I don't want you to go to the trouble and get points off
d(t) = 35km * t, where t is in hours
just so all your i's are dotted
I don't know how picky they are
and I don't want you to go to the trouble and get points off
wait I'm confused with c what do i do or put
0 answers