Mei has a large triangular stone that she wants to divide into four smaller triangular stepping stones in a pathway. Explain why
cutting along each midsegment creates four congruent stepping stones?
1 answer:
Answer : Explained.
Step-by-step explanation: As given in the question and shown in the attached figure, ΔABC be the large triangular stone that Mei wants to divide into four smaller triangular stepping stones in a pathway.
Let D, E and F be the mid-points of the sides BC, CA and AB respectively. Then, DE, EF and FD are the mid-segments of ΔABC.
Then , we have
4 × Area of ΔDEF = 4 ×Area of ΔFBD = 4 × ΔAFE = 4 × Area of ΔECD = Area of ΔABC.
Thus, we have
ΔDEF ≅ ΔFBD ≅ ΔAFE ≅ ΔECD.
Thus, in this way, cutting along mid-segments creates four congruent stepping stones.
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The correct question is:
A motorboat starts from rest (initial velocity v(0) = v_0 = 0). Its motor provides a constant acceleration of 4 ft/s², but water resistance causes a deceleration of v²/400 ft/s².
(a) Write a differential equation for the velocity v.
(b) Find v when t = 10s, and also find the limiting velocity as t → ∞ (that is, the maximum possible speed of the boat).
Answer:
(a) The differential equation is:
dv/dt = 4 - (v²/400)
(b) v = 30.46ft/s when t = 10s.
(c) The limiting velocity as t → ∞ is 40ft/s
Step-by-step explanation:
(a) The differential equation is formed by considering the changes in acceleration. At a constant acceleration of 4 ft/s², it then decelerate at v²/400 ft/s².
Adding these, we have
Acceleration, a = 4 - (v²/400)
Because acceleration is the derivative of velocity, a = dv/dt.
dv/dt = 4 - (v²/400)
(b) The differential equation obtained in (a) is solved, and evaluated at t = 10, to obtain v = 30.46 ft/s
(c) The limiting velocity, taking into consideration the properties of limit is evaluated to obtain v = 40 ft/s.
SEE ATTACHMENT FOR THE STEP BY STEP WORKINGS.
