Ellen has property whose boundary lines form a triangle, as shown in the diagram. Her house lies at Vertex A and she is going to
put a bunkhouse for the ranch hands somewhere along segment BC. She wants the placement to be such that CA/CD=B/A. What must be true about segment AD so that the proportion CA/CD=BA/BD holds
1 answer:
Given that in a ΔABC, Ellen house lies at vertex A and bunkhouse is put somewhere along BC, let it be D.
Please refer the diagram attached.
We are also given that D must be placed such that holds true.
Let us re write the above equation such that CD and BD lie on one side.
That is
Which is nothing but angle bisector theorem.
Hence AD must bisect the angle A then only the given condition will hold true.
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Use Law of Cooling:
T0 = initial temperature, TA = ambient or final temperature
First solve for k using given info, T(3) = 42
Substituting k back into cooling equation gives:
At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
Solve for x:
Sub back into original cooling equation, x = T(t)
Solve for t:
This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM
T0 = initial temperature, TA = ambient or final temperature
First solve for k using given info, T(3) = 42
Substituting k back into cooling equation gives:
At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
Solve for x:
Sub back into original cooling equation, x = T(t)
Solve for t:
This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM