Answer:
(a) ðz/ðt = 1500miles/hr
(b) 10minutes
Step-by-step explanation:
Let x rep plane one
Let y rep plane two
ðx/ðt = 1440miles/hr = speed of plane one
ðy/ðt = 420miles/hr = speed of plane 2
ðz/ðt = ? = rate of change of distance btw two plane moving at right angle to meet at point o...
See attachment
Since x² + y² = z²... equation 1
So therefore (240² + 70²) ^½= z = 250 miles = distance between two planes
Differential rate of equation 1 gives
(2x* ðx/ðt ) + (2y* ðy/ðt) = 2z* ðz/ðt
Substituting to get ðz/ðt
(2*240*1440) + (2*70*420) = 2*250*ðz/ðt
750000 = 500 ðz/ðt
ðz/ðt = 1500miles/hr
B.
Since v = d/t where d = distance = 250miles
t = time = ? = time needed for controller to divert one of e planes , v = 1500miles/hr
t = d/v = 250/1500 = 10minutes
Answer:
i just need points
Step-by-step explanation:
Answer:
![\angle N\cong \angle Z](https://tex.z-dn.net/?f=%5Cangle%20N%5Ccong%20%5Cangle%20Z)
Step-by-step explanation:
Given:
In ΔLMN and ΔXYZ, ![MN=3\,,\,LN=2\,,\,YZ=9\,,\,XZ=6](https://tex.z-dn.net/?f=MN%3D3%5C%2C%2C%5C%2CLN%3D2%5C%2C%2C%5C%2CYZ%3D9%5C%2C%2C%5C%2CXZ%3D6)
To find: criteria that needs to be shown to prove ΔLMN
ΔXYZ using SAS similarity theorem
Solution:
According to SAS Similarity Theorem, if two sides in one triangle are proportional to two sides in another triangle and the included angle between the sides are congruent, then the two triangles are said to be similar.
In ΔLMN and ΔXYZ,
![\frac{LN}{XZ}=\frac{2}{6}=\frac{1}{3}\\\frac{MN}{YZ}=\frac{3}{9}=\frac{1}{3}\\\therefore \frac{LN}{XZ}=\frac{MN}{YZ}](https://tex.z-dn.net/?f=%5Cfrac%7BLN%7D%7BXZ%7D%3D%5Cfrac%7B2%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B3%7D%5C%5C%5Cfrac%7BMN%7D%7BYZ%7D%3D%5Cfrac%7B3%7D%7B9%7D%3D%5Cfrac%7B1%7D%7B3%7D%5C%5C%5Ctherefore%20%5Cfrac%7BLN%7D%7BXZ%7D%3D%5Cfrac%7BMN%7D%7BYZ%7D)
So, ΔLMN
ΔXYZ by SAS similarity theorem if ![\angle N\cong \angle Z](https://tex.z-dn.net/?f=%5Cangle%20N%5Ccong%20%5Cangle%20Z)
Answer:
You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.