Answer:

Step-by-step explanation:
We have given:
E is (-1,6) and F is (3,9)
And ratios are 3:2
We will use the section formula to find the required coordinates:
section formula=
Here,
On substituting the values in the formula we get:



Hence, required coordinates are: 
Lets simplify each one of the rational expressions using the product rule of exponents:

and the quotient rule of exponents:

.
1.

2.

3.

4.
We can conclude that you should pair the rational expressions with their simplest form as follows:



A^2 = b^2 + c^2 -2bc * cos(A)
a^2 = 144 + 225 -360 * .5
a^2 = 189
a = 13.748
Answer:
Rate of plane 735 km/hr
Rate of wind 65 km/hr
Step-by-step explanation:
Calculation to determine the rate of the plane in still air
Let Va represent the velocity of the airplane
Let Vw represent the velocity of the wind
When flying with the wind:
(Va+Vw)*(6 hours) = 4800
6Va + 6Vw = 4800
6Vw = 4800 - 6Va
Vw=4800/6-Va
Vw = 800 - Va
When flying against the wind:
(Va-Vw)*(6 hours) = 4020 km
6Va - 6Vw = 4020
Substitute 800-Va for Vw and solve for Va:
6Va - 6(800-Va) = 4020
6Va -4800 + 6Va = 4020
12Va = 8820
Va=8820/12
Va = 735 km/hr
Therefore the rate of the plane in still air is 735 km/hr
Calculation to determine the rate of the wind
Rate of wind:
Vw = 800 - Va
Vw= 800 -735
Vw= 65 km/hr
Therefore the rate of the wind is 65 km/hr