Answer:
299.99 miles
Step-by-step explanation:
Since the plane traveled due west,
The total angle is 49.17 + 90
Represent that with θ
θ = 49.17 + 90
θ = 139.17.
Represent the sides as
A = 170
B = 150
C = unknown
Since, θ is opposite side C, side C can be calculated using cosine formula as;
C² = A² + B² - 2ABCosθ
Substitute values for A, B and θ
C² = 150² + 170² - 2 * 150 * 170 * Cos 139.17
C² = 22500 + 28900 - 51000 * Cos 139.17
C² = 51400 - 51000 (−0.7567)
C² = 51400 + 38,591.7
C² = 89,991.7
Take Square Root of both sides
C = 299.9861663477167
C = 299.99 miles (Approximated)
Hence, the distance between the plane and the airport is 299.99 miles
Reflection does not preserve orientation.
Dilation (scaling), rotation and translation (shift) do preserve it.
Answer: 
Step-by-step explanation:
First integrate f'(x) so we can find the funtion f(x):
![4\int\limits {x} \, dx =4[\frac{1}{2} x^2]=2x^2+C=f(x)](https://tex.z-dn.net/?f=4%5Cint%5Climits%20%7Bx%7D%20%5C%2C%20dx%20%3D4%5B%5Cfrac%7B1%7D%7B2%7D%20x%5E2%5D%3D2x%5E2%2BC%3Df%28x%29)
The initial conditions say that when x = 0, the function equals 5. Let's write that down:
Therefore, the integration constant 'C' must equal 5. This means that our function is:
