(a) Find the solution u(x, y) of Laplace's equation in the rectangle 0 < x < a, 0 < y < b, that satisfies the following boundary conditions u(0, y) = 0, u(a, y) = f(y), 0 < y < b, u(x, 0) = h(x), u(x, b) = 0, 0 ≤ x ≤ a. Hint: Consider the possibility of adding the solutions of two problems, one with homogeneous boundary conditions except for u(a, y) = f(y), and the other with homogeneous boundary conditions except for u(x, 0) = h(x).

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

total of apples - take away four

6-4 = 2

answer is 2 apples