Analyze the importance of the Supreme Court ruling on the Marbury v Madison case of 1803.
The Marshall Court passed judgment on a discrepancy between legislation and the Constitution as a way of ruling on the case. They decided that since the Constitution is the supreme law of the land any legislation that violates it is null and that it is the responsibility of the court system to determine whether legislation is constitutional or not. Though the power of judicial review had been brought up during the Constitutional Convention, the ruling on Marbury v Madison put it into effect and gave the court system the power it has used to rule on countless pieces of legislation since.
Find the area of the portion of the graph of r = 2 + 3cosθ located below the x-axis.
Determine the bounds: π to 2π Set up the integral: 1/2 ∫ (2 + 3cos(θ))^2 dθ Simplify the integrand: 1/2 ∫ [4 + 12cos(θ) + 9cos^2(θ)] dθ Use the double angle formula: 1/2 ∫ [4 + 12cos(θ) + 9/2(1+cos2(θ))] dθ Integrate: 1/2[17θ/4 + 6sinθ + 9/8sin(2θ)] | from 2π to π Solve: 17π/4
What is the sum of all possible solution to the equation x(x - 6) = 9 ?
Distribute the x: x^2 - 6x = 9 Set the equation up for factoring: x^2 - 6x - 9 = 0 Factor: (x - 3)(x - 3) = 0 Find solutions: x = 3 and x = 3 Final Answer: 6