Reference no: EM132308850
Answer the following Questions :
Question 1
Let a = F + 1, b = G + 1 and d = E + 1
Evaluate the integral
0∫10∫d(ax - by) dx dy
Show your method.
Question 2
Given that y' = (√x/y) Cr use Euler's method to find y(G + 1) given that y(G) = (F + 1) using a step size of 0.2. Give your answer correct to 6 significant figures.
Question 3
Let a = ((Z+3)/5)
Let b = ((Y+1)/10)
Let c = X + 1
The power consumed in an electrical resistor is given by P = (E2/R) Watts where E is the voltage drop across the resistor in volts and R is the resistance of the resistor in ohms.
(a) Write down (∂p/∂E)
(b) Write down (∂p/∂R)
(c) Determine the rate of change of the power at the time when E is increasing by a volts/s, is decreasing at b ohms/s, E = 12 volts and R = c ohms.
Question 4
1. Read the article - Polar coordinates and cardioid microphones By Murray Bourne.
(a) What is the name of the shape given by the polar equation r = 1 - sin θ?
(b) What polar curve equation is most suitable for an omni-directional microphone?
(c) What type of microphone has the graph r = (θ2)?
2. Watch the video- Conic Section 3D Animation (Youtube) and answer the following questions:
(a) What is the name of the perimeter of the base?
(b) What is the name of the angle between the generator and the axis?
(c) What shape is obtained if the angle between the plane and the axis is greater than the vertex angle?
(d) What shape is obtained if the angle between the plane and the axis is perpendicular to the axis?
(e) What is the relationship between a and b for a parabola?
(f) When a > b curve with two disjoint sections is formed. What is its name?
(g) When the plane intersects the cones at the vertex we obtain degenerate conics.
Complete the following:
• the ellipse becomes...
• the parabola becomes...
• the hyperbola becomes...
Question 6
Area Using Polar Coordinates
Find the area enclosed by one of the loops of the polar graphs of r= 3 sin 6θ (shown below)
![1903_Polar Coordinates.jpg](https://secure.expertsmind.com/CMSImages/1903_Polar Coordinates.jpg)
Attachment:- Polar Coordinates & Conic Sections.rar