What is the relationship between a and b for a parabola

Assignment Help Engineering Mathematics
Reference no: EM132308850

Answer the following Questions :

Question 1

Let a = F + 1, b = G + 1 and d = E + 1

Evaluate the integral

010d(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


Attachment:- Polar Coordinates & Conic Sections.rar

Reference no: EM132308850

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Reviews

len2308850

5/20/2019 2:49:33 AM

Read these instructions carefully before you attempt the homework. Your answers to Questions 1 and 2 must be typed into the Reflect in Your ePortfolio section in Bright Space – you will find this underneath the question in Bright Space. • Click on Reflect in ePortfolio • Enter a title, I suggest “Polar Co-ordinates & Conic Sections” • Scroll down to Reflections and type your answers in the space provided • Click the Add button to save your work • When you have finished click Tools from the main menu • Select ePortfolio You should be able to see your work • Click the drop-down arrow next to your homework’s title From here you can edit your homework if you want to • Select Share • Click Add Users and Groups • Find my name and select it • Click Share

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