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Arjun S.

Masters of Science Student at New York University

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Pre-Calculus

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Question:

Find out the roots of the equation : 2x^3 + 7x^2 + 3x -2

Arjun S.

Answer:

As, this isn't a quadratic equation we'll first try to convert it into quadratic form by taking out one root of the equation. on inserting x= -1 into the equation we get 0. Thus x +1 is a root of the equation. so we can write it as (x+1)(2x^2 + 5x -2) Now use the quadratic formula for the quadratic equation obtained. the formula is roots = {b + sq.root(d)}/2a and {b - sq.root(d)}/2a d = b^2 - 4ac d = 25 - 4(2)(2) = 25 - 16 = 9 sq root (d) = +3, -3 So, roots of the quadratic equation are : (5+3)/4 = 2 and (5-3)/4 = 0.5 So the three roots of the original equation are (x+1)(x-2)(x-0.5) therefore the 3 values of x are : x = -1, 2, 0.5

Basic Math

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Question:

A football field is rectangular in shape with dimensions of 50 feet by 150 feet. The grass in the field has to be replaced. The new grass costs $1/sq. feet Also, the field required new fencing all along the boundary which has been priced at $10 per feet and ints installation at $5 per feet. What is going to be the total cost of the project?

Arjun S.

Answer:

This problem clearly has 3 parts : 1. Find the cost of grass 2. Find the cost of the fence 3. Find the cost of installation of fence Solution 1. Area of the field (Rectangular)= length x breadth = 150x 50 = 750 sq. feet Cost of 1 sq. feet = $1 Cost of 'x' sq. feet = $1 x 'x' Cost of 750 sq. feet = 1 x 750 = $750 Solution 2. Length of boundary of field(Perimeter) = 2x(length + breadth) = 2 x (50 + 150) = 400 feet Cost of 1 feet = $10 Cost of 400 feet = $10 x 400 = $4,000 Solution 3. Length of boundary (as calculated above) = 400 feet Cost of 1 feet = $5 Cost of 400 feet = $2,000 Total cost for the project = $750+ $4,000 + $2,000 = $6,750

Electrical Engineering

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Question:

Can Electrical Transformers work on DC also?

Arjun S.

Answer:

The basic working concept of an electrical transformer is that it transfers the energy form the primary coil to the secondary coil via the changes in the magnetic field within the core material. Now in the case of an AC being applied, there is a constant change in the magnetic field within the core thus causing a current to flow within the secondary coils. The ratio of the primary and secondary currents depends on the number of primary and secondary windings. A ratio of these is known as the turns ratio usually denoted by 'N'

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