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Saiprasad M.

Physics, chemistry and Math Coach for 4.5 years

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Physics (Newtonian Mechanics)

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Question:

Let us consider the problem: A 15 kg object moving to the west with an acceleration of 10m/s2. What is the net force acting on an object?

Saiprasad M.

Answer:

Newton's Second Law of Motion Formulae: Net Force: Fnet = ma Mass = Fnet / a Acceleration = Fnet / m Where, Fnet = Net Force m = Mass a = Acceleration. Therefore, Net Force (Fnet) = 15 x 10 = 150 N

Calculus

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Question:

Are the two functions f and g defined by f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive equal?

Saiprasad M.

Answer:

Two functions are equal if their rules are equal and their domains are the same. The first function is defined for real while the second function is defined for t which is real and positive. The domains are clearly different. Hence The two functions are not equal.

Algebra

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Question:

If 16^x + 16^(x - 1) = 10, find 2^2x.

Saiprasad M.

Answer:

We are given the equation: 16^x + 16^(x - 1) = 10 We know that 4^2 = 16 and the exponent rule a^m/a^n = a^(m-n) & (a^m)^n = a^mn Expressing 16 as 4^2; 4^2x + 4^2(x-1) = 10 4^2x + 4^2x-2 = 10 4^2x + 4^2x / 4^2 = 10 //using exponent rule given above 4^2x + 4^2x / 16 = 10 //4^2 = 16 4^2x ( 1 + 1 / 16 ) = 10 //taking 4^2x common 4^2x ( 17 / 16 ) = 10 //adding 1 and 1/16 4^2x ( 17 / 16 ) = 10 // sending 17/16 to left side of the equation 4^2x = 160/17 //solve for 4^2x 4^x = 4 sqrt(10) / sqrt(17) //extract the square root 2^2x = 4^x = 4 sqrt(10) / sqrt(17) //required answer

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