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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?

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?

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.

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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