Ravish C.

Defect Analysis Manager at Tata Motors and Teaching Assistant at BITS Pilani

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Pre-Algebra

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Question:

The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction.

Ravish C.

Answer:

Let "x" be the numerator. "The denominator of the fraction exceeds the numerator" From the above information, fraction = x / (x+5) ----------(1) "If 3 be added to both, the fraction becomes 3/4" From the above information, we have (x+3) / (x+5+3) = 3/4 (x+3)/(x+8) = 3/4 ---------> 4(x+3) = 3(x+8) 4x + 12 = 3x + 24 ---------> x = 12 (1)--------> x / (x+5) = 12 / (12+5) = 12/27 Hence, the required fraction is 12/27

Calculus

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Question:

Differentiate y = x^x

Ravish C.

Answer:

Because a variable is raised to a variable power in this function, the ordinary rules of differentiation DO NOT APPLY! The function must first be revised before a derivative can be taken. Begin with y = x^x . Apply the natural logarithm to both sides of this equation getting ln y = ln x^x ln y = x ln x Differentiate both sides of this equation. The left-hand side requires the chain rule since y represents a function of x. Use the product rule on the right-hand side. Thus, beginning with ln y = ln x and differentiating, we get $ \displaystyle{ { 1 \over y } } y' = x \displaystyle{ 1 \over x } + (1) \ln x $ $ = 1 + \ln x $ . Multiply both sides of this equation by y, getting $ y' = y (1 + \ln x) = x^x (1 + \ln x) $ .

Physics

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Question:

A ball is thrown vertically upwards from the top of a tower with a speed of 100m/s.it strikes the pound near the base of the tower after 25sec. Find the height of the tower.

Ravish C.

Answer:

Hi let us suppose the total height of the tower =h and hence by appling the equation of motion s=ut+(1/2)*a*t2 by substituting the vaues (–h) = 100*25 + (1/2)(–g)(25)2 (taking above as positive and down as negative) (–h) = 2500 – (1/2)*10*625 ( i have taken g as 10 u can take it as 9.8 it depends on the question) (–h) = 2500 – 3125 (–h) = – 625 so h = 625 m

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