Recent content by Priyadarshi Raj

In both the ways I get the solutions as: ## \pi, 2\pi, 3\pi ... ## So the required sum is ## = \pi + 2\pi + 3\pi +... + 99\pi = 4950\pi ## Thanks everyone.

Sorry, I did a silly mistake there. My teacher said, the fractional part function is defined as: ## \{ x \} = x - [x] ##, where [x] is the greatest integer function. @Ray Vickson , that makes ## \{ -1.4 \} = +0.6 ## So, ## \text{When}~~ x \not\in I \\ \{ x \} + \{ -x \} \\ \qquad = (x - [x] )...

Homework Statement If ##\{ x \}## denotes the fractional part of x, then solve: ## \{ x \} + \{ -x \} = x^2 + x -6## It's provided that there are going to be 4 roots of this equation. And two of them will be integers. Homework Equations ## 0 \lt \{ x \} \lt 1~~\text{if}~~x \not\in I## ## \{...

Homework Statement Question: Sum of all the solutions of the equation: ##tan^2 (33x) = cos(2x)-1## which lie in the interval ## [0, 314] ## is: (a) 5050 π (b) 4950 π (c) 5151 π (d) none of these The correct answer is: (b) 4950 π Homework Equations ## cos(2x) = 2cos^2(x) -1 ## The Attempt...

Homework Statement A cylinder of radius ##{R}## is partially filled with water. There is an inverted cone of cone angle 90° and base radius ##{\frac{R}{2}}## which is falling in it with a constant speed ##v=30~cm/s##. Find the rate of increase of water level (in ##cm/s##) when half the...

Thank you for helping me. The problem is solved.

Okay then, I believe this is the way: v2 will be average of v1 and v3 If the avg speeds are v1 = (S/t1) , v2 = (S/t2), v3 = (S/t3), then Distance traveled during t2 is given by S = v1t2 + 0.5at22 and also a = (v3 - v1)/t2 [using Newton's laws of motion] ∴ S = v1t2 + 0.5(v3 - v1)t2...

Homework Statement Q: If a particle moving along a straight line under uniform acceleration covers successive equal distances ( S each) in time intervals t1, t2 and t3 respectively, then the expression for average speed of particle in covering the given distance of 3S is: Options: A) (S/t1)...