Recent content by trulyfalse

Hello PF. Homework Statement A function f is defined by f(x) = 1 + 2x + x2 + 2x3 + x4 + 2x5 + x6... Find the radius of convergence of the series and the explicit formula for f(x).Homework Equations The Attempt at a Solution I know that the formula for the series is going to be similar to the...

Hey PF! Homework Statement I've attached the problem to this post along with my free body diagram. Homework Equations Moment of inertia of a cylinder: 1/2MR^2The Attempt at a Solution Since the cylinder is moving at a constant velocity and is not slipping, ƩF = 0. For the torques around the...

Oh jeez, it seems I made quite an egregious error. I initially assumed that the sum of the forces would be equal to zero on the object since static friction is involved, but after reading your comment and thinking about it further I realized that's only because the velocity of the instantaneous...

Hello PF! Homework Statement A string is wrapped around the small cylinder as shown. You pull with a force F (and the cylinder does not slide). Calculate the acceleration of the cylinder CM (including direction). Here r = 3 cm, R = 5 cm, F = 0.1 N, and m = 1kg. [Make sure to define one...

Aha! Then U = sqr(x) and that can be substituted in the equation. Thanks brmath!

I put g(x^2) back into the integral. How would I simplify g(x^2) to get g(x)? Would I square every expression for x in the equation (i.e x^2 and x^3)?

Hello PF. Homework Statement Find a function g such that \int_0^{x^2} \ tg(t) \, \mathrm{d}t = x^2+x Homework Equations From the fundamental theorem of calculus: f(x) = \frac{d}{dx}\int_a^x \ f(t) \, \mathrm{d}t The Attempt at a Solution After taking the derivative of...

If the vectors are non-zero, then we can conclude that u-v must be equal to zero, and therefore u=v. We can also conclude that vectors w and (u-v) must be orthogonal because their dot product is equal to zero. However, I am not sure how to prove that the vectors are nonzero. Am I supposed to...

Hello PF! Homework Statement Prove the following: if u and v are two vectors in Rn such that u\cdotw = v\cdotw for all wεRn , then we have u = v Homework Equations The Attempt at a Solution u\cdotw - v\cdotw = 0 w\cdot(u - v) = 0 I'm not sure what to do after applying the...

Hello PF, I am currently taking linear algebra (MATH 110) at Queen's University and I am finding it very difficult to grasp simple concepts presented in the course. Although the semester has just begun, I'm concerned that I may be lacking certain prerequisites needed to succeed in linear...

Ahhhh... Thank you for elucidating me. I can see now that I have to factor and solve for x. Thank you again for your help!

Hey PF! Homework Statement Find exact solutions for the following equations over the domain 0 ≤ x <2π 2sinx = 3 + 2cscx Homework Equations sin2+cos2=1 The Attempt at a Solution 2sinx = 3 + 2cscx 2sinx = 3 +2(1/sinx) sinx = 3/2 + 1/sinx sinx - 1/sinx = 3/2 (1-1-cos2x)/sinx = 3/2 -cos2x/sinx =...

Hello PF! Homework Statement The graph of the function y = 2x2 + x +1 is stretched vertically about the x-axis by a factor of 2, stretched horizontally about the y-axis by a factor of 1/3 and translated 2 units right and 4 units down. Write the equation of the transformed function Homework...

Hahahaha thanks for your help; I'll have to be more diligent with unit conversions next time!

Hello Physics Forums! Homework Statement The student sets up a collision experiment with two masses on a horizontal air track, with two springs on each end. The mass of A is 100 g and B is 200 g. Each spring has a constant of 20 N/m. Spring 1 (left side) was initially compressed 5 cm [left] to...