Recent content by phyzz

What I meant was if we have constants in front of two vectors we want to cross product, are we allowed to multiply the constants together and perform the cross product to the vector bits? Sorry for the vagueness!

Yes, cross product Thanks for the tip!

Thank you Simon Bridge! In other news, when I work out (in this case a is a constant) \left \| T_{\gamma}(t) \right \| = \left \| \frac{1}{\sqrt{1 + a^{2}}} (-asin(t),\sqrt{1+a^{2}}cos(t),-sin(t)) \right \| I know I can just do \left \|(-asin(t),\sqrt{1+a^{2}}cos(t),-sin(t)) \right \| and...

Ohhhhh my bad I didn't see it at first. I just used sin^2 + cos^2 = 1 and the cos of the angle I found between the two vectors. Thanks!

How do you know that this is a right angle though?

Homework Statement A rotation ρ about the origin in ℝ2 drives the point P = (4,3) to the point ρ(P) = (3,4). Find the angle of rotation as well as its matrix notation. Homework Equations Ok so I made a sketch and I realized I needed to find θ = θ1 - θ2 where θ1 and θ2 equal arctan(4/3) and...

Thanks!

ok I understood n+1 > n 1/(n+1) < 1/n sin(1/(n+1)) < sin(1/n) ie sin(1/(n+1)) - sin(1/n) < 0 BUT if it's cos: n+1 > n 1/(n+1) < 1/n cos(1/(n+1)) > cos(1/n) ie cos(1/(n+1)) - cos(1/n) > 0 gonna learn it like: cos of something with a larger denominator is > cos of something with...

[cos(1/n)]' = - sin(1/n) / n^2 ie f'(n) < 0 for all n because of the negative sign, so it should be decreasing?

I don't know whether it's true or not, that's the thing cos(x) x approaching 0 is 1 right?

Homework Statement I have the series an = (-1)^{n} cos(1/n) and I have to determine whether it converges or diverges. Homework Equations I used the Leibniz criterion The Attempt at a Solution However, I determined that bn = cos(1/n) is a decreasing function because: n+1 > n 1/(n+1) < 1/n...

Homework Statement A spacecraft orbiting the Sun uses its jet engine for slowing down its orbital rotation and changing the direction of its velocity. At the moment when the velocity is directed away from the Sun and has a magnitude of v = 30 km/s, the jet engine is switched off. At the same...

Homework Statement Consider a small box of mass m sitting on a wedge with an angle θ and fixed to a spring with a spring constant k and a length in a non-stretched state L. The wedge rotates with an angular velocity ω around the vertical axis. Find the equilibrium position of the box...

Homework Statement Simplify the following expression: arccosh \left(\frac{1}{\sqrt{1 - x^2}}\right) \forall x ∈ (-1, 1) Homework Equations cosh(u) = \left(\frac{1}{\sqrt{1 - tanh^{2}u}}\right) u ∈ ℝ The Attempt at a Solution x = tanhu ∴ u = arctanhx u ∈...

Thank you for your patience. So the radial accn would be aR = v(t)^2 / R v(t) being what was found earlier from ## v(t) = a_{\tan}t + v_0 ##