# unit

1. ### Unit tangent vector vs principal normal vector difference

http://mathwiki.ucdavis.edu/Core/Ca.../The_Unit_Tangent_and_the_Unit_Normal_Vectors In the link, I cant understand that why the Principal Unit Normal Vector is defined by N(t) = T'(t) / | T'(t) | ,can someone explain.... Since tangent vector is normal to principal normal vector, why the N(t)...
2. ### laplace transform of unit step function ?

find the laplace transform of (e^-s) / [ (s)(s-3) ] since there's (e^-s) which can be found in L { f(t-a) H(t-a) } = (e^-(as)) F(s) , so , i found a = 1 , then i found F(s) = 1/ [ (s)(s-3) ] , formula : i have attached the working below , is it correct ? btw , the author's ans doesnt have...
3. ### express the function in terms of step unit function and find laplace transform

f(t) = (e^t) , 0 <t<3 0 , t>3 the formula of is L { f(t-a) H(t-a) = (e^-as)(F (s) ) why there's no need to transform (e^t)(H(t-3) ) into e^(t-3+3) H(t-3) ) ?
4. ### Probability: events selected from unit interval

Hi I'm having trouble determining which events this question is referring to maybe this wording makes more sense to you than it does to me. A number U is selected from the unit interval. Let the events A and B be A= U differs from 1/2 by more than 1/4 and B=1-U is less than 1/2. Find the...
5. ### HELP! Circles, unit circles

Representing one unit by at least five squares on your graph paper, draw the unit circle, which is centered at the origin and goes through point A = (1, 0). Use a protractor to mark the third-quadrant point P on the circle for which arc AP has angular size 215º. Estimate the coordinates ofP...
6. ### Unit step function

can someoen pls explain what does the H mean here ? my book doesnt has much explaination about it
7. ### what is the unit of pi?

Can I call the unit of pi is radians? If not, why?
8. ### Construct A Plane From A Coordinate And A Unit Vector And Find Its X,Y,Z Angles

I'm trying to learn how to figure out the X,Y,Z rotation angles of a plane so that it is normal to a unit vector. I have a coordinate point that is on the plane and a unit vector that is normal to plane to start with. Appreciate any help I can get.
9. ### Unit Tangent - # 2

Find T(t) using r(t) T(t) = \dfrac{r'(t)}{|r'(t)|} r(t) = <8\sqrt{2}t, e^{8t}, e^{-8t}> r'(t) = <8\sqrt{2}, 8e^{8t}, 8e^{-8t}> |r'(t)| = \sqrt{(8\sqrt{2})^{2} + (8e^{8t})^{2} + (8e^{-8t})^{2}} ??
10. ### Unit Tangent

Find T(t) using r(t). T(t) = \dfrac{r'(t)}{|r'(t)|} Find T(t) of r(t) = <2t^{2}, \sin(t) - t\cos(t), \cos(t) + t \sin(t)> r'(t) = <4t, \cos(t) - (t)(-\sin(t)) + (1)(\cos(t)), - \sin(t) + (t)(\cos(t)) + (1)(\sin(t))> r'(t) = <4t, \cos(t) - (t)(-\sin(t)) + (\cos(t)), - \sin(t) + (t)(\cos(t)) +...
11. ### Unit Vector Problem

\sqrt{(-4)^{2} + (4)^{2} + (2)^{2}} = \sqrt{36} = 6
12. ### Total boundedness of unit ball

Why is a unit ball not totally bounded ? I know that total boundedness means that we should be able to cover the unit ball with a finite number of elements. I don't quite understand the concept behind an open ball not being totally bounded. I need some help here, i am lost !
13. ### unit circle

1)can anyone tell me why the restriction of unit circle is 0<_t<2pi? 2)is there any reason to explain this restriction? 3) why the restriction for each parameteric equation is different? maybe it is because the type of parametric equation that is found ?
14. ### Unit Circle Trigonometry

Imgur I think I've got 1, 2, and 4, which I believe are cos(theta), sin(theta), and tan(theta) respectively. I need help on 3, 5, 6, if you could give me some tips please.
15. ### sin 180-theta=sin theta in a unit circle

Can anyone help me to show sin (180-theta) = sin theta in a unit circle.
16. ### Find Unit Vector

Given that vector a = 10j and vector b = -8i + j, find a unit vector that is parallel to a - 3b.
17. ### Unit's digit problem

Hello Find the units digit of 7^7^7^7.... Please provide some hints. Thanks
18. ### Find unit's digit

Hello Find unit's digit of 7^11^13^17 Solution : evaluate 11^13^17 = 2431 cyclicity of 7 is 4 2431%4=3 So unit's digit of 7^2431 is same as unit's digit of 7^3 = 3 Is there any method to solve this problem without evaluating 7^11^13^17? Thanks
19. ### Area and Pythagorean Theorem Question --> Quadratic Unit

Been going in circles trying to find the lengths of the missing sides. I can see the final answers (from the back of the text), but can't figure out how to arrive at them. I can get up to here: x*y=30 (using the information that the area is 15 cm^2 and the formula for the area of a triangle)...
20. ### Unit Vector Problem

Show that (\dfrac{-5}{13},\dfrac{12}{13}) is the opposite in direction of u = (5,-12) Show that (\dfrac{-8}{17},\dfrac{-15}{17}) is in the same direction as v = (-8,-15) What is the first step here? I can see where the -5, 12, -8, and -15 (the numerators) came from in the problem, but where...