final

A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has a mass of 20 kg and a radius of 1m. Assuming that the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impact is approximately...

My understanding of a rotation of a vector can be done by using a 2D rotation matrix as shown below, $R(\theta )=\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \\\end{bmatrix}$. This rotates column vectors by means of the following matrix multiplication...

150 mL of a solution contains 250 mg of Magnesium Chloride B.P. (MgCl2.6H2O, M.Wt. 203.3). What mass of sodium chloride (NaCl, M.Wt. 58.5) must be added such that when 100 mL of the solution is mixed with water and made up to 250 mL, the final concentration of chloride is 12 mmol/L? Select...

I'm very stuck on this question: A small aeroplane used for skydiving moves along a runway. The aeroplane accelerates at 2 m / s^2 from a velocity of 8 m / s. After a distance of 209 m it reaches its take-off velocity. Calculate the take-off velocity of the aeroplane. The mark scheme...

Here is the solution to proving the inflection point of y=xsinx lies on the curve y^2(x^2+4)=4x^2 y'' 2cosx - xsinx = 0 xsinx=2cosx (hereafter all are x's are x sub zero) inflection point of the curve (x, 2cos x) Prove (x,2cosx) lies on the curve y^2(x^2+4)=4x^2...

-0.2t²+1.2t+3.2 = 3.75 <-> -0.2t²+1.2t-0.55=0 <-> t=0.5 or t=5.5 how did they get to that last step? I tried a lot of things, but nothing gave me those values. Does anyone have any idea how they went from -0.2t²+1.2t-0.55=0 to t=0.5 or t=5.5?

Given an equation sq root 3/xy = 2/ x^2-y^2 (a) Change the equation to polar form and simplify the answer by using funda- mental identities. (b) Solve the trigonometric equation (for θ, 0 ≤ θ ≤ 2π) that you obtained in (a).

I might need your help desperately tonight. I have been out of school with a bacterial stomach infection. I was able to come back to school just before exams so I missed all the review. I play lacrosse so I can't do afternoon tutoring (the only time my teacher does it). I need help with this...

Solution trisecting (n-sections) and n-proper construction of the polygon using divider and straightedge. The ball shall be awarded in two equal parts, obtained half contains two areas, the circle (represents a planar geometry) and a semi-sphere (represents spherical geometry), the circle is...

Hey guys new here and could really use some last minute help. Following pictures are of my final and I am lost on #10 and don't how to do it and #9 I did but not sure about it tho.... Any help would be awesome! Specially with it all due tomorrow by noon. And sorry they are sideways. Don't know...

convergent or divergent $\sum_{n=1}^{\infty} n^6e^{-n}$ $\sum_{n=1}^{\infty} \frac{n}{n[ln(3n)]^{1/2}}$ find the first five nonzero terms in maclaurin series $f(x)=e^{4x}\sqrt{1+x}$

$\int_{0}^{\infty} \ \frac{dx}{x^2-16}$ $\int_{-\infty}^{0} \ \frac{dx}{(2+x) \sqrt{x}}$ a graph of $y=\frac{x^2}{4}$ is given with intersection point $(4,4)$. find the total force of the dam using coordinate system at the bottom of the dam. (i dont even know what this question means :unsure:)

my final is tomorrow and my instructor gave a list of questions that will be similar to the ones on the final exam and i wanna see how they should be done properly. ive been working on other problems but i cant get past these ones. thanks determine the volume using the shell method $y=5|x|$...

After much tinkering around, here is a final hypothesis on hopping between primes (checked up to 10^12). CONJECTURE: For every odd prime p, there is an increasing sequence of primes between 3 and p such that all differences between consecutive terms are products of two consecutive integers...

I have got 2 equations from graphs such that z=f(x,y) When I vary x keeping y constant I get z=0.0005x+0.0002 and when I vary y keeping x constant I get z=0.0005x^2 - 0.0405x + 0.4644 How do I get a final equation for z which includes both variables x and y? Thanks!

Hello everyone I have a question. In a 100 by 100 matrix, each of the number 1,2,3...100 appears exactly a 100 times. Show that there is a row or column that have at least 10 different numbers.

Right I am dumbfounded on this question (in attachments) What is the answer and how would you work it out

Last question I am stuck on.Many thanks to everyone who helped me today. Question is attached

Hi 1 ) 2 ) 3 ) http://www11.0zz0.com/2012/12/01/18/664448770.jpg my answer 1 ) Is the final answer will be (pi^2 ) 2 ) Is the final answer will be 2.77 3) Is the final answer will be = 2.17 ?