Prove that for n>=2,2 cdot (begin{matrix}{n}{2}end{matrix})+(begin{matrix}{n}{1}end{matrix})=n^2

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors ${\displaystyle \hat{i}}$ and ${\displaystyle \hat{j}}$.
1. (Enter in box 1) $\frac{m}{s^2}\hat{i}+(\text{ Enter in box 2 })\frac{m}{s^2}\hat{j}$
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) ${\displaystyle \frac{m}{s^2}\hat{i}+}$
5. ( Enter in box 5) ${\displaystyle \frac{m}{s^2}\hat{j}}$

Which of the following is a correct comment?
*/ Comments */
** Comment **
/* Comment */
{ Comment }
Which of the following is not a correct variable type?
float
int
real
double

The tires of a car make 65 revolutions as the car reduces its speed uniformly from 100 km/h to 50 km/h. The tires have diameter of 0.80 m. a) What was the angular acceleration? b)If the car continues to decelerate at this rate, how much more timeis required for it to stop?
For part a, I thought my method was pretty legitimate, but myanswer didn't match the one in the back of the book. The backof the book had the answer -4.4 ${\displaystyle ra\frac{d}{s^2}}$, whereas Igot $-1.59\cdot {10}^4$ ${\displaystyle ra\frac{d}{s^2}}$

A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between bat and ball is ${\displaystyle 1.00\times {10}^{-3}}$ s,calculate the average force between the bat and ball during contest.

A car heading east through a city accelerates after passing a signpost marking the city limits. It isaccelerating at constant magnitude of 3.0 m/s2. At time t = 0 the car is 5.0 m east of the signpost,moving east at 15 m/s.a) Find the car’s position at t=2.0 s.b) Find the car’s velocity at t=2.0 s.c) Where is the car when its velocity is 25 m/s.

The general solution of the differential equation
${\displaystyle y^n-9y=0}$
can be written in the form
${\displaystyle y\left(x\right)=A{e}^{m_{1}x}+B{e}^{m_{2}x}}$,
where ${\displaystyle A,B,m_1,m_2\in R}$ and ${\displaystyle m_1>m_2}$.
a) Solve the auxiliary equation, and enter the values of ${\displaystyle m_1}$ and ${\displaystyle m_2}$ in the boxes.
Do not enter decimals in your answers. Enter whole numbers, fractions or square roots as appropriate.
If you need to enter a square root, e.g. ${\displaystyle \sqrt{x}}$, enter this as $\sqrt{x}$.
${\displaystyle m_1=}$ ?
${\displaystyle m_2=}$ ?

The analysis on a mass basis of a gas mixture at ${40}^{\circ }F,14.7lbf/i{n}^2$ is 60% ${\displaystyle C{O}^2}$, 25% CO, 15% ${\displaystyle O^2}$.
Determine a. the analysis in terms of mole fractions.
b. the partial pressure of each component, in ${\displaystyle lbf/in{.}^2}$
c. the volume occupied by 10 lb of the mixture, in ${\displaystyle f{t}^3}$.