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Explain why $x^4–2x^2–3$ is a quadratic polynomial.

The regular price of a computer is x dollars. Let $f(x)=x-400andg(x)=0.75x$. Solve,
a. Describe what the functions f and g model in terms of the price of the computer.
b. Find ${\displaystyle (f\circ g)\left(x\right)}$ and describe what this models in terms of the price of the computer.
c. Repeat part (b) for ${\displaystyle (g\circ f)\left(x\right)}$.
d. Which composite function models the greater discount on the computer, ${\displaystyle f\circ g}$ or ${\displaystyle g\circ f}$?

Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.
$\sum _{n=1}^{\mathrm{\infty }}\frac{\arctan n}{n^2+1}$

If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det$(AB{A}^T)=???$

1)What is the position vector r(t) as a function of angle ${\displaystyle \theta \left(t\right)}$. For later remember that ${\displaystyle \theta \left(t\right)}$ is itself a function of time.
Give your answer in terms of ${\displaystyle R,\theta \left(t\right)}$, and unit vectors x and y corresponding to the coordinate system in thefigure. 2)For uniform circular motion, find ${\displaystyle \theta \left(t\right)}$ at an arbitrary time t.
Give your answer in terms of ${\displaystyle \omega }$ and t.
3)Find r, a position vector at time.
Give your answer in terms of R and unit vectors x and/or y.
4)Determine an expression for the positionvector of a particle that starts on the positive y axis at (i.e., at ,$(x_0,y_0)=(0,R)$) and subsequently moves with constant ${\displaystyle \omega }$.
Express your answer in terms of R, $\omega$ ,t ,and unit vectors x and