As Mark Ellon is getting ready for a meeting, the room goes dark. He fishes for a green shirt in his

Solve for y: 0=u-5y+1.

Soo, fix $0\le ϵ\le 1$. Given $\lambda \ge 1,x_i\ge 0$, I know that $\sum _{i=1}^n{x}_i\ge \lambda n$. I also know that $\sum _{i=1}^n{x}_i^2\le {\lambda }^{2}n+ϵ$. I am trying to prove a multiplicative error on each $x_i$, mainly something along the lines of
$|x_i-\lambda |\le f(ϵ)\lambda$
Where $f(ϵ)$ is some function of $ϵ$, say $f(ϵ)=2ϵ$. Is there any inequality that would bound that distance?

T-Shirts The Physics Club sells ${\displaystyle E=m{c}^2}$.
T-shirts at the local flea market. Unfortunately, the club’s previous
administration has been losing money for years, so you decide to do an
analysis of the sales. A quadratic
regression based on old sales data reveals the following demand equation for the T-shirts:
${\displaystyle q=-2p+33p(9\le p\le 15)2}$
 Here, p is the price the club charges per T-shirt and q is the
number it can sell each day at the flea market. a. Obtain a formula for
the price elasticity of demand for ${\displaystyle E=m{c}^2}$ T-shirts. b. Compute the
elasticity of demand if the price is set at $10 per shirt. Interpret the
result. c. How much should the Physics Club charge for the T-shirts to
obtain the maximum daily revenue? What will this revenue be?"

4.3-16. Two random variables X and Y have a joint density
${\displaystyle f_{x,y}(x,y)=\frac{10}{4}[u\left(x\right)-u(x-4)]u\left(y\right)y^3\exp [-(x+1)y^2]}$
Find the marginal densities and distributions of X and Y.

Solve for w in the equation y-1=4wy-6.

COnsider the multivariable function ${\displaystyle g(x,y)=x^2-3y^4{x}^2+\sin \left(xy\right)}$. Find the following partial derivatives: ${\displaystyle g_x.g_y,g_{xy},g(\times ),g\left(yy\right)}$.

1. Given a complex valued function can be written as $f(z)=w=u(x,y)+iv(x,y)$, where w is the real part of w and v is the imaginary part of v. Using algebraic manipulation figure out what wu and v is if
${\displaystyle f\left(z\right)=\bar{z}(1-e^{i(z+\bar{z})})}$
Here ${\displaystyle \bar{z}}$ denotes the complex conjugate of z.
2. Using the concept of limits figure out what the second derivative of ${\displaystyle f\left(z\right)=z(1-z)}$ is.
3. Use the theorems of Limits that have been discussed before to show that
${\displaystyle \underset{z\to 1-i}{lim}[x+i(2x+y)]=1+i.[\text{Hint: Use }z=x+iy]}$