How does a large population create problems for a developing country?

Find the critical numbers of the function.

$$h ( t ) = t ^ { 3 / 4 } - 2 t ^ { 1 / 4 }$$

Let $V$ and $W$ be vector spaces, and let $S$ be a subset of $V .$ Define $S^{0}=\{T \in \mathcal{L}(V, W) : T(x)=0$ for all $x \in S\} .$ Prove the following statements. $\\$ (a)$S^{0}$is a subspace of$$\mathcal{L}$($\mathrm{V}$, $\mathrm{W}$) $(b) If$S_{1}$and$S_{2}$are subsets of$$\mathrm{V} and$S_{1} \subseteq S_{2},$then$S_{2}^{0} \subseteq S_{1}^{0} $(c) If$$\mathrm{V}${1}$and$$\mathrm{V}${2}$are subspaces of$$\mathrm{V}$,$then$\left($\mathrm{V}${1}+$\mathrm{V}${2}\right)^{0}=$\mathrm{V}${1}^{0} \cap $\mathrm{V}${2}^{0}$

Indicate whether the following statements are true or false. Explain. The refrigerant flowing through the compressor in a vaporcompression refrigeration system is generally in the super-heated vapor phase.

Using $f(x)=\sin x$ or $f(x)=\cos x$ as a guide, graph each function. Identify the $x$ -intercepts and phase shift.
$h(x)=\cos \left(x+\frac{5 \pi}{4}\right)$

Explain how to find the critical value $z_{\frac{\alpha}{2}}$ that corresponds to a $93$ confidence level?

Answer the following questions about the functions whose derivatives are given. What are the critical points of f?

$$f^{\prime}(x)=x(x-1)$$

Find the critical points for

$$R(t)= -0.2 t^3 + 1.64 t^2 + 1.31t + 3.2$$

Find the critical points, relative extrema, and saddle points of the function. $f(x, y)=x^{2}+y^{2}+2 x-6 y+6$

Explain what is meant by a phase difference. Sketch graphs of i(t) and $v_C(t)$ given tat the current leads the voltage by $\pi / 2$ radians.

In what ways was the Confederation too weak to handle the nation's problems?

Write these problems in vertical form. Then multiply.

$$603 \times 250$$

After shuffling a deck of 52 cards, a dealer deals out 5. Let X = the number of suits represented in the five-card hand. a. Show that the pmf of X is

$$\begin{matrix} \text{x} & \text{1} & \text{2} & \text{3} & \text{4}\\ \text{p(x)} & \text{.002} & \text{.146} & \text{.588} & \text{.264}\\ \end{matrix}$$

[Hint: p(1) = 4P(all are spades), p(2) = 6P(only spades and hearts with at least one of each suit), and p(4) = 4P(2 spades $\cap$ one of each other suit).] b. Compute $\mu, \sigma^{2},$ and $\sigma$.

Critical Thinking Write equations of two lines that satisfy each description. parallel and neither has a y-intercept