Why are each of the following statements confusing, and how would you make them clear using metric (SI) units?

a. I rode my bicycle for a distance of 15 today.

b. My dog weighs 15 .

c. It is hot today. It is 30 .

d. I lost 1.5 last week.

Write an equation of the line with the given characteristics.

points: $(5,0),(-3,2)$

Let

$$\mathbf{F}=\frac{y}{x^2+y^2} \mathbf{i}-\frac{x}{x^2+y^2} \mathbf{j}=M \mathbf{i}+N \mathbf{j}$$

(a) Show that $\partial N / \partial x=\partial M / \partial y$.

(b) Show, by using the parametrization $x=\cos t, y=\sin t$, that $\oint_C M d x+N d y=-2 \pi$, where C is the unit circle.

(c) Why doesn't this contradict Green's Theorem?

Each family in a neighborhood is contributing $\$ 20$ worth of food to the neighborhood picnic. The Harlin family is bringing 12 packnges of buns. The hamburger buns cost $\$ 2.00$ per package. The hot-dog buns cost $\$ 1.50$ per package. How many packages of each type of bun did they buy?

Using $\iint_R \nabla^2 w d x d y=\oint_C \frac{\partial w}{\partial n} d s$, evaluate $\oint_C \frac{\partial w}{\partial n} d s$ counterclockwise over the boundary curve $C$ of the region $R$. (Show the details of your work.) $w=x^5 y+x y^5, \quad R: x^2+y^2 \leqq 1, x \geqq 0, y \geqq 0$.

Determine the partial derivative with respect to x and the partial derivative with respect to y at x=3 and y=2 for $f(x, y)=7 x^2 y^5+2 y+5 x^3+1$.

Draw and Label the bones and features indicated on the anterior view of the Right knee , using the terms provided
Femur

Compare and contrast rotation and revolution from the point of view of angular motion. Then give an astronomical example of each.

An analog switch uses an $n$-channel MOSFET with $V_{\mathrm{GS}(\mathrm{th})}=4 \mathrm{~V}$. A voltage of $+8 \mathrm{~V}$ is applied to the gate. Determine the maximum peak-to-peak input signal that can be applied if the drainto-source voltage drop is neglected.

The flow in a long shallow channel is modeled by the velocity field $F=\left\langle 0,1-x^2\right\rangle$, where $R=\{(x, y):|x| \leq 1$ and $|y|<5\}$. How do you explain the fact that the curl of $F$ is nonzero at points of $R$, but the circulation is zero?

Combine the four sentences into an effective topic sentence, or write a topic sentence accompanied by one or more supporting details.
a. Ernie sells hot dogs. b. He is weird, yet lovable. c. Everyone in town knows and likes him. d. He is part of what makes our town interesting.

A hot-air balloon is rising vertically. From a point on level ground $125$ feet from the point directly under the passenger compartment, the angle of elevation to the ballon changes from $19.2^{\circ}$ to $31.7^{\circ}$. How far, to the nearest tenth of a foot, does the balloon rise during this period?

A hot-air balloon rises vertically from the ground so that its height after t sec is $h=\frac{1}{2} t^{2}+\frac{1}{2} t \mathrm{ft}(0 \leq t \leq 60)$

What is the velocity of the balloon at the end of 40 sec?

The most common type of mirage is an illusion that light from faraway objects is reflected by a pool of water that is not really there. Mirages are generally observed in deserts, when there is a hot layer of air near the ground. Given that the refractive index of air is lower for air at higher temperatures, explain how mirages can be formed.