A pilot of a small airplane wants to travel at 225 kilometers per hour over the ground. She knows that she is flying directly into a wind that is blowing at 38 kilometers per hour. What should the speedometer of her airplane read, in order to maintain a ground speed of 225 km/hr?

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the x-axis.

$$y=x+2, y=x+6, x=0, \text { and } x=5$$

Fill in the blanks with the correct vocabulary term from the Study Guide page. The field of __________ uses computers to index and organize information created by sequencing the human genome.

Show that the given equation has no rational roots. $x ^ { 3 } + 13 x ^ { 2 } - 6 x - 2 = 0$

Find $y^{\prime}$ and $y^{\prime \prime}$

$$x^{2}-y^{2}=4+5 x$$

How many eight-bit strings contain exactly three 0's?

If $f(x)$ has a vertical asymptote and $x=c$, then either $\lim _{x \rightarrow c^{-}} f(x)=\lim _{x \rightarrow c^{+}} f(x)=\infty$ or $\lim _{x \rightarrow c^{-}} f(x)=\lim _{x \rightarrow c^{+}} f(x)=-\infty$. Justify your answer.

Solve the given differential equation.

$$\frac { d y } { d x } + \frac { 2 x } { 1 - x ^ { 2 } } y = 4 x , \quad - 1 < x < 1$$

Completa cada frase con la palabra apropiada: Paco y Ana son mis tíos. Sus hijos son mis BLANK.

Factor the expression completely. $\left(a^{2}-1\right) b^{2}-4\left(a^{2}-1\right)$

A shadow from a surgeon’s hand obstructs her view while operating. Make suggestions for an alternative light source that avoids this difficulty. Include one or more sketches for your proposed plan.

Assume that scores on a bone mineral density test are normally distributed with a mean of 0 and a standard deviation of 1. Find the score separating the lowest 9% of scores from the highest 91 %.

In the article "On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals," by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: "Independent simple random samples, each of size 200, have been drawn, and 112 people in the first sample have the attribute, whereas 88 people in the second sample have the attribute." Construct individual 95% confidence interval estimates for each of the two population proportions. After comparing the overlap between the two confidence intervals, what do you conclude about the equality of p1 and p2?

Imagine you are a bio-engineer, designing the perfect vegetable. Determine your vegetable’s health and/or food production benefits. Describe its color, texture, flavor, and how it would be prepared. Provide a written description and visual sketch of your vegetable.