Complete each statement by writing the correct word or words. Relatively minor changes in an organism's genome can produce major changes in an organism's _.

Explain how the Venn diagrams in this lesson show that all integers and all whole numbers are rational numbers.

Aimez-vous ces choses? Utilisez leur/leurs ou son/sa/ses dans vos r$\'e$ponses.

les CD de Sting

Determine whether the series is convergent or divergent. If it is convergent, find its sum.

$$\displaystyle\sum_{k=1}^{\infty}(\cos 1)^k$$

Prove that a nonempty subset A of V is an affine subset of V if and only if $\lambda v+(1-\lambda) w \in A$ for all $v, w \in A$ and all $\lambda \in \mathbf{F}.$

Match each equation in Column I with the appropriate description in Column II.

$$\begin{array}{ll} \mathbf{I}&\mathbf{II}\\ (y-1)^2-(x-2)^2=36&\text{A. Circle; center }(1,-2); \text{radius} 6\\ &\text{B. Hyperbola; center }(2,1)\\ &\text{C. Ellipse; major axis on }x\text{-axis}\\ &\text{D. Ellipse; major axis on }y\text{-axis}\\ &\text{E. Parabola; opens right}\\ &\text{F. Hyperbola; transverse axis on $y$-axis}\\ \end{array}$$

Consider the following statements:

int num1, num2, num3;
double length, width, height;
double volume;
num1 = 6; num2 = 7; num3 = 4;
length = 6.2; width = 2.3; height = 3.4;
and the function prototype:
double box(double, double, double);

Is given statement valid? If not, explain why. cout << box(6.2, , height) << endl

Estimate the deceleration of a water particle in a raindrop as it strikes the sidewalk. List all assumptions and show all calculations.

Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum.

$$a+a b^2+a b^4+a b^6+\cdots, \quad|b|<1$$

Determine whether $\displaystyle\int_{-\infty}^6 r e^{r / 3} d r$ is convergent or divergent. Evaluate if the integral is convergent.

Use Cramer's rule to solve the following system. See the earlier examples.

$$\left\{\begin{aligned} 23 x+21 y & =-4 \\ x-3 y & =-8\end{aligned}\right.$$

Determine whether the series is convergent or divergent. If it is convergent, find its sum.

$$\sum_{n=1}^{\infty}\left[(0.8)^{n-1}-(0.3)^n\right]$$

Numerical and Graphical Analysis An open box is to be made from a square piece of material, $36$ inches on a side, by cutting equal squares with sides of length $x$ from the corners and turning up the sides (see figure).

(c ) Use a graphing utility to create a table that shows box heights $x$ and the corresponding volumes $V$. Use the table to estimate the dimensions that will produce a maximum volume.

Suppose that f is differentiable for all $x \in \mathbf{R}$ with f(2) = 3 and $f^{\prime}(x)=0$ for all $x \in \mathbf{R}.$ Find f(x).