Work cooperatively. Use a graphing calculator to find where each pair of graphs intersect.

$$\begin{array}{l}{2 x+4 y=4} \\ {x+3 y=13}\end{array}$$

On what interval is the curve

$$y=\int_{0}^{x}\frac{t^2}{t^2+t+2} d t$$

The graphs of r = cos theta and r = 2 cos 2 theta intersect in how many points?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Simplify the expression.

$$\frac{3 t^2}{t+2} \cdot \frac{t+2}{t^2}$$

In this exercise, verify each identity.

$$\frac{\tan ^2 t}{\sec t}=\sec t-\cos t$$

Find the indefinite integral. $\int \frac{t^{3}+\sqrt[3]{t}}{t^{2}} d t$

Determine whether the following statements are true and give an explanation or counterexample. The graphs of

$$r \cos \theta = 4$$

and

$$r \sin \theta = - 2$$

intersect exactly once.

If one root of a polynomial equation with real coefficients is 4 + 2i, is it certain that 4 - 2i is also a root of the equation? Explain.

Find the point at which the given lines intersect: r=<1, 1, 0>+t<1, -1, 2>, r=<2, 0, 2>+s<-1, 1, 0>

Find all of the points at which the parabolas below intersect. Write your solution(s) in (x, y) form.

$$\begin{array} { l } { y = x ^ { 2 } - x + 12 } \\ { y = 2 x ^ { 2 } + 3 x + 7 } \end{array}$$

Your classmate says, "If the diagonals of a quadrilateral intersect to form four congruent triangles, then the quadrilateral is always a parallelogram." How would you correct this statement? Explain your answer.

In this exercise, verify each identity.

$$\frac{\cot ^2 t}{\csc t}=\csc t-\sin t$$

Multiply.

$$\frac{4 t+4}{t-3} \cdot\left(t^2-t-6\right)$$

Put the following in order, from smallest and simplest, to largest and most complex, and describe their individual roles in homeostasis: organ, molecule, organelle, atom, organ system, tissue, organism, cell, macromolecule.