The term dialysis is based on the Greek word dialuein. meaning "to break up or to dissolve." Explain how this meaning relates to the process of dialysis.

Let R be the fourth-quadrant region bounded by y=x(x-3) and the x-axis.

Write a definite integral in one variable whose value equals the volume of the solid formed when R is revolved about the line x=4.

Write the equation of each line in slope-intercept form. Then graph the line. Through (-6, 2) and (3, 6)

Solve the equation algebraically. Write an equation for the line through the point (-1,2) and parallel to the line 4x+5y=2

A balloon is rising at a constant speed of 5 ft/s. A boy is cycling along a straight road at a speed of 15 ft/s. When he passes under the balloon, it is 45 ft above him. How fast is the distance between the boy and the balloon increasing 3 s later?

It is said that a hospital wants to design a dinner menu containing two items, $M$ and $N$. Each ounce of $M$ provides $1$ unit of vita$\min A$ and $2$ units of vitamin $B$. Each ounce of $N$ provides $1$ unit of $\operatorname{vitamin} A$ and $1$ unit of vitamin $B$. The two dishes must provide at least $7$ units of vitamin $A$ and at least $10$ units of vitamin $B$. If each ounce of $M$ costs $8$ cents and each ounce of $N$ costs $12$ cents, how many ounces of each item should the hospital serve to minimize cost?

A balloon is rising at a constant speed of 5 ft/s. A boy is cycling along a straight road at a speed of 15 ft/s. When he passes under the balloon, it is 45 ft above him. How fast is the distance between the boy and the balloon increasing 3 s later?

An isocost line (iso means “same”) shows the different combinations of labor and capital (the value of factory buildings, machinery, and so on) a company may buy for the same total cost. An isocost line has equation $w L+r K=C$ for $L \geq 0, \ K \geq 0$ where L is the units of labor costing w dollars per unit, K is the units of capital purchased at r dollars per unit, and C is the total cost. Since both L and K must be non-negative, an isocost line is a line segment in just the first quadrant. a. Write the equation of the isocost line with $w = 8, r = 6, C = 15,000,$ and graph it in the first quadrant. b. Verify that the following (L, K) pairs all have the same total cost. (1875, 0), (1200, 900), (600, 1700), (0, 2500)

When a nonideal $1.0~ \mathrm{H}$ inductor is short-circuited, its magnetic energy drops to one-fourth of its original value in $3.6 \mathrm{~s}$. What is its resistance?

Find an equation of the line perpendicular to the line with equation y - 2 = -5(x - 1) passing through the point (-10, 7)

Decide whether the following statement is true or false Explain your reasoning. Jack made the length of the string one-fourth of its original length, and the pitch went up two octaves.

Nolen was cycling toward his home. After $2 \mathrm{~h}$ of cycling he was $55 \mathrm{~km}$ from home, and after $4.5 \mathrm{~h}$ of cycling he was $17.5 \mathrm{~km}$ from home. Assuming he was cycling at a constant rate, how fast was he cycling?

A statement describing the relationship between the variables x, y, and z is given. (a) Express the statement as an equation of proportionality. (b) If x is tripled and y is doubled, by what factor does z change? z is directly proportional to the square of x and inversely proportional to the fourth power of y.

(a) Find an equation of the tangent line to the graph of f at the indicated point. (b) Graph the function and the tangent line. $f(x)=\sin x$ at (0, 0)