Chapter 1: Fundamentals

Dimension of a Garden A homeowner wishes to fence in three adjoining garden plots, one for each of her children, as shown in the figure. If each plot is to be $80{\text{ft}}^2$in area and she has $88\text{ft}$of fencing material at hand, what dimensions should each plot have?

Solve the absolute value Inequality. Express the answer using interval notation and graph the solution set.

$|x+6|\le 0.001$

Some scientists believe that the average surface temperature of the world has been rising steadily. The average surface temperature can bemodeled by where Tis temperature in${}^{\circ }c$ and tis years since 1950.

$T=0.02t+15.0$

(a)What do the slope and T-intercept represent?

(b)Use the equation to predict the average global surface temperature in 2050.

Solve the inequality $\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{>}\mathbf{-}\mathbf{11}$, express the solution using interval notation and graph the solution set on real number line.

Write the number indicated in each statement in scientific notation.

1. A light-year, the distance the light travels in one year, is about $5,900,000,000,000\text{mi}$.
2. The diameter of an electron is about $0.0000000000004\text{cm}$

c. A drop of water contains more than 33 billion billion molecules.

Find the real solutions of the quadratic equation $\frac{x^2}{x+100}=50$.

Factor the expression by grouping terms

$5x^3+x^2+5x+1$

Find the center and radius of the circle, and sketch its graph.

${\left(x+3\right)}^2+{\left(y-4\right)}^2=25$

The post office will accept only packages for which the length plus the “girth” (distance around) is no more than 108 in. Thus, for the package in the figure, we must have $\mathbf{L}\mathbf{+}\mathbf{2}\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{)}\mathbf{\pounds }\mathbf{108}$

(a) Will the post office accept a package that is 6 in. wide, 8 in. deep, and 5 ft long? What about a package that measures 2 ft by 2 ft by 4 ft?

(b) What is the greatest acceptable length for a package that has a square base measuring 9 in. by 9 in.?

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains$1000{\mathrm{ft}}^3$of grains?