Foundations for geometry | Practice Problems, Examples & Solutions

Points, Lines and Planes

Calculus: Early Transcendental Functions

You are asked to work with vectors of dimension higher than three. Use rules analogous to those introduced for two and three dimensions.
$$\|\mathbf{a}+\mathbf{b}\| \text { for } \mathbf{a}=\langle 1,-2,4,1\rangle \text { and } \mathbf{b}=\langle-1,4,2,-4\rangle$$

Vectors and the Geometry of Space

Vectors in Space

03:29

Calculus: Early Transcendental Functions

In the accompanying figure, two ropes are attached to a $500-$ pound crate. Rope $A$ exerts a force of {10,-130,200} pounds on the crate, and rope $B$ exerts a force of {-20,180,160} pounds on the crate. If no further ropes are added, find the net force on the crate and the direction it will move. If a third rope $C$ is added to balance the crate, what force must this rope exert on the crate?
(FIGURE CAN'T COPY)

Vectors and the Geometry of Space

Vectors in Space

02:13

Calculus: Early Transcendental Functions

Find the displacement vectors $\overrightarrow{P Q}$ and $\overrightarrow{Q R}$ and determine whether the points $P=(2,3,1), Q=(4,2,2)$ and $R=(8,0,4)$ are colinear (on the same line).

Vectors and the Geometry of Space

Vectors in Space

Intersections

48 Practice Problems

01:03

Precalculus : Building Concepts and Connections

Find the intersection of the two lines.
$$x=-1, y=2$$

Systems of Equations and Inequalities

Systems of Linear Equations and Inequalities in Two Variables

00:28

Precalculus : Building Concepts and Connections

A jogger on a pre-set treadmill burns 3.2 calories per minute. How long must she jog to burn at least 200 calories?

Functions, Graphs, and Applications

Intersections of Lines and Linear Inequalities

00:29

Precalculus : Building Concepts and Connections

Applications In this set of exercises you will use the concepts of intersection of lines and linear inequalities to study real-world problems.
Cost and Revenue In Exercises $69-72,$ for each set of cost and revenue functions, (a) find the break-even point and (b) calculate the values of $q$ for cohich retucnue exceeds cost.
$$\begin{aligned} &C(q)=8 q+150\\ &R(q)=10 q \end{aligned}$$

Functions, Graphs, and Applications

Intersections of Lines and Linear Inequalities

Constructions

91 Practice Problems

02:06

Basic Mathematical Skills with Geometry

The closing prices for Kellogg Company stock are shown during the same 2 -week period in 2003 as the Adobe Systems data in exercise 37.
CAN'T COPY THE TABLE
(a) Construct a box-and-whisker plot for the Kellogg Company closing stock price data.
(b) Describe any distinctive features shown by the plot.
(c) Compare your plot with the one constructed in exercise 37 .

Data Analysis and Statistics

Describing and Summarizing Data Sets

05:03

Basic Mathematical Skills with Geometry

This table gives the total U.S. population by age group, according to the 2000 census.
\begin{array}{cl}
\hline \text { Age } & \text { Population } \\
\hline 0-14 & 60,224,094 \\
15-34 & 79,079,301 \\
35-54 & 82,737,774 \\
55-74 & 42,494,571 \\
75+ & 16,603,839 \\
\hline \text {Source: U.S. Census Bureau. }
\end{array}
Construct a bar graph from this information.

Data Analysis and Statistics

Creating Bar Graphs and Pie Charts

02:46

Basic Mathematical Skills with Geometry

The graph and table show the income to the Hospital Insurance Trust Fund. Use this information to predict the income in the year 2005 .
$$\begin{array}{ll} \text { Year } & \text { Total Income (in millions of } \mathbf{S} \text { ) } \\ \hline 1975 & 12,568 \\ 1980 & 25,415 \\ 1990 & 79,563 \\ 1995 & 114,847 \\ 2000 & 130,559 \end{array}$$

Data Analysis and Statistics

Line Graphs and Predictions