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Calculus With Trigonometry and Analytic Geometry

John Saxon, Frank Wang, Diana Harvey

Chapter 12

Absolute value as a distance - The line as a locus - The circle as a locus - all with Video Answers

Educators

Chapter Questions

03:17

Problem 1

On the assembly line, $w$ workers worked $h$ hours to produce $x$ items. If $y$ workers quit, how many hours would it take the remaining workers to produce the same number of items?

JP
Jiji Peter
Numerade Educator
00:56

Problem 2

The ratio of scallops to crayfish was 3 to 1 and the ratio of crayfish to prawns was 2 to 1 . If there were 18 scallops, crayfish, and prawns in all, how many of each were there?

Alison Rodriguez
Alison Rodriguez
Numerade Educator
02:47

Problem 3

Evelyn and Jeannie each had containers which held mixtures of alcohol and disinfectant. Evelyn's container was $40 \%$ disinfectant and Jeannie's container was $80 \%$ disinfectant. If Derek wants 600 milliliters of a solution that is $p \%$ disinfectant, how much solution should he use from Evelyn's container and how much from Jeannie's container?

Daniel Carr
Daniel Carr
Numerade Educator
00:27

Problem 4

Graph the set $\{x \in \mathbb{R}|| x-3 \mid<4\}$ on the number line.

Amy Jiang
Amy Jiang
Numerade Educator
00:33

Problem 5

Graph the set of all integers such that $|2 x-1|>6$.

Amy Jiang
Amy Jiang
Numerade Educator
02:36

Problem 6

Write the general form of the equation of the straight line whose points are equidistant from the points $(1,-3)$ and $(-1,2)$.

Aman Gupta
Aman Gupta
Numerade Educator
00:36

Problem 7

Write the standard form and the general form of the equation of the circle whose center is the point $(-1,3)$ and whose radius is 3 .

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:05

Problem 8

Describe the circle whose equation is given by
$$
x^2+y^2+6 x-6 y+2=0
$$

Carson Merrill
Carson Merrill
Numerade Educator
00:44

Problem 9

Represent the real vector $-i+\sqrt{3} j$ in polar coordinates.

Wendi Zhao
Wendi Zhao
Numerade Educator
00:34

Problem 10

Compute the value of $\left(2\right.$ cis $\left.20^{\circ}\right)\left(3\right.$ cis $\left.25^{\circ}\right)$ and write the answer in rectangular form. (All numbers must be exact.)

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:34

Problem 11

Sketch the graph of $y=e^{-x}$.

Gregory Higby
Gregory Higby
Numerade Educator
02:05

Problem 12

Divide by $\sin ^2 x$ and $\cos ^2 x$ to develop two other forms of the identity $\sin ^2 x+$ $\cos ^2 x=1$.

Linh Vu
Linh Vu
Numerade Educator
04:19

Problem 13

Simplify: $\sin (-\theta) \sec (-\theta) \cos ^2 \theta \csc \left(\frac{\pi}{2}-\theta\right)$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:20

Problem 14

Show that: $\left(\csc ^2 \theta-1\right) \sin ^2 \theta \sec (-\theta)=\cos \theta$

Shubham Purohit
Shubham Purohit
Numerade Educator
03:03

Problem 15

Find the value of $\cos \left(\frac{\pi}{2}-\beta\right) \sin (-\beta)$ if $\sin \beta=\frac{1}{3}$.

Linh Vu
Linh Vu
Numerade Educator
00:29

Problem 16

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the quadratic function $y=2 x^2+2 x-3$.

Amrita Bhasin
Amrita Bhasin
Numerade Educator
02:43

Problem 17

Solve for $b$ in terms of $x$ and $y$ in the figure shown.
(Figure can't copy)

Debasish Das
Debasish Das
Numerade Educator
01:39

Problem 18

Sketch the sinusoid $y=-2+3 \sin \left(x+\frac{\pi}{2}\right)$.

Linh Vu
Linh Vu
Numerade Educator
02:39

Problem 19

Find the domain and range of $y=x^2-1$.

Gregory Higby
Gregory Higby
Numerade Educator
00:40

Problem 20

If $f(x)=x^2$, evaluate: $\sum_{i=1}^3 f(i)$

Ad F
Ad F
Numerade Educator
00:23

Problem 21

State the contrapositive of the following statement: If the light is on, then the switch is on.

MB
Manav Bhatia
Numerade Educator
00:41

Problem 22

If $x<0$, compare: A. $x$
B. $x^2$

Alex Roush
Alex Roush
Numerade Educator
04:42

Problem 23

If $\overline{A D}$ is the angle bisector of $\angle A$ of $\triangle \mathrm{ABC}$ as shown, and if $\overline{A B}, \overline{A C}, \overline{B D}$, and $\overline{D C}$ have lengths $x, y, x^2$, and $z$, respectively, then solve for $x$ in terms of $y$ and $z$.
(Figure can't copy)

Anas Venkitta
Anas Venkitta
Numerade Educator