Question 1

Find the vertex and equation of the axis of the parabola $y=2 x^{2}-7 x-15$.

Accepted Answer

The answer of Find the vertex and equation of the...

Question 2

$r=6 \cos 4 \theta$

Accepted Answer

The answer of $r=6 \cos 4 \theta$...

Question 3

Find the $x$ - coordinate(s) of the solution of the system of equations $9 y^{2}-16 x^{2}=144$ and $y=-0.5 x+$ 4.

Accepted Answer

A)  -1.2 and 3.82 
B)  3.4 and 5.91 
C)  -3.82 and 1.2 
D)  1.2 
A)  -1.2 and 3.82 
B)  3.4 and 5.91 
C)  -3.82 and 1.2 
D)  1.2

Question 4

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes.
-  $\frac{y^{2}}{100}-\frac{x^{2}}{81}=1$

Accepted Answer

The answer of For the problems below, find the vertices,...

Question 5

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse.
-  $25 x^{2}+144 y^{2}=3600$

Accepted Answer

The answer of For the problems below, find the vertices,...

Question 6

Graph each equation.
- $3 x-2 y=12$

Accepted Answer

The answer of Graph each equation.
- $3 x-2 y=12$...

Question 7

An object dropped from an airplane $3250 \mathrm{~m}$ above the ground falls according to the equation $\mathrm{h}=$ $3250-4.95 t^{2}$, where $h$ is the height in metres above the ground and $t$ is the time in seconds. Find the time for the object to fall a height of $2755 \mathrm{~m}$ above the ground.

Accepted Answer

A)  $8.0 \mathrm{~s}$ 
B)  $1 \overline{0} \mathrm{~s}$ 
C)  $17 \mathrm{~s}$ 
D)  $2 \overline{0} \mathrm{~s}$ 
A)  $8.0 \mathrm{~s}$ 
B)  $1 \overline{0} \mathrm{~s}$ 
C)  $17 \mathrm{~s}$ 
D)  $2 \overline{0} \mathrm{~s}$

Question 8

Determine whether or not triangle $\mathrm{ABC}$ is a right triangle. A $(-1.6,4.2), B(8,9), C(5,-9)$

Accepted Answer

A) True 
 B)False

Question 9

Determine whether or not each relation is a function. Write its domain and range.
-  $\{(-3,4),(-3,6),(-3,8),(-3,10)\}$

Accepted Answer

The answer of Determine whether or not each relation is...

Question 10

Change the point $\left(5, \frac{2 \pi}{3}\right)$ in the polar coordinate system to the equivalent point in the rectangular coordinate system.

Accepted Answer

A)  $(-2.5,-4.33)$ 
B)  $(-2.5,4.33)$ 
C)  $(4.33,-2.5)$ 
D)  $(-4.33,2.5)$ 
A)  $(-2.5,-4.33)$ 
B)  $(-2.5,4.33)$ 
C)  $(4.33,-2.5)$ 
D)  $(-4.33,2.5)$

Question 11

Ellipse with center at (-3, 7), vertices at (-3, 20) and (-3, - 6) and minor axis of length 10.

Accepted Answer

The answer of Ellipse with center at (-3, 7), vertices...

Question 12

Graph the circle with center at ( $-2,-3)$ and $r=4$.

Accepted Answer

The answer of Graph the circle with center at (...

Question 13

Find the focus and the directrix of the parabola $y^{2}=-20 x$.

Accepted Answer

The answer of Find the focus and the directrix of...

Question 14

Use the substitution method to find the real solutions for the following system of equations. Round to two significant digits. $\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$ and $(x-3)^{2}+y^{2}=9$

Accepted Answer

The answer of Use the substitution method to find the...

Question 15

Find the equation of a line that passes through the point $(3,-8)$ and is parallel to $2 x-y=6$.

Accepted Answer

The answer of Find the equation of a line that...

Question 16

For the problems below, find the equation of each curve from the given information.
-Parabola with vertex at $(3,4)$, focus at $(3,6)$ and directrix $y=2$.

Accepted Answer

The answer of For the problems below, find the equation...

Question 17

Write the equation of the ellipse with center at (3, 4), vertices at (10, 4) and (-4, 4), and foci at (7, 4) and $(-1,4)$.

Accepted Answer

A)  $\frac{(\mathrm{x}-3)^{2}}{49}+\frac{(\mathrm{y}-4)^{2}}{33}=1$ 
B)  $\frac{(\mathrm{x}-3)^{2}}{49}+\frac{(\mathrm{y}-4)^{2}}{16}=1$ 
C)  $\frac{(\mathrm{x}-3)^{2}}{33}+\frac{(\mathrm{y}-4)^{2}}{49}=1$ 
D)  $\frac{(x+3)^{2}}{49}+\frac{(y+4)^{2}}{33}=1$ 
A)  $\frac{(\mathrm{x}-3)^{2}}{49}+\frac{(\mathrm{y}-4)^{2}}{33}=1$ 
B)  $\frac{(\mathrm{x}-3)^{2}}{49}+\frac{(\mathrm{y}-4)^{2}}{16}=1$ 
C)  $\frac{(\mathrm{x}-3)^{2}}{33}+\frac{(\mathrm{y}-4)^{2}}{49}=1$ 
D)  $\frac{(x+3)^{2}}{49}+\frac{(y+4)^{2}}{33}=1$

Question 18

Find the equation of the parabola with focus $\mathrm{F}(0,-3)$ and directrix $\mathrm{y}=3$.

Accepted Answer

The answer of Find the equation of the parabola with...

Question 19

Find the slope of the line perpendicular to $y=\frac{3}{5} x+2$.

Accepted Answer

The answer of Find the slope of the line perpendicular...

Question 20

Find the equation of the circle (in standard form) with center at $(7,3)$ and passing through $(6,-2)$.

Accepted Answer

The answer of Find the equation of the circle (in...

Find the vertex and equation of the axis of the parabola $y=2 x^{2}-7 x-15$ .

$r=6 \cos 4 \theta$

Find the $x$ - coordinate(s) of the solution of the system of equations $9 y^{2}-16 x^{2}=144$ and $y=-0.5 x+$ 4.

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes. - $\frac{y^{2}}{100}-\frac{x^{2}}{81}=1$

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse. - $25 x^{2}+144 y^{2}=3600$

Graph each equation. - $3 x-2 y=12$

Determine whether or not triangle $\mathrm{ABC}$ is a right triangle. A $(-1.6,4.2), B(8,9), C(5,-9)$

Determine whether or not each relation is a function. Write its domain and range. - $\{(-3,4),(-3,6),(-3,8),(-3,10)\}$

Change the point $\left(5, \frac{2 \pi}{3}\right)$ in the polar coordinate system to the equivalent point in the rectangular coordinate system.

Ellipse with center at (-3, 7), vertices at (-3, 20) and (-3, - 6) and minor axis of length 10.

Graph the circle with center at ( $-2,-3)$ and $r=4$ .

Find the focus and the directrix of the parabola $y^{2}=-20 x$ .

Use the substitution method to find the real solutions for the following system of equations. Round to two significant digits. $\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$ and $(x-3)^{2}+y^{2}=9$

Find the equation of a line that passes through the point $(3,-8)$ and is parallel to $2 x-y=6$ .

For the problems below, find the equation of each curve from the given information. -Parabola with vertex at $(3,4)$ , focus at $(3,6)$ and directrix $y=2$ .

Write the equation of the ellipse with center at (3, 4), vertices at (10, 4) and (-4, 4), and foci at (7, 4) and $(-1,4)$ .

Find the equation of the parabola with focus $\mathrm{F}(0,-3)$ and directrix $\mathrm{y}=3$ .

Find the slope of the line perpendicular to $y=\frac{3}{5} x+2$ .

Find the equation of the circle (in standard form) with center at $(7,3)$ and passing through $(6,-2)$ .

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Exam 1: Analytic Geometry

Find the vertex and equation of the axis of the parabola y=2x2−7x−15y=2 x^{2}-7 x-15y=2x2−7x−15 .

r=6cos⁡4θr=6 \cos 4 \thetar=6cos4θ

Find the xxx - coordinate(s) of the solution of the system of equations 9y2−16x2=1449 y^{2}-16 x^{2}=1449y2−16x2=144 and y=−0.5x+y=-0.5 x+y=−0.5x+ 4.

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes. - y2100−x281=1\frac{y^{2}}{100}-\frac{x^{2}}{81}=1100y2​−81x2​=1

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse. - 25x2+144y2=360025 x^{2}+144 y^{2}=360025x2+144y2=3600

Graph each equation. - 3x−2y=123 x-2 y=123x−2y=12

Determine whether or not triangle ABC\mathrm{ABC}ABC is a right triangle. A (−1.6,4.2),B(8,9),C(5,−9)(-1.6,4.2), B(8,9), C(5,-9)(−1.6,4.2),B(8,9),C(5,−9)

Determine whether or not each relation is a function. Write its domain and range. - {(−3,4),(−3,6),(−3,8),(−3,10)}\{(-3,4),(-3,6),(-3,8),(-3,10)\}{(−3,4),(−3,6),(−3,8),(−3,10)}

Change the point (5,2π3)\left(5, \frac{2 \pi}{3}\right)(5,32π​) in the polar coordinate system to the equivalent point in the rectangular coordinate system.

Ellipse with center at (-3, 7), vertices at (-3, 20) and (-3, - 6) and minor axis of length 10.

Graph the circle with center at ( −2,−3)-2,-3)−2,−3) and r=4r=4r=4 .

Find the focus and the directrix of the parabola y2=−20xy^{2}=-20 xy2=−20x .

Use the substitution method to find the real solutions for the following system of equations. Round to two significant digits. x216−y225=1\frac{x^{2}}{16}-\frac{y^{2}}{25}=116x2​−25y2​=1 and (x−3)2+y2=9(x-3)^{2}+y^{2}=9(x−3)2+y2=9

Find the equation of a line that passes through the point (3,−8)(3,-8)(3,−8) and is parallel to 2x−y=62 x-y=62x−y=6 .

For the problems below, find the equation of each curve from the given information. -Parabola with vertex at (3,4)(3,4)(3,4) , focus at (3,6)(3,6)(3,6) and directrix y=2y=2y=2 .

Write the equation of the ellipse with center at (3, 4), vertices at (10, 4) and (-4, 4), and foci at (7, 4) and (−1,4)(-1,4)(−1,4) .

Find the equation of the parabola with focus F(0,−3)\mathrm{F}(0,-3)F(0,−3) and directrix y=3\mathrm{y}=3y=3 .

Find the slope of the line perpendicular to y=35x+2y=\frac{3}{5} x+2y=53​x+2 .

Find the equation of the circle (in standard form) with center at (7,3)(7,3)(7,3) and passing through (6,−2)(6,-2)(6,−2) .

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Find the vertex and equation of the axis of the parabola $y=2 x^{2}-7 x-15$ .

$r=6 \cos 4 \theta$

Find the $x$ - coordinate(s) of the solution of the system of equations $9 y^{2}-16 x^{2}=144$ and $y=-0.5 x+$ 4.

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes. - $\frac{y^{2}}{100}-\frac{x^{2}}{81}=1$

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse. - $25 x^{2}+144 y^{2}=3600$

Graph each equation. - $3 x-2 y=12$

Determine whether or not triangle $\mathrm{ABC}$ is a right triangle. A $(-1.6,4.2), B(8,9), C(5,-9)$

Determine whether or not each relation is a function. Write its domain and range. - $\{(-3,4),(-3,6),(-3,8),(-3,10)\}$

Change the point $\left(5, \frac{2 \pi}{3}\right)$ in the polar coordinate system to the equivalent point in the rectangular coordinate system.

Graph the circle with center at ( $-2,-3)$ and $r=4$ .

Find the focus and the directrix of the parabola $y^{2}=-20 x$ .

Use the substitution method to find the real solutions for the following system of equations. Round to two significant digits. $\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$ and $(x-3)^{2}+y^{2}=9$

Find the equation of a line that passes through the point $(3,-8)$ and is parallel to $2 x-y=6$ .

For the problems below, find the equation of each curve from the given information. -Parabola with vertex at $(3,4)$ , focus at $(3,6)$ and directrix $y=2$ .

Write the equation of the ellipse with center at (3, 4), vertices at (10, 4) and (-4, 4), and foci at (7, 4) and $(-1,4)$ .

Find the equation of the parabola with focus $\mathrm{F}(0,-3)$ and directrix $\mathrm{y}=3$ .

Find the slope of the line perpendicular to $y=\frac{3}{5} x+2$ .

Find the equation of the circle (in standard form) with center at $(7,3)$ and passing through $(6,-2)$ .