Resources

Resources

Write equations of cosine functions using properties

y = -\frac{1}{2}x + \frac{1}{4}

defines a relationship between

x

y

x

is the input and

y

is the output. Which statements about the relationship are true? Select all that apply.

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Multi-select Choices:

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(A)The graph is a straight line.

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(B)When the input is

2

, the output is

-1

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(C)The rate of change is constant.

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y

is a function of

x

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(E)The y-intercept is

(0,-\frac{1}{2})

Which formulas represent linear relationships? Select all that apply.

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Multi-select Choices:

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(A)the area of a circle,

A = \pi r^2

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(B)the perimeter of a regular hexagon,

P = 6s

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(C)the volume of a sphere,

V = \frac{4}{3} \pi r^3

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(D)the perimeter of an isosceles right triangle,

P = (2 + \sqrt{2})s

Determine whether or not

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F

is a conservative vector field. If it is, find a function

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f

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F= f

. (If the vector field is not conservative, enter DNE.)

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f(x,y)=\square(x,y)=(ye^{x}+\sin(y))i+(e^{x}+x \cos(y))j

Function A is a linear function. An equation for Function A is

3x + 4y = 28

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Which of the following functions has the same slope as Function A?

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y = -\frac{3}{4}x + \frac{4}{3}

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y = \frac{3}{4}x - \frac{4}{3}

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y = \frac{4}{3}x - \frac{3}{4}

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y = -\frac{4}{3}x + \frac{3}{4}

A

is a linear function whose graph includes the points

(0,-7)

(3,0)

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Which of the following functions has the same

y

-intercept as Function

A

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y = -7

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y = -\frac{7}{3}x

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y = 3

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y = \frac{7}{3}x

Function A is a linear function whose graph includes the points

(0,-7)

(3,0)

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Which of the following functions has the same

y

-intercept as Function A?

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y = -\frac{7}{3}x

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y = \frac{7}{3}x

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y = 3

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y = -7

At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is

50^{\circ}

Celsius. This causes the cake to cool and the temperature difference loses

\frac{1}{5}

of its value every minute.

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Write a function that gives the temperature difference in degrees Celsius,

D(t), t

minutes after the cake was put in the cooler.

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D(t)=

\square

The derivative of a function

g

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g^{\prime}(x)=3 \sin (x)+\ln (x) \text {. }

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How many relative extremum points does the graph of

g

have on the interval

1<x<5

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Use a graphing calculator.

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1

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A fly is standing on a boulder, which is rolling down a hill. The forward torque the fly exerts on the boulder when it has rolled

x

meters, in newton meters, is given by

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\tau(x)=\frac{2}{1000} \sin \left(\frac{2 \pi(x+0.2)}{4}\right) .

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What is the midline of this function? Give an exact answer.

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y=

A circle has a circumference of

4\pi \, \text{ft}

x

, in this circle has a central angle of

240^{\circ}

. What is the length of

x

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1

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\frac{4\pi}{3}\,\text{ft}

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\frac{8\pi}{3}\,\text{ft}

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480\,\text{ft}

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960\,\text{ft}

For the rotation

-311^{\circ}

, find the coterminal angle from

0^{\circ} \leq \theta<360^{\circ}

, the quadrant, and the reference angle.

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The coterminal angle is

\square^{\circ}

, which lies in Quadrant

\square

, with a reference angle of

\square^{\circ}

For the rotation

1415^{\circ}

, find the coterminal angle from

0^{\circ} \leq \theta<360^{\circ}

, the quadrant, and the reference angle.

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The coterminal angle is

\square^{\circ}

, which lies in Quadrant

\square

, with a reference angle of

\square^{\circ}

A quadratic function

f

f(x) = ax^{2} + bx + c

a

0

. Select ali the statements that must be true about the graph of

f

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y

-intercept of the graph is at

(0, c)

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(B) The graph has an

x

(c, 0)

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a<0

the graph opens downward.

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(D) The graph has two

x

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b=0

, then the vertex is on the

y

AB

CD

be two perpendicular diameters of a circle with centre

O

. Consider point

M

on the diameter

AB

, different from

A

B

CM

cuts the circle again at

N

. The tangent at

N

to the circle and perpendicular at

M

AM

P

OP=CM

y=g(x)+2

x y

y

1

g

is an exponential function, which of the following could define

g

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1

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g(x)=\left(\frac{1}{4}\right)^{x}-1

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g(x)=2\left(\frac{2}{3}\right) x+1

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g(x)=2^{x}+3

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g(x)=3^{x}-2

2d \sin(\theta) = \lambda

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Molecules in many solids are arranged in a crystal lattice with distinct patterns and layers. These layers reflect and scatter light rays according to Bragg's law. The Bragg equation relates the distance,

d

, between layers of molecules to the angle,

\theta

, of incoming light rays with wavelength

\lambda

. Which of the following is the correct equation for the distance in terms of the angle and the wavelength?

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1

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d = \frac{\lambda}{2\sin(\theta)}

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d = \frac{2\lambda}{\sin(\theta)}

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d = \frac{2\sin(\theta)}{\lambda}

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d = \frac{\sin(\theta)}{2\lambda}

An exponential function,

f(x)

, passes through

(4,-2)

(5,10)

and has a horizontal asymptote at

y=-8

. What is an equation of

f(x)

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f(x)=\square

Verify that with

\sigma=(1\,2)

\tau=(1\,2\,3)

, the standard representation l as a basis

\alpha=(\omega,1,\omega^{2})

\beta=(1,\omega,\omega^{2})

\tau \alpha=\omega \alpha

\tau \beta=\omega^{2}\beta

\sigma \alpha=\beta

\sigma \beta=\alpha

The area of a rectangle is

14

square units. It has side lengths

x

y

. Given each value for

x

y

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x=2\frac{1}{3}

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x=4\frac{1}{5}

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x=\frac{7}{6}

y=g(x+5)

xy

-plane passes through the point

(-5,4)

g

is an exponential function, which of the following could define

g

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1

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g(x)=-5(4)^{x}+1

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g(x)=4^{x}

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g(x)=4\left(\frac{4}{5}\right)^{x}

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g(x)=4(2)^{x}-5

v

has an equation of

y=-\frac{1}{5} x+9

w

includes the point

(-10,1)

and is parallet to line

v

. What is the equation of line w?

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

2,8,32, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

25,15,5, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

2,6,18, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

3,6,12, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

7,1,-5, \ldots

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a_{n}=

The formula for the density of an object is

d=\frac{m}{V}

m

is the mass and

V

is the volume. Solve the formula for

m

d

V

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m=

The formula for the density of an object is

d=\frac{m}{V}

m

is the mass and

V

is the volume. Solve the formula for

V

d

m

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V=

Trapezoid MNOP is dilated by a scale factor of

2

to form trapezoid

\mathrm{M}^{\prime} \mathrm{N}^{\prime} \mathrm{O}^{\prime} \mathrm{P}^{\prime}

. Side NO measures

29

. What is the measure of side

\mathrm{N}^{\prime} \mathrm{O}^{\prime}

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A curve is defined by the parametric equations

x(t)=-6 \sin (-9 t)

y(t)=4 \cos (4 t)

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=-9 \cos (4 t)

y(t)=-6 \sin (5 t)

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=-7 \cos (-6 t)

y(t)=9 \sin (6 t)

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=-3 \cos (9 t)

y(t)=-9 e^{-10 t}

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=-4 \cos (-5 t)

y(t)=3 \sin (-8 t)

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=3 \cos (-5 t)

y(t)=7 \sin (-8 t)

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=-4 \sin (-5 t)

y(t)=-3 e^{-8 t}

\frac{d y}{d x}

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A curve is defined by the parametric equations

x(t)=-3 \cos (-t)

y(t)=5 e^{-9 t}

\frac{d y}{d x}

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Given the substitutions

\ln 2=a, \ln 3=b

\ln 5=c

, find the value of

\ln (4 \sqrt{5})

a, b

c

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Given the substitutions

\ln 2=a, \ln 3=b

\ln 5=c

, find the value of

\ln (5 \sqrt{2})

a, b

c

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Consider the curve given by the equation

4 x^{2}+48 x+9 y^{2}-36 y=-144 \text {. }

It can be shown that

\frac{d y}{d x}=\frac{4(x+6)}{9(2-y)} \text {. }

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x

-coordinate of the point where the line tangent to the curve is the

x

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x=

A joint is moving at an angular velocity of

0.2 e^{0.2 t}

radians per second (where

t

is the time in seconds since the joint was at rest).

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Through how many radians does the joint move between

t=1

t=3

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1

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e^{0.4}

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e^{0.6}-e^{0.2}

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0.2\left(e^{0.6}-e^{0.2}\right)

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0.2 e^{0.4}

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=24

\theta_{1}=5^{\circ}

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z_{1}

in rectangular form, as

z_{1}=a+b i

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a

b

to the nearest thousandth.

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z_{1}=\square+\square i

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=8

\theta_{1}=67^{\circ}

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z_{1}

in rectangular form, as

z_{1}=a+b i

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a

b

to the nearest thousandth.

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z_{1}=\square+\square i

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=12

\theta_{1}=45^{\circ}

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z_{1}

in rectangular form, as

z_{1}=a+b i

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a+b i

in exact terms.

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z_{1}=

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=10

\theta_{1}=210^{\circ}

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z_{1}

in rectangular form, as

z_{1}=a+b i

\newline

a+b i

in exact terms.

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z_{1}=\square

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=13

\theta_{1}=315^{\circ}

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z_{1}

in rectangular form, as

z_{1}=a+b i

\newline

a+b i

in exact terms.

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z_{1}=\square

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=11

\theta_{1}=180^{\circ}

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z_{1}

in rectangular form, as

z_{1}=a+b i

\newline

a+b i

in exact terms.

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z_{1}=\square

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=2

\theta_{1}=39^{\circ}

\newline

z_{1}

in rectangular form, as

z_{1}=a+b i

\newline

a

b

to the nearest thousandth.

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z_{1}=\square+\square i

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=20

\theta_{1}=281^{\circ}

\newline

z_{1}

in rectangular form, as

z_{1}=a+b i

\newline

a

b

to the nearest thousandth.

\newline

z_{1}=\square+\square i

A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=10

\theta_{1}=84^{\circ}

\newline

z_{1}

in rectangular form, as

z_{1}=a+b i

\newline

a

b

to the nearest thousandth.

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z_{1}=\square+\square i