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Evaluate variable expressions for number sequences

(b) Here are the first five terms of a different sequence.

\newline

Find an expression for the

n

th term of this sequence.

\newline

U_{1}=a=0

\newline

u_{2}=0+3

\newline

3+2(n-1)

27

2

\newline

3

) Pablo has a collection of stamps. He records the heights of the stamps in inches.

\newline

\frac{1}{2}, 1,1 \frac{1}{2}, 2 \frac{1}{2}, 3,2,2, \frac{1}{2}, 1,1,2 \frac{1}{2}, 2,1 \frac{1}{2}, 1,2 \frac{1}{2}

\newline

Complete a line plot of Pablo's data. Label each tick mark for this line plot.

\newline

\newline

Mountain gorilla

\newline

Height (in inches)

\newline

\newline

4

) Pablo also records the widths of some of the stamps in inches.

\newline

\frac{3}{4}, 1,1 \frac{1}{2}, 1 \frac{1}{4}, 1 \frac{1}{2}, 1,1 \frac{3}{4}, 1 \frac{3}{4}, 1 \frac{1}{2}, \frac{1}{2}

\newline

Make a line plot of Pablo's data for stamp widths.

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 2(2)^n

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 5n + 2

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -6n + 10

\newline

_____, _____, _____, _____, _____

Find the first four terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -10n + 4

\newline

_____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -9n + 1

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -9n + 10

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 8n − 6

\newline

_____, _____, _____, _____, _____

Find the first three terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 3n + 4

\newline

_____, _____, _____

Find the first four terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 6n − 1

\newline

_____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -10n + 2

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -9n + 6

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -6n - 7

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 4n − 6

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -3n

\newline

\_\_

\_\_

\_\_

\_\_

\_\_

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -8n - 10

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 8n + 7

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -8n - 6

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = n - 7

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 4n − 8

\newline

_____, _____, _____, _____, _____

Find the first three terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 7n

\newline

3

boxes of candy. Each box holds

10

pieces of candy. He shared the pieces equally between him and his friend. How many pieces of candy will each person get?

5

: Use the given flight data to compute the ground speed, the drift angle, and the course (round your answers to two decimal places). The heading and air speed are

45^{\circ}

275 \mathrm{mph}

, respectively, the wind is

50 \mathrm{mph}

135^{\circ}

1

\newline

ADVANCED DYNAMICS

\newline

2024

1

\newline

Rotations of a cube.

\newline

2

21

. A cube with sides length of

l=1

\newline

Consider a cube with sides length of

L=I

as is shown in Figure

2

21

. The corners of the cube are at

\mathrm{A}(1,0,0), \mathrm{B}(1,1,0), \mathrm{C}(0,1,0), \mathrm{D}(0,0,0), \mathrm{E}(1,0,1), \mathrm{F}(1,1,1), \mathrm{G}(0,1,1), \mathrm{H}(0,0,1)

. Let call this original configuration, the rest position.

\newline

a. Turn the cube

45

deg about the axis connecting point

\mathrm{D}

and the center of square EFGH and determine the coordinates of all corners in G-frame. (

10

\newline

b. After the rotation in part a, turn the cube

45 \mathrm{deg}

about the axis connecting point

\mathrm{D}

and the center of square ABFE and determine the coordinates of all corners in G-frame. (

20

\newline

c. After the rotation in part b, turn the cube

45 \mathrm{deg}

about the axis connecting point

\mathrm{D}

and the center of square BCGF and determine the coordinates of all corners in G-frame. (

30

\newline

d. After the rotation in part

\mathrm{c}

, determine one axis and angle of rotation that turns the cube back to its original orientation. (

20

\newline

e. Determine the intersection point of the axis of rotation of part

\mathrm{d}

with the cube. (

20

\Delta \mathrm{UVW}, w=5.3 \mathrm{~cm}, v=4.8 \mathrm{~cm}

\angle \mathrm{V}=151^{\circ}

. Find all possible values of

\angle \mathrm{W}

, to the nearest

10

th of a degree.

\newline

\triangle \mathrm{EFG}, e=680 \mathrm{~cm}, g=940 \mathrm{~cm}

\angle \mathrm{G}=21^{\circ}

. Find all possible values of

\angle \mathrm{E}

, to the nearest degree.

\newline

\Delta \mathrm{GHI}, g=9.8 \mathrm{~cm}, i=9.6 \mathrm{~cm}

\angle \mathrm{I}=43^{\circ}

. Find all possible values of

\angle \mathrm{G}

, to the nearest

10

th of a degree.

\newline

\triangle \mathrm{JKL}, j=4.1 \mathrm{~cm}, l=1.2 \mathrm{~cm}

\angle \mathrm{L}=29^{\circ}

. Find all possible values of

\angle \mathrm{J}

, to the nearest

10

th of a degree.

\newline

Find all angles,

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

, that satisfy the equation below, to the nearest tenth of a degree.

\newline

-6 \cos ^{2} \theta-10 \cos \theta-1=-3 \cos \theta

\newline

\theta=

Find all angles,

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

, that satisfy the equation below, to the nearest tenth of a degree.

\newline

16 \cot ^{2} \theta-1=0

\newline

\theta=

The first three terms of a geometric sequence are as follows.

\newline

5,10,20

\newline

Find the next two terms of this sequence.

\newline

5,10,20, \square, \square

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 10n

\newline

_____, _____, _____, _____, _____

Find the first four terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 3n - 5

\newline

_____, _____, _____, _____

Find the first three terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 2(4)^n

\newline

\_\_

\_\_

\_\_

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 7n + 8

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -7n + 8

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 6n − 4

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 5n + 6

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = n + 7

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = n - 8

\newline

_____, _____, _____, _____, _____

Find the first three terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 4n − 8

\newline

_____, _____, _____

Find the first four terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 10n − 2

\newline

_____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 4n + 8

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -7n + 7

\newline

_____, _____, _____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -9n + 5

\newline

_____, _____, _____, _____, _____

Find the first three terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 7n − 6

\newline

_____, _____, _____

Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = -10n - 9

\newline

_____, _____, _____, _____, _____

Find the first three terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 8n − 7

\newline

_____, _____, _____

Find the first four terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

\newline

a_n = 7n + 7

\newline

_____, _____, _____, _____