Exam 7: Arithmetic Sequence: Common Difference and First n Terms

Evaluate the sum using the given information. - $x _ { 1 } = - 5 , x _ { 2 } = - 4 , x _ { 3 } = - 1 , x _ { 4 } = 1 , \text { and } \Delta x = - 0.5 ; f ( x ) = \frac { 5 } { 2 x + 5 }$ $\sum _ { \mathrm { i } = 1 } ^ { 4 } \mathrm { f } \left( \mathrm { x } _ { \mathrm { i } } \right) \Delta \mathrm { x }$ (Round to the nearest tenth, if necessary.)

(Multiple Choice)

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Question 341

The orbit of Jupiter around the sun is an ellipse with equation $\frac { x ^ { 2 } } { 6561 } + \frac { y ^ { 2 } } { 5329 } = 1$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

(Multiple Choice)

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Question 342

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $3 x ^ { 2 } = 16 - 3 y ^ { 2 }$

(Multiple Choice)

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Question 343

Provide an appropriate response. -How many terms are in the expansion of (x $( x + y ) ^ { 8 }$ ?

(Short Answer)

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Question 344

Find the probability. -A lottery game contains 25 balls numbered 1 through 25. What is the probability of choosing a ball numbered 26?

(Multiple Choice)

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Question 345

You have to draw an ellipse such that the length of the major axis is fixed at 20 cm. The length of the minor axis can have the values 10, 14, or 16 cm. You are told that your ellipse should be as flat as possible. Which value of length of minor axis would you choose and why? (Do not calculate).

(Essay)

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Question 346

A baseball manager has 11 players of the same ability. How many 9 player starting lineups can he create?

(Multiple Choice)

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Question 347

Give the focus, directrix, and axis for the parabola. - $y ^ { 2 } = - 8 x$

(Multiple Choice)

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Question 348

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the poin $( - 4,0 ) \text { is one-fourth of the distance from the line } x = - 10 \text {. }$

(Multiple Choice)

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Question 349

A projectile is thrown upward so that its distance above the ground after t seconds is $h = - 15 t ^ { 2 } + 660 t$ What is its maximum height?

(Multiple Choice)

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Question 350

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $y=-\sqrt{1-\frac{x^{2}}{36}}$ $Graph the equation. Give the domain and range. Identify whether the equation is a function. - y=-\sqrt{1-\frac{x^{2}}{36}}$

(Multiple Choice)

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Question 351

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $a _ { 1 } = - 4.339 , r = 1.475$ (Round to the nearest hundredth)

(Multiple Choice)

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Question 352

Write an equation for the hyperbola. -vertices at $( 0,1 )$ and $( 8,1 )$ , passing through the point $( - 5,16 )$

(Multiple Choice)

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Question 353

How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed?

(Multiple Choice)

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Question 354

How many different three-digit numbers can be written using digits from the set {5, 6, 7, 8, 9} without any repeating digits?

(Multiple Choice)

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Question 355

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\text { a5 } = 3 , \mathrm {~d} = - 1 , \mathrm { n } = 5$

(Multiple Choice)

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Question 356

Evaluate the sum. - $\sum _ { k = 1 } ^ { 6 } ( 4 - 9 k )$

(Multiple Choice)

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Question 357

Graph the conic section. - $y^{2}-6 y+12 x+57=0$ $Graph the conic section. - y^{2}-6 y+12 x+57=0$

(Multiple Choice)

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Question 358

Match the equation of the parabola with the appropriate description. - $y + 6 = 2 ( x + 9 ) ^ { 2 }$

(Multiple Choice)

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Question 359

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. -2, 10, 18, 26, 34, . . .

(Multiple Choice)

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Question 360

The orbit of Jupiter around the sun is an ellipse with equation $\frac { x ^ { 2 } } { 6561 } + \frac { y ^ { 2 } } { 5329 } = 1$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $3 x ^ { 2 } = 16 - 3 y ^ { 2 }$

Provide an appropriate response. -How many terms are in the expansion of (x $( x + y ) ^ { 8 }$ ?

Find the probability. -A lottery game contains 25 balls numbered 1 through 25. What is the probability of choosing a ball numbered 26?

You have to draw an ellipse such that the length of the major axis is fixed at 20 cm. The length of the minor axis can have the values 10, 14, or 16 cm. You are told that your ellipse should be as flat as possible. Which value of length of minor axis would you choose and why? (Do not calculate).

A baseball manager has 11 players of the same ability. How many 9 player starting lineups can he create?

Give the focus, directrix, and axis for the parabola. - $y ^ { 2 } = - 8 x$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the poin $( - 4,0 ) \text { is one-fourth of the distance from the line } x = - 10 \text {. }$

A projectile is thrown upward so that its distance above the ground after t seconds is $h = - 15 t ^ { 2 } + 660 t$ What is its maximum height?

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $y=-\sqrt{1-\frac{x^{2}}{36}}$ $Graph the equation. Give the domain and range. Identify whether the equation is a function. - y=-\sqrt{1-\frac{x^{2}}{36}}$

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $a _ { 1 } = - 4.339 , r = 1.475$ (Round to the nearest hundredth)

Write an equation for the hyperbola. -vertices at $( 0,1 )$ and $( 8,1 )$ , passing through the point $( - 5,16 )$

How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed?

How many different three-digit numbers can be written using digits from the set {5, 6, 7, 8, 9} without any repeating digits?

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\text { a5 } = 3 , \mathrm {~d} = - 1 , \mathrm { n } = 5$

Evaluate the sum. - $\sum _ { k = 1 } ^ { 6 } ( 4 - 9 k )$

Graph the conic section. - $y^{2}-6 y+12 x+57=0$ $Graph the conic section. - y^{2}-6 y+12 x+57=0$

Match the equation of the parabola with the appropriate description. - $y + 6 = 2 ( x + 9 ) ^ { 2 }$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. -2, 10, 18, 26, 34, . . .

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Exam 7: Arithmetic Sequence: Common Difference and First n Terms

The orbit of Jupiter around the sun is an ellipse with equation x26561+y25329=1\frac { x ^ { 2 } } { 6561 } + \frac { y ^ { 2 } } { 5329 } = 16561x2​+5329y2​=1 where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 3x2=16−3y23 x ^ { 2 } = 16 - 3 y ^ { 2 }3x2=16−3y2

Provide an appropriate response. -How many terms are in the expansion of (x (x+y)8( x + y ) ^ { 8 }(x+y)8 ?

Find the probability. -A lottery game contains 25 balls numbered 1 through 25. What is the probability of choosing a ball numbered 26?

You have to draw an ellipse such that the length of the major axis is fixed at 20 cm. The length of the minor axis can have the values 10, 14, or 16 cm. You are told that your ellipse should be as flat as possible. Which value of length of minor axis would you choose and why? (Do not calculate).

A baseball manager has 11 players of the same ability. How many 9 player starting lineups can he create?

Give the focus, directrix, and axis for the parabola. - y2=−8xy ^ { 2 } = - 8 xy2=−8x

A projectile is thrown upward so that its distance above the ground after t seconds is h=−15t2+660th = - 15 t ^ { 2 } + 660 th=−15t2+660t What is its maximum height?

Graph the equation. Give the domain and range. Identify whether the equation is a function. - y=−1−x236y=-\sqrt{1-\frac{x^{2}}{36}}y=−1−36x2​​

Use the formula for Sn to find the sum of the first five terms of the geometric sequence. - a1=−4.339,r=1.475a _ { 1 } = - 4.339 , r = 1.475a1​=−4.339,r=1.475 (Round to the nearest hundredth)

Write an equation for the hyperbola. -vertices at (0,1)( 0,1 )(0,1) and (8,1)( 8,1 )(8,1) , passing through the point (−5,16)( - 5,16 )(−5,16)

How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed?

How many different three-digit numbers can be written using digits from the set {5, 6, 7, 8, 9} without any repeating digits?

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - a5 =3, d=−1,n=5\text { a5 } = 3 , \mathrm {~d} = - 1 , \mathrm { n } = 5 a5 =3, d=−1,n=5

Evaluate the sum. - ∑k=16(4−9k)\sum _ { k = 1 } ^ { 6 } ( 4 - 9 k )∑k=16​(4−9k)

Graph the conic section. - y2−6y+12x+57=0y^{2}-6 y+12 x+57=0y2−6y+12x+57=0

Match the equation of the parabola with the appropriate description. - y+6=2(x+9)2y + 6 = 2 ( x + 9 ) ^ { 2 }y+6=2(x+9)2

Find an and a6a _ { n } \text { and } a _ { 6 }an​ and a6​ for the following arithmetic sequence. -2, 10, 18, 26, 34, . . .

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

The orbit of Jupiter around the sun is an ellipse with equation $\frac { x ^ { 2 } } { 6561 } + \frac { y ^ { 2 } } { 5329 } = 1$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $3 x ^ { 2 } = 16 - 3 y ^ { 2 }$

Provide an appropriate response. -How many terms are in the expansion of (x $( x + y ) ^ { 8 }$ ?

Give the focus, directrix, and axis for the parabola. - $y ^ { 2 } = - 8 x$

A projectile is thrown upward so that its distance above the ground after t seconds is $h = - 15 t ^ { 2 } + 660 t$ What is its maximum height?

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $y=-\sqrt{1-\frac{x^{2}}{36}}$ $Graph the equation. Give the domain and range. Identify whether the equation is a function. - y=-\sqrt{1-\frac{x^{2}}{36}}$

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $a _ { 1 } = - 4.339 , r = 1.475$ (Round to the nearest hundredth)

Write an equation for the hyperbola. -vertices at $( 0,1 )$ and $( 8,1 )$ , passing through the point $( - 5,16 )$

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\text { a5 } = 3 , \mathrm {~d} = - 1 , \mathrm { n } = 5$

Evaluate the sum. - $\sum _ { k = 1 } ^ { 6 } ( 4 - 9 k )$

Graph the conic section. - $y^{2}-6 y+12 x+57=0$ $Graph the conic section. - y^{2}-6 y+12 x+57=0$

Match the equation of the parabola with the appropriate description. - $y + 6 = 2 ( x + 9 ) ^ { 2 }$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. -2, 10, 18, 26, 34, . . .