BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 100RE

a.

To determine

Plot the points on coordinate plane.

Expert Solution

Answer to Problem 100RE

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 100RE , additional homework tip  1

Explanation of Solution

Given information:

The given points are, P(7,1),Q(2,11) .

Calculation:

Consider the given points,

  P(7,1),Q(2,11)

Now plot the points on coordinate plane.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 100RE , additional homework tip  2

Hence, the points are plotted.

b.

To determine

Find the distance between the points.

Expert Solution

Answer to Problem 100RE

  d=125 .

Explanation of Solution

Given information:

The given points are, P(7,1),Q(2,11) .

Calculation:

Consider the given points,

  P(7,1),Q(2,11)

Now apply distance formula,

  d=(x2x1)2+(y2y1)2d=(27)2+(11+1)2=(5)2+(10)2=25+100d=125

Hence, the distance between the points is d=125 .

c.

To determine

Find the midpoint of line segment PQ.

Expert Solution

Answer to Problem 100RE

  92,6 .

Explanation of Solution

Given information:

The given points are, P(7,1),Q(2,11) .

Calculation:

Consider the given points,

  P(7,1),Q(2,11)

Now apply midpoint formula for points (x1,y1),(x2,y2) ,

  x=x1+x22,y=y1+y22x=7+22,y=1112x=9/2,y=6

Hence, midpoints are 92,6 .

d.

To determine

Find the equation in slope-intercept form.

Expert Solution

Answer to Problem 100RE

  y=(127)x247 .

Explanation of Solution

Given information:

The given points are, P(7,1),Q(2,11) .

Calculation:

Consider the given points,

  P(7,1),Q(2,11)

Line plotted between the points,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 100RE , additional homework tip  3

Now find slope of line to calculate the equation in slope-intercept form.

  y=mx+bm=y2y1x2x1=11+127=105m=2

To find yintercept line passes through points (7,1) .

  y=2x+b1=2×7+bb=15[y=mx+b]y=2x15

Hence, the equation in slope-intercept form is, y=2x15

e.

To determine

Find the equation of this circle and draw the circle.

Expert Solution

Answer to Problem 100RE

  (x7)2+(y+1)2=125

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 100RE , additional homework tip  4

Explanation of Solution

Given information:

The given points are, P(7,1),Q(2,11) .

Calculation:

Consider the given points,

  P(7,1),Q(2,11)

The standard formula for circle has radius r centred at (a,b) centred point (7,1) circle passes through the points (2,11) is,

Radius equal to distance between two points, r=125

  (xa)2+(yb)2=r2r=125a=7,b=1now,putthevalues,(x7)2+(y+1)2=125

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 100RE , additional homework tip  5

Hence, the equation of circle is (x7)2+(y+1)2=125 .

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