The vector ~v represents the displacement vector from Portland, Oregon to Houston, Texas. The vector w~ represents the displacement vector from Houston, Texas to Akron, Ohio. Use the vectors ~v and w~ to answer the following questions: a. What is the displacement vector Of a plane which flies from Akron, Ohio to Houston, Texas?
b. In order to fly home from Portland to Akron I have a layover in Houston. Find a vector which describes my total displacement over the whole trip.
c. It is approximately 3000 km from Portland to Houston. It is approximately 5500 km from Anchorage, Alaska to Houston. A plane flies in a straight line from Houston to Anchorage and during the flight it passes directly over Portland. Find a vector which describes the displacement of the plane.

a

the displacement of the plane is  

b

The displacement of plane  from Portland to Akron with layover at Houston is  

c

  the vector which defines this displacement is  

Step-by-step explanation:

From the question we are the

   The displacement from Portland, Oregon to Houston, Texas. is  

    The displacement  from Houston, Texas to Akron, Ohio.  is a

a

   The motion of the plane in question a is in the opposite direction to vector

So the displacement of the plane is  

b

The motion of Portland to Houston to Akron is in the direction of both vector and    so

The displacement of plane  from Portland to Akron with layover at Houston is  

c

From the question we are told that the plane flies over Portland to get to  Anchorage, Alaska which implies that it is moving in opposite direction to the vector

   Give that distance from Portland to Houston is  

           and the distance from Portland to  Anchorage is km

Then the vector which defines this displacement is mathematically represented as

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

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