A car is merging onto a freeway (beginning at rest), accelerating at a constant rate of 10ft/sec2. How long does it take to reach merging speed at 70mph?

Step-by-step explanation:

Step one:

given data

acceleration,a= 10ft/sec^2

final velocity v= 70mph

first, let is convert mph to ft/sec

1mph is 1.46667 ft/sec

70 mph is x

cross multiply we have

x= 102.7ft/s

Step two:

we are using the first equation of motion

v=u+at

initial velocity u= 0m/s

102.7=0+10*t

102.7=10t

divide both sides by 10

t=10.3seconds

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}

it's