A runner’s resultant velocity is 8 miles per hour due west running with a wind of 3 miles per hour N 28° W. What is the runner’s speed, to the nearest mile per hour, without the effect of the wind.

7.07 miles/hour W 22° S.

Step-by-step explanation:

Given that the resultant velocity of the runner, miles/hour due west.

Wind speed, miles/hour N 28° W.

Assuming that the absolute velocity of the runner, miles/ hour W \alpha S as shown in the figure.

By using vector addition, .

Now, from the figure,

And

Dividing equation (ii) by equation (i), we have

Putting the value of \alpha in equation (ii), we have

miles/hour

Hence, the runner speed, without the effect of the wind, is 7.07 miles/hour W 22° S.

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}

the answer is 24

step-by-step explanation: