A car travels 10 km southeast and then 15 km in a direction 60° north of
east. Find the magnitude of the car's
resultant vector.
[?] km
Round to the nearest tenth.

Here,

Therefore,

According to parallelogram law of resultant vector

If two vectors are represented by two adjacent sides of a parallelogram drawn from a point , the their resultant is equal to the diagonal of the parallelogram.

That is,

But, we have to calculate the magnitude of the resultant vector

Subsitute the required values,

Hence, The magnitude of the car resultant vector is 22.02 km.

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}

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation: