5. A robot that picks up tennis balls is on a straight path from (8,6) toward a ball at (-10,-5). The robot picks up a ball at (-10,-5) and then turns 90° right. What are the coordinates of appoint that the robot can move toward to pick up the last ball?​

Step-by-step explanation:

so this question is about perpendicular lines.    keep in mind that a perpendicular line has a reciprocal slope of opposite sign, from the line it's perpendicular to .  :)  okay so what is that line the robot is on, let's first  

find the slope  , m

m = (y2 - y1)  / ( x2 - x1)  

P1 = (8,6)  in the form ( x1,y1)

P2= (-10,-5) in the form (x2,y2)

then

m = (-5-6) / (-10-8)

m = -11 / -18

m = 11/ 18

and then lets use the point-slope formula with the slope we just found and one of the given points, let's pick  P1

y-6 = 11/18(x-8)

y = 11/18x - 88/18 + 6

y = 11/18x -88/18 + 108/18

y = 11/18x + 20/18

now let's take the reciprocal of the slope and change the sign,  then we have

y = - 18/11x +20/18  ( coordinates robot can move on )

on the graph I'm attaching the green line is the one where the robot first moves, then the purple one.. is the one it turns 90 ° on to .

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.